id	sid	tid	token	lemma	pos
ejpam-4431	1	1	european	european	PROPN
ejpam-4431	1	2	journal	journal	PROPN
ejpam-4431	1	3	of	of	ADP
ejpam-4431	1	4	pure	pure	ADJ
ejpam-4431	1	5	and	and	CCONJ
ejpam-4431	1	6	applied	apply	VERB
ejpam-4431	1	7	mathematics	mathematic	NOUN
ejpam-4431	1	8	vol	vol	NOUN
ejpam-4431	1	9	.	.	PROPN
ejpam-4431	2	1	15	15	NUM
ejpam-4431	2	2	,	,	PUNCT
ejpam-4431	2	3	no	no	INTJ
ejpam-4431	2	4	.	.	NOUN
ejpam-4431	2	5	3	3	NUM
ejpam-4431	2	6	,	,	PUNCT
ejpam-4431	2	7	2022	2022	NUM
ejpam-4431	2	8	,	,	PUNCT
ejpam-4431	2	9	1015	1015	NUM
ejpam-4431	2	10	-	-	SYM
ejpam-4431	2	11	1022	1022	NUM
ejpam-4431	2	12	issn	issn	PROPN
ejpam-4431	2	13	1307	1307	NUM
ejpam-4431	2	14	-	-	SYM
ejpam-4431	2	15	5543	5543	NUM
ejpam-4431	2	16	–	–	PUNCT
ejpam-4431	3	1	ejpam.com	ejpam.com	X
ejpam-4431	3	2	published	publish	VERB
ejpam-4431	3	3	by	by	ADP
ejpam-4431	3	4	new	new	PROPN
ejpam-4431	3	5	york	york	PROPN
ejpam-4431	3	6	business	business	PROPN
ejpam-4431	3	7	global	global	ADJ
ejpam-4431	3	8	variative	variative	ADJ
ejpam-4431	3	9	problems	problem	NOUN
ejpam-4431	3	10	in	in	ADP
ejpam-4431	3	11	teaching	teach	VERB
ejpam-4431	3	12	mathematics	mathematic	NOUN
ejpam-4431	3	13	samed	samed	PROPN
ejpam-4431	3	14	j.aliyev1∗	j.aliyev1∗	NOUN
ejpam-4431	3	15	,	,	PUNCT
ejpam-4431	3	16	bahadur	bahadur	PROPN
ejpam-4431	3	17	o.tahirov1	o.tahirov1	PROPN
ejpam-4431	3	18	,	,	PUNCT
ejpam-4431	3	19	tarana	tarana	PROPN
ejpam-4431	3	20	a.hashimova1	a.hashimova1	PROPN
ejpam-4431	3	21	1	1	NUM
ejpam-4431	3	22	department	department	NOUN
ejpam-4431	3	23	of	of	ADP
ejpam-4431	3	24	methods	method	NOUN
ejpam-4431	3	25	of	of	ADP
ejpam-4431	3	26	mathematics	mathematic	NOUN
ejpam-4431	3	27	and	and	CCONJ
ejpam-4431	3	28	its	its	PRON
ejpam-4431	3	29	teaching	teaching	NOUN
ejpam-4431	3	30	,	,	PUNCT
ejpam-4431	3	31	faculty	faculty	NOUN
ejpam-4431	3	32	of	of	ADP
ejpam-4431	3	33	mechanics	mechanic	NOUN
ejpam-4431	3	34	and	and	CCONJ
ejpam-4431	3	35	mathematics	mathematic	NOUN
ejpam-4431	3	36	,	,	PUNCT
ejpam-4431	3	37	baku	baku	PROPN
ejpam-4431	3	38	state	state	PROPN
ejpam-4431	3	39	university	university	PROPN
ejpam-4431	3	40	,	,	PUNCT
ejpam-4431	3	41	baku	baku	PROPN
ejpam-4431	3	42	,	,	PUNCT
ejpam-4431	3	43	z.khalilov	z.khalilov	PROPN
ejpam-4431	3	44	str.23	str.23	NOUN
ejpam-4431	3	45	„	„	ADJ
ejpam-4431	3	46	az1148	az1148	PROPN
ejpam-4431	3	47	,	,	PUNCT
ejpam-4431	3	48	azerbaijan	azerbaijan	PROPN
ejpam-4431	3	49	abstract	abstract	NOUN
ejpam-4431	3	50	.	.	PUNCT
ejpam-4431	4	1	the	the	DET
ejpam-4431	4	2	article	article	NOUN
ejpam-4431	4	3	discusses	discuss	VERB
ejpam-4431	4	4	problems	problem	NOUN
ejpam-4431	4	5	with	with	ADP
ejpam-4431	4	6	ambiguous	ambiguous	ADJ
ejpam-4431	4	7	conditions	condition	NOUN
ejpam-4431	4	8	,	,	PUNCT
ejpam-4431	4	9	the	the	DET
ejpam-4431	4	10	solution	solution	NOUN
ejpam-4431	4	11	of	of	ADP
ejpam-4431	4	12	which	which	PRON
ejpam-4431	4	13	leads	lead	VERB
ejpam-4431	4	14	to	to	ADP
ejpam-4431	4	15	several	several	ADJ
ejpam-4431	4	16	variants	variant	NOUN
ejpam-4431	4	17	of	of	ADP
ejpam-4431	4	18	answer	answer	NOUN
ejpam-4431	4	19	.	.	PUNCT
ejpam-4431	5	1	such	such	ADJ
ejpam-4431	5	2	problems	problem	NOUN
ejpam-4431	5	3	are	be	AUX
ejpam-4431	5	4	called	call	VERB
ejpam-4431	5	5	variative	variative	ADJ
ejpam-4431	5	6	problem	problem	NOUN
ejpam-4431	5	7	.	.	PUNCT
ejpam-4431	6	1	the	the	DET
ejpam-4431	6	2	role	role	NOUN
ejpam-4431	6	3	of	of	ADP
ejpam-4431	6	4	variative	variative	ADJ
ejpam-4431	6	5	problems	problem	NOUN
ejpam-4431	6	6	in	in	ADP
ejpam-4431	6	7	intellectual	intellectual	ADJ
ejpam-4431	6	8	development	development	NOUN
ejpam-4431	6	9	of	of	ADP
ejpam-4431	6	10	schoolchildren	schoolchildren	NOUN
ejpam-4431	6	11	in	in	ADP
ejpam-4431	6	12	mathematics	mathematic	NOUN
ejpam-4431	6	13	classes	class	NOUN
ejpam-4431	6	14	are	be	AUX
ejpam-4431	6	15	described	describe	VERB
ejpam-4431	6	16	in	in	ADP
ejpam-4431	6	17	this	this	DET
ejpam-4431	6	18	article	article	NOUN
ejpam-4431	6	19	.	.	PUNCT
ejpam-4431	7	1	proposed	propose	VERB
ejpam-4431	7	2	a	a	DET
ejpam-4431	7	3	methodology	methodology	NOUN
ejpam-4431	7	4	for	for	ADP
ejpam-4431	7	5	including	include	VERB
ejpam-4431	7	6	variative	variative	ADJ
ejpam-4431	7	7	problems	problem	NOUN
ejpam-4431	7	8	in	in	ADP
ejpam-4431	7	9	the	the	DET
ejpam-4431	7	10	process	process	NOUN
ejpam-4431	7	11	of	of	ADP
ejpam-4431	7	12	teaching	teaching	NOUN
ejpam-4431	7	13	mathematics	mathematic	NOUN
ejpam-4431	7	14	.	.	PUNCT
ejpam-4431	8	1	2020	2020	NUM
ejpam-4431	8	2	mathematics	mathematic	NOUN
ejpam-4431	8	3	subject	subject	NOUN
ejpam-4431	8	4	classifications	classification	NOUN
ejpam-4431	8	5	:	:	PUNCT
ejpam-4431	8	6	97g10	97g10	NUM
ejpam-4431	8	7	,	,	PUNCT
ejpam-4431	8	8	97g30	97g30	NUM
ejpam-4431	8	9	,	,	PUNCT
ejpam-4431	8	10	97g40	97g40	NUM
ejpam-4431	8	11	key	key	ADJ
ejpam-4431	8	12	words	word	NOUN
ejpam-4431	8	13	and	and	CCONJ
ejpam-4431	8	14	phrases	phrase	NOUN
ejpam-4431	8	15	:	:	PUNCT
ejpam-4431	8	16	variative	variative	ADJ
ejpam-4431	8	17	problem	problem	NOUN
ejpam-4431	8	18	,	,	PUNCT
ejpam-4431	8	19	variation	variation	NOUN
ejpam-4431	8	20	of	of	ADP
ejpam-4431	8	21	problem	problem	NOUN
ejpam-4431	8	22	conditions	condition	NOUN
ejpam-4431	8	23	,	,	PUNCT
ejpam-4431	8	24	multivariate	multivariate	NOUN
ejpam-4431	8	25	problems	problem	NOUN
ejpam-4431	8	26	.	.	PUNCT
ejpam-4431	9	1	1	1	X
ejpam-4431	9	2	.	.	X
ejpam-4431	9	3	introduction	introduction	NOUN
ejpam-4431	9	4	the	the	DET
ejpam-4431	9	5	experience	experience	NOUN
ejpam-4431	9	6	says	say	VERB
ejpam-4431	9	7	that	that	SCONJ
ejpam-4431	9	8	one	one	NUM
ejpam-4431	9	9	of	of	ADP
ejpam-4431	9	10	the	the	DET
ejpam-4431	9	11	most	most	ADV
ejpam-4431	9	12	common	common	ADJ
ejpam-4431	9	13	drawbacks	drawback	NOUN
ejpam-4431	9	14	of	of	ADP
ejpam-4431	9	15	students	student	NOUN
ejpam-4431	9	16	’	'	PUNCT
ejpam-4431	9	17	thinking	thinking	NOUN
ejpam-4431	9	18	process	process	NOUN
ejpam-4431	9	19	is	be	AUX
ejpam-4431	9	20	its	its	PRON
ejpam-4431	9	21	linearity	linearity	NOUN
ejpam-4431	9	22	,	,	PUNCT
ejpam-4431	9	23	in	in	ADP
ejpam-4431	9	24	other	other	ADJ
ejpam-4431	9	25	words	word	NOUN
ejpam-4431	9	26	,	,	PUNCT
ejpam-4431	9	27	its	its	PRON
ejpam-4431	9	28	lack	lack	NOUN
ejpam-4431	9	29	of	of	ADP
ejpam-4431	9	30	variative	variative	ADJ
ejpam-4431	9	31	perception	perception	NOUN
ejpam-4431	9	32	of	of	ADP
ejpam-4431	9	33	surrounding	surround	VERB
ejpam-4431	9	34	ideas	idea	NOUN
ejpam-4431	9	35	and	and	CCONJ
ejpam-4431	9	36	phenomena	phenomenon	NOUN
ejpam-4431	9	37	.	.	PUNCT
ejpam-4431	10	1	this	this	PRON
ejpam-4431	10	2	can	can	AUX
ejpam-4431	10	3	be	be	AUX
ejpam-4431	10	4	seen	see	VERB
ejpam-4431	10	5	by	by	ADP
ejpam-4431	10	6	the	the	DET
ejpam-4431	10	7	fact	fact	NOUN
ejpam-4431	10	8	that	that	SCONJ
ejpam-4431	10	9	the	the	DET
ejpam-4431	10	10	schoolchildren	schoolchildren	NOUN
ejpam-4431	10	11	prove	prove	VERB
ejpam-4431	10	12	incapable	incapable	ADJ
ejpam-4431	10	13	of	of	ADP
ejpam-4431	10	14	considering	consider	VERB
ejpam-4431	10	15	the	the	DET
ejpam-4431	10	16	situation	situation	NOUN
ejpam-4431	10	17	under	under	ADP
ejpam-4431	10	18	different	different	ADJ
ejpam-4431	10	19	angle	angle	NOUN
ejpam-4431	10	20	,	,	PUNCT
ejpam-4431	10	21	interpreting	interpret	VERB
ejpam-4431	10	22	the	the	DET
ejpam-4431	10	23	data	datum	NOUN
ejpam-4431	10	24	differently	differently	ADV
ejpam-4431	10	25	,	,	PUNCT
ejpam-4431	10	26	finding	find	VERB
ejpam-4431	10	27	alternative	alternative	ADJ
ejpam-4431	10	28	ways	way	NOUN
ejpam-4431	10	29	of	of	ADP
ejpam-4431	10	30	problem	problem	NOUN
ejpam-4431	10	31	solution	solution	NOUN
ejpam-4431	10	32	.	.	PUNCT
ejpam-4431	11	1	studying	study	VERB
ejpam-4431	11	2	mathematics	mathematic	NOUN
ejpam-4431	11	3	provides	provide	VERB
ejpam-4431	11	4	large	large	ADJ
ejpam-4431	11	5	opportunities	opportunity	NOUN
ejpam-4431	11	6	to	to	PART
ejpam-4431	11	7	overcome	overcome	VERB
ejpam-4431	11	8	these	these	DET
ejpam-4431	11	9	drawbacks	drawback	NOUN
ejpam-4431	11	10	of	of	ADP
ejpam-4431	11	11	thinking	thinking	NOUN
ejpam-4431	11	12	.	.	PUNCT
ejpam-4431	12	1	variety	variety	NOUN
ejpam-4431	12	2	of	of	ADP
ejpam-4431	12	3	problems	problem	NOUN
ejpam-4431	12	4	can	can	AUX
ejpam-4431	12	5	serve	serve	VERB
ejpam-4431	12	6	this	this	DET
ejpam-4431	12	7	objective	objective	NOUN
ejpam-4431	12	8	,	,	PUNCT
ejpam-4431	12	9	provided	provide	VERB
ejpam-4431	12	10	that	that	SCONJ
ejpam-4431	12	11	they	they	PRON
ejpam-4431	12	12	are	be	AUX
ejpam-4431	12	13	regularly	regularly	ADV
ejpam-4431	12	14	stated	state	VERB
ejpam-4431	12	15	and	and	CCONJ
ejpam-4431	12	16	their	their	PRON
ejpam-4431	12	17	variative	variative	ADJ
ejpam-4431	12	18	content	content	NOUN
ejpam-4431	12	19	is	be	AUX
ejpam-4431	12	20	discussed	discuss	VERB
ejpam-4431	12	21	with	with	ADP
ejpam-4431	12	22	the	the	DET
ejpam-4431	12	23	students	student	NOUN
ejpam-4431	12	24	.	.	PUNCT
ejpam-4431	13	1	these	these	DET
ejpam-4431	13	2	days	day	NOUN
ejpam-4431	13	3	,	,	PUNCT
ejpam-4431	13	4	there	there	PRON
ejpam-4431	13	5	is	be	VERB
ejpam-4431	13	6	a	a	DET
ejpam-4431	13	7	great	great	ADJ
ejpam-4431	13	8	demand	demand	NOUN
ejpam-4431	13	9	for	for	ADP
ejpam-4431	13	10	the	the	DET
ejpam-4431	13	11	capabilities	capability	NOUN
ejpam-4431	13	12	of	of	ADP
ejpam-4431	13	13	searching	search	VERB
ejpam-4431	13	14	for	for	ADP
ejpam-4431	13	15	different	different	ADJ
ejpam-4431	13	16	,	,	PUNCT
ejpam-4431	13	17	not	not	PART
ejpam-4431	13	18	obvious	obvious	ADJ
ejpam-4431	13	19	at	at	ADP
ejpam-4431	13	20	first	first	ADJ
ejpam-4431	13	21	sight	sight	NOUN
ejpam-4431	13	22	ways	way	NOUN
ejpam-4431	13	23	to	to	PART
ejpam-4431	13	24	solve	solve	VERB
ejpam-4431	13	25	some	some	DET
ejpam-4431	13	26	problems	problem	NOUN
ejpam-4431	13	27	,	,	PUNCT
ejpam-4431	13	28	the	the	DET
ejpam-4431	13	29	capabilities	capability	NOUN
ejpam-4431	13	30	of	of	ADP
ejpam-4431	13	31	comparing	compare	VERB
ejpam-4431	13	32	different	different	ADJ
ejpam-4431	13	33	possible	possible	ADJ
ejpam-4431	13	34	actions	action	NOUN
ejpam-4431	13	35	and	and	CCONJ
ejpam-4431	13	36	analysis	analysis	NOUN
ejpam-4431	13	37	of	of	ADP
ejpam-4431	13	38	their	their	PRON
ejpam-4431	13	39	consequences	consequence	NOUN
ejpam-4431	13	40	,	,	PUNCT
ejpam-4431	13	41	the	the	DET
ejpam-4431	13	42	capabilities	capability	NOUN
ejpam-4431	13	43	of	of	ADP
ejpam-4431	13	44	making	make	VERB
ejpam-4431	13	45	most	most	ADV
ejpam-4431	13	46	optimal	optimal	ADJ
ejpam-4431	13	47	decision	decision	NOUN
ejpam-4431	13	48	in	in	ADP
ejpam-4431	13	49	multiple	multiple	ADJ
ejpam-4431	13	50	choice	choice	NOUN
ejpam-4431	13	51	conditions	condition	NOUN
ejpam-4431	13	52	.	.	PUNCT
ejpam-4431	14	1	professionals	professional	NOUN
ejpam-4431	14	2	from	from	ADP
ejpam-4431	14	3	various	various	ADJ
ejpam-4431	14	4	fields	field	NOUN
ejpam-4431	14	5	of	of	ADP
ejpam-4431	14	6	human	human	ADJ
ejpam-4431	14	7	activity	activity	NOUN
ejpam-4431	14	8	are	be	AUX
ejpam-4431	14	9	facing	face	VERB
ejpam-4431	14	10	today	today	NOUN
ejpam-4431	14	11	the	the	DET
ejpam-4431	14	12	situations	situation	NOUN
ejpam-4431	14	13	which	which	PRON
ejpam-4431	14	14	demand	demand	VERB
ejpam-4431	14	15	the	the	DET
ejpam-4431	14	16	above	above	ADJ
ejpam-4431	14	17	capabilities	capability	NOUN
ejpam-4431	14	18	.	.	PUNCT
ejpam-4431	15	1	teaching	teach	VERB
ejpam-4431	15	2	mathematics	mathematic	NOUN
ejpam-4431	15	3	provides	provide	VERB
ejpam-4431	15	4	large	large	ADJ
ejpam-4431	15	5	opportunities	opportunity	NOUN
ejpam-4431	15	6	for	for	SCONJ
ejpam-4431	15	7	teacher	teacher	NOUN
ejpam-4431	15	8	to	to	PART
ejpam-4431	15	9	develop	develop	VERB
ejpam-4431	15	10	variative	variative	ADJ
ejpam-4431	15	11	properties	property	NOUN
ejpam-4431	15	12	of	of	ADP
ejpam-4431	15	13	student	student	NOUN
ejpam-4431	15	14	thinking	thinking	NOUN
ejpam-4431	15	15	.	.	PUNCT
ejpam-4431	16	1	let	let	VERB
ejpam-4431	16	2	’s	’s	PRON
ejpam-4431	16	3	discuss	discuss	VERB
ejpam-4431	16	4	some	some	PRON
ejpam-4431	16	5	of	of	ADP
ejpam-4431	16	6	them	they	PRON
ejpam-4431	16	7	.	.	PUNCT
ejpam-4431	17	1	∗corresponding	∗corresponde	VERB
ejpam-4431	17	2	author	author	NOUN
ejpam-4431	17	3	.	.	PUNCT
ejpam-4431	18	1	doi	doi	NOUN
ejpam-4431	18	2	:	:	PUNCT
ejpam-4431	18	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4431	https://doi.org/10.29020/nybg.ejpam.v15i3.4431	ADP
ejpam-4431	18	4	email	email	NOUN
ejpam-4431	18	5	addresses	address	NOUN
ejpam-4431	18	6	:	:	PUNCT
ejpam-4431	18	7	samed59@bk.ru	samed59@bk.ru	PROPN
ejpam-4431	18	8	(	(	PUNCT
ejpam-4431	18	9	samed	samed	PROPN
ejpam-4431	18	10	j.aliyev	j.aliyev	NOUN
ejpam-4431	18	11	)	)	PUNCT
ejpam-4431	18	12	,	,	PUNCT
ejpam-4431	18	13	qarabah48@mail.ru	qarabah48@mail.ru	PROPN
ejpam-4431	18	14	(	(	PUNCT
ejpam-4431	18	15	bahadur	bahadur	PROPN
ejpam-4431	18	16	o.tahirov),tarana0202@gmail.com	o.tahirov),tarana0202@gmail.com	PROPN
ejpam-4431	18	17	(	(	PUNCT
ejpam-4431	18	18	tarana	tarana	PROPN
ejpam-4431	18	19	a.hashimova	a.hashimova	PROPN
ejpam-4431	18	20	)	)	PUNCT
ejpam-4431	18	21	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4431	18	22	1015	1015	NUM
ejpam-4431	19	1	©	©	PROPN
ejpam-4431	19	2	2022	2022	NUM
ejpam-4431	19	3	ejpam	ejpam	VERB
ejpam-4431	19	4	all	all	DET
ejpam-4431	19	5	rights	right	NOUN
ejpam-4431	19	6	reserved	reserve	VERB
ejpam-4431	19	7	.	.	PUNCT
ejpam-4431	20	1	s.	s.	PROPN
ejpam-4431	20	2	j.aliyev	j.aliyev	PROPN
ejpam-4431	20	3	,	,	PUNCT
ejpam-4431	20	4	b.	b.	PROPN
ejpam-4431	20	5	o.tahirov	o.tahirov	PROPN
ejpam-4431	20	6	,	,	PUNCT
ejpam-4431	20	7	t.	t.	PROPN
ejpam-4431	20	8	a.hashimova	a.hashimova	PROPN
ejpam-4431	20	9	/	/	SYM
ejpam-4431	20	10	eur	eur	PROPN
ejpam-4431	20	11	.	.	PUNCT
ejpam-4431	21	1	j.	j.	PROPN
ejpam-4431	21	2	pure	pure	PROPN
ejpam-4431	21	3	appl	appl	PROPN
ejpam-4431	21	4	.	.	PROPN
ejpam-4431	21	5	math	math	PROPN
ejpam-4431	21	6	,	,	PUNCT
ejpam-4431	21	7	15	15	NUM
ejpam-4431	21	8	(	(	PUNCT
ejpam-4431	21	9	3	3	NUM
ejpam-4431	21	10	)	)	PUNCT
ejpam-4431	21	11	(	(	PUNCT
ejpam-4431	21	12	2022	2022	NUM
ejpam-4431	21	13	)	)	PUNCT
ejpam-4431	21	14	,	,	PUNCT
ejpam-4431	21	15	1015	1015	NUM
ejpam-4431	21	16	-	-	SYM
ejpam-4431	21	17	1022	1022	NUM
ejpam-4431	21	18	1016	1016	NUM
ejpam-4431	21	19	let	let	VERB
ejpam-4431	21	20	’s	’s	NOUN
ejpam-4431	21	21	first	first	ADV
ejpam-4431	21	22	consider	consider	VERB
ejpam-4431	21	23	the	the	DET
ejpam-4431	21	24	problems	problem	NOUN
ejpam-4431	21	25	with	with	ADP
ejpam-4431	21	26	ambiguous	ambiguous	ADJ
ejpam-4431	21	27	conditions	condition	NOUN
ejpam-4431	21	28	.	.	PUNCT
ejpam-4431	22	1	when	when	SCONJ
ejpam-4431	22	2	treating	treat	VERB
ejpam-4431	22	3	such	such	ADJ
ejpam-4431	22	4	problems	problem	NOUN
ejpam-4431	22	5	,	,	PUNCT
ejpam-4431	22	6	you	you	PRON
ejpam-4431	22	7	have	have	VERB
ejpam-4431	22	8	to	to	PART
ejpam-4431	22	9	consider	consider	VERB
ejpam-4431	22	10	several	several	ADJ
ejpam-4431	22	11	possible	possible	ADJ
ejpam-4431	22	12	situations	situation	NOUN
ejpam-4431	22	13	,	,	PUNCT
ejpam-4431	22	14	which	which	PRON
ejpam-4431	22	15	usually	usually	ADV
ejpam-4431	22	16	leads	lead	VERB
ejpam-4431	22	17	to	to	ADP
ejpam-4431	22	18	several	several	ADJ
ejpam-4431	22	19	variants	variant	NOUN
ejpam-4431	22	20	of	of	ADP
ejpam-4431	22	21	solution	solution	NOUN
ejpam-4431	22	22	.	.	PUNCT
ejpam-4431	23	1	in	in	ADP
ejpam-4431	23	2	particular	particular	ADJ
ejpam-4431	23	3	,	,	PUNCT
ejpam-4431	23	4	such	such	ADJ
ejpam-4431	23	5	multivariative	multivariative	ADJ
ejpam-4431	23	6	problems	problem	NOUN
ejpam-4431	23	7	can	can	AUX
ejpam-4431	23	8	be	be	AUX
ejpam-4431	23	9	easily	easily	ADV
ejpam-4431	23	10	created	create	VERB
ejpam-4431	23	11	in	in	ADP
ejpam-4431	23	12	geometric	geometric	ADJ
ejpam-4431	23	13	framework	framework	NOUN
ejpam-4431	23	14	.	.	PUNCT
ejpam-4431	24	1	it	it	PRON
ejpam-4431	24	2	’s	’	VERB
ejpam-4431	24	3	best	good	ADJ
ejpam-4431	24	4	if	if	SCONJ
ejpam-4431	24	5	such	such	ADJ
ejpam-4431	24	6	problems	problem	NOUN
ejpam-4431	24	7	are	be	AUX
ejpam-4431	24	8	discussed	discuss	VERB
ejpam-4431	24	9	in	in	ADP
ejpam-4431	24	10	classes	class	NOUN
ejpam-4431	24	11	regularly	regularly	ADV
ejpam-4431	24	12	and	and	CCONJ
ejpam-4431	24	13	without	without	ADP
ejpam-4431	24	14	warning	warning	NOUN
ejpam-4431	24	15	,	,	PUNCT
ejpam-4431	24	16	because	because	SCONJ
ejpam-4431	24	17	then	then	ADV
ejpam-4431	24	18	the	the	DET
ejpam-4431	24	19	students	student	NOUN
ejpam-4431	24	20	get	get	VERB
ejpam-4431	24	21	accustomed	accustomed	ADJ
ejpam-4431	24	22	to	to	ADP
ejpam-4431	24	23	the	the	DET
ejpam-4431	24	24	necessity	necessity	NOUN
ejpam-4431	24	25	of	of	ADP
ejpam-4431	24	26	individually	individually	ADV
ejpam-4431	24	27	considering	consider	VERB
ejpam-4431	24	28	several	several	ADJ
ejpam-4431	24	29	different	different	ADJ
ejpam-4431	24	30	variants	variant	NOUN
ejpam-4431	24	31	of	of	ADP
ejpam-4431	24	32	the	the	DET
ejpam-4431	24	33	solution	solution	NOUN
ejpam-4431	24	34	of	of	ADP
ejpam-4431	24	35	the	the	DET
ejpam-4431	24	36	problem	problem	NOUN
ejpam-4431	24	37	.	.	PUNCT
ejpam-4431	25	1	the	the	DET
ejpam-4431	25	2	works	work	NOUN
ejpam-4431	25	3	[	[	X
ejpam-4431	25	4	1,2,3,5	1,2,3,5	NUM
ejpam-4431	25	5	]	]	PUNCT
ejpam-4431	25	6	are	be	AUX
ejpam-4431	25	7	dedicated	dedicate	VERB
ejpam-4431	25	8	to	to	ADP
ejpam-4431	25	9	the	the	DET
ejpam-4431	25	10	practical	practical	ADJ
ejpam-4431	25	11	issues	issue	NOUN
ejpam-4431	25	12	of	of	ADP
ejpam-4431	25	13	using	use	VERB
ejpam-4431	25	14	variative	variative	ADJ
ejpam-4431	25	15	problems	problem	NOUN
ejpam-4431	25	16	.	.	PUNCT
ejpam-4431	26	1	in	in	ADP
ejpam-4431	26	2	[	[	X
ejpam-4431	26	3	4,6,7,8	4,6,7,8	NUM
ejpam-4431	26	4	]	]	PUNCT
ejpam-4431	26	5	,	,	PUNCT
ejpam-4431	26	6	the	the	DET
ejpam-4431	26	7	solution	solution	NOUN
ejpam-4431	26	8	of	of	ADP
ejpam-4431	26	9	some	some	DET
ejpam-4431	26	10	kinds	kind	NOUN
ejpam-4431	26	11	of	of	ADP
ejpam-4431	26	12	variative	variative	ADJ
ejpam-4431	26	13	problems	problem	NOUN
ejpam-4431	26	14	is	be	AUX
ejpam-4431	26	15	presented	present	VERB
ejpam-4431	26	16	.	.	PUNCT
ejpam-4431	27	1	2	2	X
ejpam-4431	27	2	.	.	X
ejpam-4431	27	3	a	a	DET
ejpam-4431	27	4	study	study	NOUN
ejpam-4431	27	5	of	of	ADP
ejpam-4431	27	6	the	the	DET
ejpam-4431	27	7	variative	variative	ADJ
ejpam-4431	27	8	problems	problem	NOUN
ejpam-4431	27	9	the	the	DET
ejpam-4431	27	10	main	main	ADJ
ejpam-4431	27	11	characteristic	characteristic	NOUN
ejpam-4431	27	12	of	of	ADP
ejpam-4431	27	13	the	the	DET
ejpam-4431	27	14	latter	latter	ADJ
ejpam-4431	27	15	is	be	AUX
ejpam-4431	27	16	the	the	DET
ejpam-4431	27	17	ambiguous	ambiguous	ADJ
ejpam-4431	27	18	location	location	NOUN
ejpam-4431	27	19	of	of	ADP
ejpam-4431	27	20	objects	object	NOUN
ejpam-4431	27	21	appearing	appear	VERB
ejpam-4431	27	22	in	in	ADP
ejpam-4431	27	23	the	the	DET
ejpam-4431	27	24	conditions	condition	NOUN
ejpam-4431	27	25	of	of	ADP
ejpam-4431	27	26	the	the	DET
ejpam-4431	27	27	problem	problem	NOUN
ejpam-4431	27	28	,	,	PUNCT
ejpam-4431	27	29	which	which	PRON
ejpam-4431	27	30	leads	lead	VERB
ejpam-4431	27	31	to	to	ADP
ejpam-4431	27	32	the	the	DET
ejpam-4431	27	33	necessity	necessity	NOUN
ejpam-4431	27	34	of	of	ADP
ejpam-4431	27	35	considering	consider	VERB
ejpam-4431	27	36	several	several	ADJ
ejpam-4431	27	37	situations	situation	NOUN
ejpam-4431	27	38	.	.	PUNCT
ejpam-4431	28	1	to	to	PART
ejpam-4431	28	2	solve	solve	VERB
ejpam-4431	28	3	variative	variative	ADJ
ejpam-4431	28	4	problem	problem	NOUN
ejpam-4431	28	5	is	be	AUX
ejpam-4431	28	6	to	to	PART
ejpam-4431	28	7	consider	consider	VERB
ejpam-4431	28	8	all	all	DET
ejpam-4431	28	9	possible	possible	ADJ
ejpam-4431	28	10	variants	variant	NOUN
ejpam-4431	28	11	of	of	ADP
ejpam-4431	28	12	location	location	NOUN
ejpam-4431	28	13	of	of	ADP
ejpam-4431	28	14	objects	object	NOUN
ejpam-4431	28	15	,	,	PUNCT
ejpam-4431	28	16	which	which	PRON
ejpam-4431	28	17	leads	lead	VERB
ejpam-4431	28	18	to	to	ADP
ejpam-4431	28	19	several	several	ADJ
ejpam-4431	28	20	answers	answer	NOUN
ejpam-4431	28	21	.	.	PUNCT
ejpam-4431	29	1	from	from	ADP
ejpam-4431	29	2	a	a	DET
ejpam-4431	29	3	practical	practical	ADJ
ejpam-4431	29	4	point	point	NOUN
ejpam-4431	29	5	of	of	ADP
ejpam-4431	29	6	view	view	NOUN
ejpam-4431	29	7	,	,	PUNCT
ejpam-4431	29	8	it	it	PRON
ejpam-4431	29	9	is	be	AUX
ejpam-4431	29	10	also	also	ADV
ejpam-4431	29	11	important	important	ADJ
ejpam-4431	29	12	that	that	SCONJ
ejpam-4431	29	13	such	such	ADJ
ejpam-4431	29	14	problems	problem	NOUN
ejpam-4431	29	15	can	can	AUX
ejpam-4431	29	16	be	be	AUX
ejpam-4431	29	17	considered	consider	VERB
ejpam-4431	29	18	even	even	ADV
ejpam-4431	29	19	in	in	ADP
ejpam-4431	29	20	the	the	DET
ejpam-4431	29	21	lower	low	ADJ
ejpam-4431	29	22	grades	grade	NOUN
ejpam-4431	29	23	.	.	PUNCT
ejpam-4431	30	1	in	in	ADP
ejpam-4431	30	2	particular	particular	ADJ
ejpam-4431	30	3	,	,	PUNCT
ejpam-4431	30	4	they	they	PRON
ejpam-4431	30	5	can	can	AUX
ejpam-4431	30	6	be	be	AUX
ejpam-4431	30	7	easily	easily	ADV
ejpam-4431	30	8	obtained	obtain	VERB
ejpam-4431	30	9	from	from	ADP
ejpam-4431	30	10	the	the	DET
ejpam-4431	30	11	simplest	simple	ADJ
ejpam-4431	30	12	”	"	PUNCT
ejpam-4431	30	13	standard	standard	ADJ
ejpam-4431	30	14	”	"	PUNCT
ejpam-4431	30	15	problems	problem	NOUN
ejpam-4431	30	16	by	by	ADP
ejpam-4431	30	17	some	some	DET
ejpam-4431	30	18	incompleteness	incompleteness	NOUN
ejpam-4431	30	19	in	in	ADP
ejpam-4431	30	20	the	the	DET
ejpam-4431	30	21	conditions	condition	NOUN
ejpam-4431	30	22	.	.	PUNCT
ejpam-4431	31	1	problem	problem	NOUN
ejpam-4431	31	2	1	1	NUM
ejpam-4431	31	3	.	.	PUNCT
ejpam-4431	32	1	the	the	DET
ejpam-4431	32	2	price	price	NOUN
ejpam-4431	32	3	of	of	ADP
ejpam-4431	32	4	the	the	DET
ejpam-4431	32	5	good	good	NOUN
ejpam-4431	32	6	has	have	AUX
ejpam-4431	32	7	been	be	AUX
ejpam-4431	32	8	twice	twice	ADV
ejpam-4431	32	9	changed	change	VERB
ejpam-4431	32	10	by	by	ADP
ejpam-4431	32	11	10%.by	10%.by	PROPN
ejpam-4431	32	12	how	how	SCONJ
ejpam-4431	32	13	many	many	ADJ
ejpam-4431	32	14	percent	percent	NOUN
ejpam-4431	32	15	did	do	VERB
ejpam-4431	32	16	the	the	DET
ejpam-4431	32	17	price	price	NOUN
ejpam-4431	32	18	change	change	NOUN
ejpam-4431	32	19	at	at	ADV
ejpam-4431	32	20	all	all	ADV
ejpam-4431	32	21	?	?	PUNCT
ejpam-4431	33	1	depending	depend	VERB
ejpam-4431	33	2	on	on	ADP
ejpam-4431	33	3	whether	whether	SCONJ
ejpam-4431	33	4	the	the	DET
ejpam-4431	33	5	price	price	NOUN
ejpam-4431	33	6	rose	rise	VERB
ejpam-4431	33	7	or	or	CCONJ
ejpam-4431	33	8	dropped	drop	VERB
ejpam-4431	33	9	in	in	ADP
ejpam-4431	33	10	two	two	NUM
ejpam-4431	33	11	cases	case	NOUN
ejpam-4431	33	12	(	(	PUNCT
ejpam-4431	33	13	total	total	NOUN
ejpam-4431	33	14	of	of	ADP
ejpam-4431	33	15	four	four	NUM
ejpam-4431	33	16	situations	situation	NOUN
ejpam-4431	33	17	are	be	AUX
ejpam-4431	33	18	possible	possible	ADJ
ejpam-4431	33	19	)	)	PUNCT
ejpam-4431	33	20	,	,	PUNCT
ejpam-4431	33	21	there	there	PRON
ejpam-4431	33	22	are	be	VERB
ejpam-4431	33	23	three	three	NUM
ejpam-4431	33	24	variants	variant	NOUN
ejpam-4431	33	25	of	of	ADP
ejpam-4431	33	26	answer	answer	NOUN
ejpam-4431	33	27	:	:	PUNCT
ejpam-4431	33	28	1	1	X
ejpam-4431	33	29	)	)	PUNCT
ejpam-4431	33	30	if	if	SCONJ
ejpam-4431	33	31	the	the	DET
ejpam-4431	33	32	price	price	NOUN
ejpam-4431	33	33	of	of	ADP
ejpam-4431	33	34	the	the	DET
ejpam-4431	33	35	good	good	NOUN
ejpam-4431	33	36	dropped	drop	VERB
ejpam-4431	33	37	by	by	ADP
ejpam-4431	33	38	10	10	NUM
ejpam-4431	33	39	%	%	NOUN
ejpam-4431	33	40	in	in	ADP
ejpam-4431	33	41	both	both	DET
ejpam-4431	33	42	cases	case	NOUN
ejpam-4431	33	43	,	,	PUNCT
ejpam-4431	33	44	then	then	ADV
ejpam-4431	33	45	the	the	DET
ejpam-4431	33	46	total	total	ADJ
ejpam-4431	33	47	drop	drop	NOUN
ejpam-4431	33	48	of	of	ADP
ejpam-4431	33	49	the	the	DET
ejpam-4431	33	50	price	price	NOUN
ejpam-4431	33	51	is	be	AUX
ejpam-4431	33	52	19	19	NUM
ejpam-4431	33	53	%	%	NOUN
ejpam-4431	33	54	.	.	PUNCT
ejpam-4431	34	1	2	2	X
ejpam-4431	34	2	)	)	PUNCT
ejpam-4431	34	3	if	if	SCONJ
ejpam-4431	34	4	the	the	DET
ejpam-4431	34	5	price	price	NOUN
ejpam-4431	34	6	of	of	ADP
ejpam-4431	34	7	the	the	DET
ejpam-4431	34	8	good	good	ADJ
ejpam-4431	34	9	first	first	ADV
ejpam-4431	34	10	dropped	drop	VERB
ejpam-4431	34	11	by	by	ADP
ejpam-4431	34	12	10	10	NUM
ejpam-4431	34	13	%	%	NOUN
ejpam-4431	34	14	,	,	PUNCT
ejpam-4431	34	15	and	and	CCONJ
ejpam-4431	34	16	then	then	ADV
ejpam-4431	34	17	rose	rise	VERB
ejpam-4431	34	18	by	by	ADP
ejpam-4431	34	19	10	10	NUM
ejpam-4431	34	20	%	%	NOUN
ejpam-4431	34	21	,	,	PUNCT
ejpam-4431	34	22	then	then	ADV
ejpam-4431	34	23	the	the	DET
ejpam-4431	34	24	price	price	NOUN
ejpam-4431	34	25	dropped	drop	VERB
ejpam-4431	34	26	in	in	ADP
ejpam-4431	34	27	total	total	NOUN
ejpam-4431	34	28	by	by	ADP
ejpam-4431	34	29	1	1	NUM
ejpam-4431	34	30	%	%	NOUN
ejpam-4431	34	31	.	.	PUNCT
ejpam-4431	35	1	3	3	X
ejpam-4431	35	2	)	)	PUNCT
ejpam-4431	35	3	if	if	SCONJ
ejpam-4431	35	4	the	the	DET
ejpam-4431	35	5	price	price	NOUN
ejpam-4431	35	6	of	of	ADP
ejpam-4431	35	7	the	the	DET
ejpam-4431	35	8	good	good	ADJ
ejpam-4431	35	9	first	first	ADV
ejpam-4431	35	10	rose	rise	VERB
ejpam-4431	35	11	by	by	ADP
ejpam-4431	35	12	10	10	NUM
ejpam-4431	35	13	%	%	NOUN
ejpam-4431	35	14	,	,	PUNCT
ejpam-4431	35	15	and	and	CCONJ
ejpam-4431	35	16	then	then	ADV
ejpam-4431	35	17	dropped	drop	VERB
ejpam-4431	35	18	by	by	ADP
ejpam-4431	35	19	10	10	NUM
ejpam-4431	35	20	%	%	NOUN
ejpam-4431	35	21	,	,	PUNCT
ejpam-4431	35	22	then	then	ADV
ejpam-4431	35	23	the	the	DET
ejpam-4431	35	24	price	price	NOUN
ejpam-4431	35	25	dropped	drop	VERB
ejpam-4431	35	26	in	in	ADP
ejpam-4431	35	27	total	total	NOUN
ejpam-4431	35	28	by	by	ADP
ejpam-4431	35	29	1	1	NUM
ejpam-4431	35	30	%	%	NOUN
ejpam-4431	35	31	.	.	PUNCT
ejpam-4431	36	1	4	4	X
ejpam-4431	36	2	)	)	PUNCT
ejpam-4431	36	3	if	if	SCONJ
ejpam-4431	36	4	the	the	DET
ejpam-4431	36	5	price	price	NOUN
ejpam-4431	36	6	of	of	ADP
ejpam-4431	36	7	the	the	DET
ejpam-4431	36	8	good	good	ADJ
ejpam-4431	36	9	rose	rise	VERB
ejpam-4431	36	10	by	by	ADP
ejpam-4431	36	11	10%in	10%in	NUM
ejpam-4431	36	12	both	both	DET
ejpam-4431	36	13	cases	case	NOUN
ejpam-4431	36	14	,	,	PUNCT
ejpam-4431	36	15	then	then	ADV
ejpam-4431	36	16	the	the	DET
ejpam-4431	36	17	total	total	ADJ
ejpam-4431	36	18	rise	rise	NOUN
ejpam-4431	36	19	of	of	ADP
ejpam-4431	36	20	the	the	DET
ejpam-4431	36	21	price	price	NOUN
ejpam-4431	36	22	is	be	AUX
ejpam-4431	36	23	21	21	NUM
ejpam-4431	36	24	%	%	NOUN
ejpam-4431	36	25	.	.	PUNCT
ejpam-4431	37	1	problem	problem	NOUN
ejpam-4431	37	2	2	2	NUM
ejpam-4431	37	3	.	.	PUNCT
ejpam-4431	38	1	the	the	DET
ejpam-4431	38	2	distance	distance	NOUN
ejpam-4431	38	3	between	between	ADP
ejpam-4431	38	4	two	two	NUM
ejpam-4431	38	5	cyclists	cyclist	NOUN
ejpam-4431	38	6	is	be	AUX
ejpam-4431	38	7	currently	currently	ADV
ejpam-4431	38	8	60	60	NUM
ejpam-4431	38	9	km	km	NOUN
ejpam-4431	38	10	.	.	PUNCT
ejpam-4431	39	1	what	what	PRON
ejpam-4431	39	2	will	will	AUX
ejpam-4431	39	3	be	be	AUX
ejpam-4431	39	4	the	the	DET
ejpam-4431	39	5	distance	distance	NOUN
ejpam-4431	39	6	between	between	ADP
ejpam-4431	39	7	them	they	PRON
ejpam-4431	39	8	in	in	ADP
ejpam-4431	39	9	two	two	NUM
ejpam-4431	39	10	hours	hour	NOUN
ejpam-4431	39	11	,	,	PUNCT
ejpam-4431	39	12	if	if	SCONJ
ejpam-4431	39	13	their	their	PRON
ejpam-4431	39	14	speeds	speed	NOUN
ejpam-4431	39	15	are	be	AUX
ejpam-4431	39	16	10	10	NUM
ejpam-4431	39	17	km	km	NOUN
ejpam-4431	39	18	/	/	SYM
ejpam-4431	39	19	h	h	NOUN
ejpam-4431	39	20	and	and	CCONJ
ejpam-4431	39	21	15	15	NUM
ejpam-4431	39	22	km	km	NOUN
ejpam-4431	39	23	/	/	SYM
ejpam-4431	39	24	h	h	NOUN
ejpam-4431	39	25	,	,	PUNCT
ejpam-4431	39	26	respectively	respectively	ADV
ejpam-4431	39	27	?	?	PUNCT
ejpam-4431	40	1	(	(	PUNCT
ejpam-4431	40	2	both	both	DET
ejpam-4431	40	3	cyclists	cyclist	NOUN
ejpam-4431	40	4	are	be	AUX
ejpam-4431	40	5	driving	drive	VERB
ejpam-4431	40	6	on	on	ADP
ejpam-4431	40	7	the	the	DET
ejpam-4431	40	8	same	same	ADJ
ejpam-4431	40	9	straight	straight	ADJ
ejpam-4431	40	10	driveway	driveway	NOUN
ejpam-4431	40	11	with	with	ADP
ejpam-4431	40	12	no	no	DET
ejpam-4431	40	13	turns	turn	NOUN
ejpam-4431	40	14	)	)	PUNCT
ejpam-4431	40	15	.	.	PUNCT
ejpam-4431	41	1	depending	depend	VERB
ejpam-4431	41	2	on	on	ADP
ejpam-4431	41	3	the	the	DET
ejpam-4431	41	4	kind	kind	NOUN
ejpam-4431	41	5	of	of	ADP
ejpam-4431	41	6	movement	movement	NOUN
ejpam-4431	41	7	(	(	PUNCT
ejpam-4431	41	8	cyclists	cyclist	NOUN
ejpam-4431	41	9	driving	drive	VERB
ejpam-4431	41	10	towards	towards	ADP
ejpam-4431	41	11	each	each	DET
ejpam-4431	41	12	other	other	ADJ
ejpam-4431	41	13	,	,	PUNCT
ejpam-4431	41	14	in	in	ADP
ejpam-4431	41	15	different	different	ADJ
ejpam-4431	41	16	directions	direction	NOUN
ejpam-4431	41	17	,	,	PUNCT
ejpam-4431	41	18	chasing	chase	VERB
ejpam-4431	41	19	each	each	DET
ejpam-4431	41	20	other	other	ADJ
ejpam-4431	41	21	,	,	PUNCT
ejpam-4431	41	22	or	or	CCONJ
ejpam-4431	41	23	one	one	NUM
ejpam-4431	41	24	lagging	lag	VERB
ejpam-4431	41	25	behind	behind	ADP
ejpam-4431	41	26	other	other	ADJ
ejpam-4431	41	27	)	)	PUNCT
ejpam-4431	41	28	,	,	PUNCT
ejpam-4431	41	29	there	there	PRON
ejpam-4431	41	30	are	be	VERB
ejpam-4431	41	31	four	four	NUM
ejpam-4431	41	32	variants	variant	NOUN
ejpam-4431	41	33	of	of	ADP
ejpam-4431	41	34	answer	answer	NOUN
ejpam-4431	41	35	:	:	PUNCT
ejpam-4431	41	36	situation	situation	NOUN
ejpam-4431	41	37	1	1	NUM
ejpam-4431	41	38	.	.	PUNCT
ejpam-4431	41	39	figure	figure	NOUN
ejpam-4431	41	40	1	1	NUM
ejpam-4431	41	41	:	:	PUNCT
ejpam-4431	41	42	cyclists	cyclist	NOUN
ejpam-4431	41	43	driving	drive	VERB
ejpam-4431	41	44	towards	towards	ADP
ejpam-4431	41	45	each	each	DET
ejpam-4431	41	46	other	other	ADJ
ejpam-4431	41	47	s.	s.	PROPN
ejpam-4431	41	48	j.aliyev	j.aliyev	PROPN
ejpam-4431	41	49	,	,	PUNCT
ejpam-4431	41	50	b.	b.	PROPN
ejpam-4431	41	51	o.tahirov	o.tahirov	PROPN
ejpam-4431	41	52	,	,	PUNCT
ejpam-4431	41	53	t.	t.	PROPN
ejpam-4431	41	54	a.hashimova	a.hashimova	PROPN
ejpam-4431	41	55	/	/	SYM
ejpam-4431	41	56	eur	eur	PROPN
ejpam-4431	41	57	.	.	PUNCT
ejpam-4431	42	1	j.	j.	PROPN
ejpam-4431	42	2	pure	pure	PROPN
ejpam-4431	42	3	appl	appl	PROPN
ejpam-4431	42	4	.	.	PROPN
ejpam-4431	42	5	math	math	PROPN
ejpam-4431	42	6	,	,	PUNCT
ejpam-4431	42	7	15	15	NUM
ejpam-4431	42	8	(	(	PUNCT
ejpam-4431	42	9	3	3	NUM
ejpam-4431	42	10	)	)	PUNCT
ejpam-4431	42	11	(	(	PUNCT
ejpam-4431	42	12	2022	2022	NUM
ejpam-4431	42	13	)	)	PUNCT
ejpam-4431	42	14	,	,	PUNCT
ejpam-4431	42	15	1015	1015	NUM
ejpam-4431	42	16	-	-	SYM
ejpam-4431	42	17	1022	1022	NUM
ejpam-4431	42	18	1017	1017	NUM
ejpam-4431	42	19	in	in	ADP
ejpam-4431	42	20	this	this	DET
ejpam-4431	42	21	case	case	NOUN
ejpam-4431	42	22	,	,	PUNCT
ejpam-4431	42	23	the	the	DET
ejpam-4431	42	24	answer	answer	NOUN
ejpam-4431	42	25	is	be	AUX
ejpam-4431	42	26	10	10	NUM
ejpam-4431	42	27	km	km	NOUN
ejpam-4431	42	28	.	.	PUNCT
ejpam-4431	43	1	situation	situation	NOUN
ejpam-4431	43	2	2	2	NUM
ejpam-4431	43	3	.	.	PUNCT
ejpam-4431	44	1	in	in	ADP
ejpam-4431	44	2	this	this	DET
ejpam-4431	44	3	case	case	NOUN
ejpam-4431	44	4	,	,	PUNCT
ejpam-4431	44	5	the	the	DET
ejpam-4431	44	6	answer	answer	NOUN
ejpam-4431	44	7	is	be	AUX
ejpam-4431	44	8	50	50	NUM
ejpam-4431	44	9	km	km	NOUN
ejpam-4431	44	10	.	.	PUNCT
ejpam-4431	45	1	figure	figure	NOUN
ejpam-4431	45	2	2	2	NUM
ejpam-4431	45	3	:	:	PUNCT
ejpam-4431	45	4	cyclists	cyclist	NOUN
ejpam-4431	45	5	chasing	chase	VERB
ejpam-4431	45	6	each	each	DET
ejpam-4431	45	7	other	other	ADJ
ejpam-4431	45	8	situation	situation	NOUN
ejpam-4431	45	9	3	3	X
ejpam-4431	45	10	.	.	PUNCT
ejpam-4431	46	1	in	in	ADP
ejpam-4431	46	2	this	this	DET
ejpam-4431	46	3	case	case	NOUN
ejpam-4431	46	4	,	,	PUNCT
ejpam-4431	46	5	the	the	DET
ejpam-4431	46	6	answer	answer	NOUN
ejpam-4431	46	7	is	be	AUX
ejpam-4431	46	8	70	70	NUM
ejpam-4431	46	9	km	km	NOUN
ejpam-4431	46	10	.	.	PUNCT
ejpam-4431	47	1	figure	figure	VERB
ejpam-4431	47	2	3	3	NUM
ejpam-4431	47	3	:	:	PUNCT
ejpam-4431	47	4	one	one	NUM
ejpam-4431	47	5	of	of	ADP
ejpam-4431	47	6	cyclists	cyclist	NOUN
ejpam-4431	47	7	lagging	lag	VERB
ejpam-4431	47	8	behind	behind	ADP
ejpam-4431	47	9	the	the	DET
ejpam-4431	47	10	other	other	ADJ
ejpam-4431	47	11	situation	situation	NOUN
ejpam-4431	47	12	4	4	NUM
ejpam-4431	47	13	.	.	PUNCT
ejpam-4431	48	1	in	in	ADP
ejpam-4431	48	2	this	this	DET
ejpam-4431	48	3	case	case	NOUN
ejpam-4431	48	4	,	,	PUNCT
ejpam-4431	48	5	the	the	DET
ejpam-4431	48	6	answer	answer	NOUN
ejpam-4431	48	7	is	be	AUX
ejpam-4431	48	8	110	110	NUM
ejpam-4431	48	9	km	km	NOUN
ejpam-4431	48	10	.	.	PUNCT
ejpam-4431	49	1	figure	figure	VERB
ejpam-4431	49	2	4	4	NUM
ejpam-4431	49	3	:	:	PUNCT
ejpam-4431	49	4	cyclists	cyclist	NOUN
ejpam-4431	49	5	driving	drive	VERB
ejpam-4431	49	6	in	in	ADP
ejpam-4431	49	7	different	different	ADJ
ejpam-4431	49	8	directions	direction	NOUN
ejpam-4431	49	9	that	that	PRON
ejpam-4431	49	10	’s	’	VERB
ejpam-4431	49	11	what	what	PRON
ejpam-4431	49	12	’s	’s	AUX
ejpam-4431	49	13	called	call	VERB
ejpam-4431	49	14	”	"	PUNCT
ejpam-4431	49	15	thinking	thinking	NOUN
ejpam-4431	49	16	activity	activity	NOUN
ejpam-4431	49	17	”	"	PUNCT
ejpam-4431	49	18	?	?	PUNCT
ejpam-4431	50	1	it	it	PRON
ejpam-4431	50	2	includes	include	VERB
ejpam-4431	50	3	the	the	DET
ejpam-4431	50	4	consideration	consideration	NOUN
ejpam-4431	50	5	of	of	ADP
ejpam-4431	50	6	different	different	ADJ
ejpam-4431	50	7	variants	variant	NOUN
ejpam-4431	50	8	,	,	PUNCT
ejpam-4431	50	9	imposition	imposition	NOUN
ejpam-4431	50	10	of	of	ADP
ejpam-4431	50	11	additional	additional	ADJ
ejpam-4431	50	12	conditions	condition	NOUN
ejpam-4431	50	13	,	,	PUNCT
ejpam-4431	50	14	statement	statement	NOUN
ejpam-4431	50	15	of	of	ADP
ejpam-4431	50	16	new	new	ADJ
ejpam-4431	50	17	problems	problem	NOUN
ejpam-4431	50	18	,	,	PUNCT
ejpam-4431	50	19	abstraction	abstraction	NOUN
ejpam-4431	50	20	,	,	PUNCT
ejpam-4431	50	21	and	and	CCONJ
ejpam-4431	50	22	finding	find	VERB
ejpam-4431	50	23	a	a	DET
ejpam-4431	50	24	general	general	ADJ
ejpam-4431	50	25	method	method	NOUN
ejpam-4431	50	26	for	for	ADP
ejpam-4431	50	27	solving	solve	VERB
ejpam-4431	50	28	the	the	DET
ejpam-4431	50	29	considered	consider	VERB
ejpam-4431	50	30	problem	problem	NOUN
ejpam-4431	50	31	.	.	PUNCT
ejpam-4431	51	1	in	in	ADP
ejpam-4431	51	2	this	this	DET
ejpam-4431	51	3	case	case	NOUN
ejpam-4431	51	4	,	,	PUNCT
ejpam-4431	51	5	the	the	DET
ejpam-4431	51	6	removal	removal	NOUN
ejpam-4431	51	7	of	of	ADP
ejpam-4431	51	8	some	some	DET
ejpam-4431	51	9	condition	condition	NOUN
ejpam-4431	51	10	in	in	ADP
ejpam-4431	51	11	standard	standard	ADJ
ejpam-4431	51	12	problem	problem	NOUN
ejpam-4431	51	13	leads	lead	VERB
ejpam-4431	51	14	to	to	ADP
ejpam-4431	51	15	the	the	DET
ejpam-4431	51	16	variative	variative	ADJ
ejpam-4431	51	17	problem	problem	NOUN
ejpam-4431	51	18	.	.	PUNCT
ejpam-4431	52	1	here	here	ADV
ejpam-4431	52	2	are	be	AUX
ejpam-4431	52	3	some	some	DET
ejpam-4431	52	4	other	other	ADJ
ejpam-4431	52	5	examples	example	NOUN
ejpam-4431	52	6	of	of	ADP
ejpam-4431	52	7	variative	variative	ADJ
ejpam-4431	52	8	problems	problem	NOUN
ejpam-4431	52	9	.	.	PUNCT
ejpam-4431	53	1	problem	problem	NOUN
ejpam-4431	53	2	3	3	NUM
ejpam-4431	53	3	.	.	PUNCT
ejpam-4431	54	1	given	give	VERB
ejpam-4431	54	2	two	two	NUM
ejpam-4431	54	3	vertices	vertex	NOUN
ejpam-4431	54	4	m	m	VERB
ejpam-4431	54	5	(	(	PUNCT
ejpam-4431	54	6	3	3	NUM
ejpam-4431	54	7	,	,	PUNCT
ejpam-4431	54	8	2	2	NUM
ejpam-4431	54	9	)	)	PUNCT
ejpam-4431	54	10	and	and	CCONJ
ejpam-4431	54	11	n	n	CCONJ
ejpam-4431	54	12	(	(	PUNCT
ejpam-4431	54	13	6	6	NUM
ejpam-4431	54	14	,	,	PUNCT
ejpam-4431	54	15	5	5	NUM
ejpam-4431	54	16	)	)	PUNCT
ejpam-4431	54	17	,	,	PUNCT
ejpam-4431	54	18	construct	construct	VERB
ejpam-4431	54	19	a	a	DET
ejpam-4431	54	20	square	square	NOUN
ejpam-4431	54	21	.	.	PUNCT
ejpam-4431	55	1	there	there	PRON
ejpam-4431	55	2	is	be	VERB
ejpam-4431	55	3	no	no	DET
ejpam-4431	55	4	information	information	NOUN
ejpam-4431	55	5	in	in	ADP
ejpam-4431	55	6	this	this	DET
ejpam-4431	55	7	problem	problem	NOUN
ejpam-4431	55	8	about	about	ADP
ejpam-4431	55	9	whether	whether	SCONJ
ejpam-4431	55	10	the	the	DET
ejpam-4431	55	11	given	give	VERB
ejpam-4431	55	12	vertices	vertex	NOUN
ejpam-4431	55	13	are	be	AUX
ejpam-4431	55	14	consecutive	consecutive	ADJ
ejpam-4431	55	15	or	or	CCONJ
ejpam-4431	55	16	opposite	opposite	ADJ
ejpam-4431	55	17	to	to	ADP
ejpam-4431	55	18	each	each	DET
ejpam-4431	55	19	other	other	ADJ
ejpam-4431	55	20	.	.	PUNCT
ejpam-4431	56	1	therefore	therefore	ADV
ejpam-4431	56	2	,	,	PUNCT
ejpam-4431	56	3	we	we	PRON
ejpam-4431	56	4	have	have	VERB
ejpam-4431	56	5	to	to	PART
ejpam-4431	56	6	consider	consider	VERB
ejpam-4431	56	7	all	all	DET
ejpam-4431	56	8	possible	possible	ADJ
ejpam-4431	56	9	variants	variant	NOUN
ejpam-4431	56	10	of	of	ADP
ejpam-4431	56	11	locations	location	NOUN
ejpam-4431	56	12	of	of	ADP
ejpam-4431	56	13	vertices	vertex	NOUN
ejpam-4431	56	14	,	,	PUNCT
ejpam-4431	56	15	which	which	PRON
ejpam-4431	56	16	leads	lead	VERB
ejpam-4431	56	17	to	to	ADP
ejpam-4431	56	18	three	three	NUM
ejpam-4431	56	19	answers	answer	NOUN
ejpam-4431	56	20	:	:	PUNCT
ejpam-4431	56	21	1	1	NUM
ejpam-4431	56	22	)	)	PUNCT
ejpam-4431	56	23	square	square	ADJ
ejpam-4431	56	24	mndc	mndc	NOUN
ejpam-4431	56	25	with	with	ADP
ejpam-4431	56	26	the	the	DET
ejpam-4431	56	27	vertices	vertex	NOUN
ejpam-4431	56	28	m	m	VERB
ejpam-4431	56	29	(	(	PUNCT
ejpam-4431	56	30	3	3	NUM
ejpam-4431	56	31	,	,	PUNCT
ejpam-4431	56	32	2	2	NUM
ejpam-4431	56	33	)	)	PUNCT
ejpam-4431	56	34	,	,	PUNCT
ejpam-4431	56	35	n	n	CCONJ
ejpam-4431	56	36	(	(	PUNCT
ejpam-4431	56	37	6	6	NUM
ejpam-4431	56	38	,	,	PUNCT
ejpam-4431	56	39	5	5	NUM
ejpam-4431	56	40	)	)	PUNCT
ejpam-4431	56	41	,	,	PUNCT
ejpam-4431	57	1	d	d	X
ejpam-4431	57	2	(	(	PUNCT
ejpam-4431	57	3	3	3	NUM
ejpam-4431	57	4	,	,	PUNCT
ejpam-4431	57	5	8)	8)	NUM
ejpam-4431	57	6	and	and	CCONJ
ejpam-4431	57	7	c	c	PROPN
ejpam-4431	57	8	(	(	PUNCT
ejpam-4431	57	9	0	0	NUM
ejpam-4431	57	10	,	,	PUNCT
ejpam-4431	57	11	5	5	NUM
ejpam-4431	57	12	)	)	PUNCT
ejpam-4431	57	13	.	.	PUNCT
ejpam-4431	58	1	2	2	X
ejpam-4431	58	2	)	)	PUNCT
ejpam-4431	58	3	square	square	ADJ
ejpam-4431	58	4	mnqp	mnqp	NOUN
ejpam-4431	58	5	with	with	ADP
ejpam-4431	58	6	the	the	DET
ejpam-4431	58	7	vertices	vertex	NOUN
ejpam-4431	58	8	m	m	VERB
ejpam-4431	58	9	(	(	PUNCT
ejpam-4431	58	10	3	3	NUM
ejpam-4431	58	11	,	,	PUNCT
ejpam-4431	58	12	2	2	NUM
ejpam-4431	58	13	)	)	PUNCT
ejpam-4431	58	14	,	,	PUNCT
ejpam-4431	58	15	n	n	CCONJ
ejpam-4431	58	16	(	(	PUNCT
ejpam-4431	58	17	6	6	NUM
ejpam-4431	58	18	,	,	PUNCT
ejpam-4431	58	19	5	5	NUM
ejpam-4431	58	20	)	)	PUNCT
ejpam-4431	58	21	,	,	PUNCT
ejpam-4431	58	22	q	q	X
ejpam-4431	58	23	(	(	PUNCT
ejpam-4431	58	24	9	9	NUM
ejpam-4431	58	25	,	,	PUNCT
ejpam-4431	58	26	2	2	NUM
ejpam-4431	58	27	)	)	PUNCT
ejpam-4431	58	28	and	and	CCONJ
ejpam-4431	58	29	p	p	X
ejpam-4431	58	30	(	(	PUNCT
ejpam-4431	58	31	6,−1	6,−1	NUM
ejpam-4431	58	32	)	)	PUNCT
ejpam-4431	58	33	.	.	PUNCT
ejpam-4431	59	1	3	3	X
ejpam-4431	59	2	)	)	PUNCT
ejpam-4431	59	3	square	square	ADJ
ejpam-4431	59	4	menf	menf	NOUN
ejpam-4431	59	5	with	with	ADP
ejpam-4431	59	6	the	the	DET
ejpam-4431	59	7	vertices	vertex	NOUN
ejpam-4431	59	8	m	m	VERB
ejpam-4431	59	9	(	(	PUNCT
ejpam-4431	59	10	3	3	NUM
ejpam-4431	59	11	,	,	PUNCT
ejpam-4431	59	12	2	2	NUM
ejpam-4431	59	13	)	)	PUNCT
ejpam-4431	59	14	,	,	PUNCT
ejpam-4431	59	15	e	e	X
ejpam-4431	59	16	(	(	PUNCT
ejpam-4431	59	17	6	6	NUM
ejpam-4431	59	18	,	,	PUNCT
ejpam-4431	59	19	2	2	NUM
ejpam-4431	59	20	)	)	PUNCT
ejpam-4431	59	21	,	,	PUNCT
ejpam-4431	59	22	n	n	CCONJ
ejpam-4431	59	23	(	(	PUNCT
ejpam-4431	59	24	6	6	NUM
ejpam-4431	59	25	,	,	PUNCT
ejpam-4431	59	26	5	5	NUM
ejpam-4431	59	27	)	)	PUNCT
ejpam-4431	59	28	and	and	CCONJ
ejpam-4431	59	29	f	f	PROPN
ejpam-4431	59	30	(	(	PUNCT
ejpam-4431	59	31	3	3	NUM
ejpam-4431	59	32	,	,	PUNCT
ejpam-4431	59	33	5	5	NUM
ejpam-4431	59	34	)	)	PUNCT
ejpam-4431	59	35	(	(	PUNCT
ejpam-4431	59	36	see	see	VERB
ejpam-4431	59	37	fig	fig	NOUN
ejpam-4431	59	38	.	.	PUNCT
ejpam-4431	60	1	5	5	NUM
ejpam-4431	60	2	)	)	PUNCT
ejpam-4431	60	3	.	.	PUNCT
ejpam-4431	61	1	using	use	VERB
ejpam-4431	61	2	the	the	DET
ejpam-4431	61	3	derivative	derivative	NOUN
ejpam-4431	61	4	,	,	PUNCT
ejpam-4431	61	5	we	we	PRON
ejpam-4431	61	6	solve	solve	VERB
ejpam-4431	61	7	the	the	DET
ejpam-4431	61	8	following	follow	VERB
ejpam-4431	61	9	multivariate	multivariate	NOUN
ejpam-4431	61	10	problem	problem	NOUN
ejpam-4431	61	11	.	.	PUNCT
ejpam-4431	62	1	s.	s.	PROPN
ejpam-4431	62	2	j.aliyev	j.aliyev	PROPN
ejpam-4431	62	3	,	,	PUNCT
ejpam-4431	62	4	b.	b.	PROPN
ejpam-4431	62	5	o.tahirov	o.tahirov	PROPN
ejpam-4431	62	6	,	,	PUNCT
ejpam-4431	62	7	t.	t.	PROPN
ejpam-4431	62	8	a.hashimova	a.hashimova	PROPN
ejpam-4431	62	9	/	/	SYM
ejpam-4431	62	10	eur	eur	PROPN
ejpam-4431	62	11	.	.	PUNCT
ejpam-4431	63	1	j.	j.	PROPN
ejpam-4431	63	2	pure	pure	PROPN
ejpam-4431	63	3	appl	appl	PROPN
ejpam-4431	63	4	.	.	PROPN
ejpam-4431	63	5	math	math	PROPN
ejpam-4431	63	6	,	,	PUNCT
ejpam-4431	63	7	15	15	NUM
ejpam-4431	63	8	(	(	PUNCT
ejpam-4431	63	9	3	3	NUM
ejpam-4431	63	10	)	)	PUNCT
ejpam-4431	63	11	(	(	PUNCT
ejpam-4431	63	12	2022	2022	NUM
ejpam-4431	63	13	)	)	PUNCT
ejpam-4431	63	14	,	,	PUNCT
ejpam-4431	63	15	1015	1015	NUM
ejpam-4431	63	16	-	-	SYM
ejpam-4431	63	17	1022	1022	NUM
ejpam-4431	63	18	1018	1018	NUM
ejpam-4431	63	19	figure	figure	NOUN
ejpam-4431	63	20	5	5	NUM
ejpam-4431	63	21	:	:	PUNCT
ejpam-4431	63	22	squares	square	NOUN
ejpam-4431	63	23	mndc	mndc	NOUN
ejpam-4431	63	24	,	,	PUNCT
ejpam-4431	63	25	mnqp	mnqp	NOUN
ejpam-4431	63	26	,	,	PUNCT
ejpam-4431	63	27	menf	menf	PROPN
ejpam-4431	63	28	constructed	construct	VERB
ejpam-4431	63	29	on	on	ADP
ejpam-4431	63	30	the	the	DET
ejpam-4431	63	31	given	give	VERB
ejpam-4431	63	32	vertices	vertex	NOUN
ejpam-4431	63	33	m	m	VERB
ejpam-4431	63	34	and	and	CCONJ
ejpam-4431	63	35	n	n	PRON
ejpam-4431	63	36	problem	problem	NOUN
ejpam-4431	63	37	4	4	NUM
ejpam-4431	63	38	.	.	PUNCT
ejpam-4431	64	1	for	for	ADP
ejpam-4431	64	2	each	each	DET
ejpam-4431	64	3	value	value	NOUN
ejpam-4431	64	4	of	of	ADP
ejpam-4431	64	5	p	p	NOUN
ejpam-4431	64	6	find	find	VERB
ejpam-4431	64	7	the	the	DET
ejpam-4431	64	8	number	number	NOUN
ejpam-4431	64	9	of	of	ADP
ejpam-4431	64	10	roots	root	NOUN
ejpam-4431	64	11	of	of	ADP
ejpam-4431	64	12	the	the	DET
ejpam-4431	64	13	equation	equation	NOUN
ejpam-4431	64	14	x3	x3	NOUN
ejpam-4431	64	15	−	−	PROPN
ejpam-4431	64	16	3x2	3x2	NUM
ejpam-4431	65	1	−	−	PROPN
ejpam-4431	65	2	p	p	NOUN
ejpam-4431	65	3	=	=	NOUN
ejpam-4431	65	4	0	0	X
ejpam-4431	65	5	.	.	PUNCT
ejpam-4431	65	6	find	find	VERB
ejpam-4431	65	7	the	the	DET
ejpam-4431	65	8	intervals	interval	NOUN
ejpam-4431	65	9	of	of	ADP
ejpam-4431	65	10	increase	increase	NOUN
ejpam-4431	65	11	and	and	CCONJ
ejpam-4431	65	12	decrease	decrease	NOUN
ejpam-4431	65	13	of	of	ADP
ejpam-4431	65	14	the	the	DET
ejpam-4431	65	15	function	function	NOUN
ejpam-4431	65	16	f(x	f(x	PROPN
ejpam-4431	65	17	)	)	PUNCT
ejpam-4431	65	18	=	=	PUNCT
ejpam-4431	66	1	x3	x3	ADJ
ejpam-4431	66	2	−	−	PROPN
ejpam-4431	66	3	3x2	3x2	NUM
ejpam-4431	66	4	.	.	PUNCT
ejpam-4431	67	1	since	since	SCONJ
ejpam-4431	67	2	f	f	PROPN
ejpam-4431	67	3	′(x	′(x	PROPN
ejpam-4431	67	4	)	)	PUNCT
ejpam-4431	67	5	=	=	SYM
ejpam-4431	68	1	3x2	3x2	NUM
ejpam-4431	68	2	−	−	NOUN
ejpam-4431	68	3	6x	6x	NOUN
ejpam-4431	68	4	=	=	SYM
ejpam-4431	68	5	3x	3x	NUM
ejpam-4431	68	6	(	(	PUNCT
ejpam-4431	68	7	x−	x−	PROPN
ejpam-4431	68	8	2	2	NUM
ejpam-4431	68	9	)	)	PUNCT
ejpam-4431	68	10	,	,	PUNCT
ejpam-4431	68	11	then	then	ADV
ejpam-4431	68	12	f	f	PROPN
ejpam-4431	68	13	′(x	′(x	PROPN
ejpam-4431	68	14	)	)	PUNCT
ejpam-4431	68	15	<	<	X
ejpam-4431	68	16	0	0	NUM
ejpam-4431	69	1	for	for	ADP
ejpam-4431	69	2	0	0	NUM
ejpam-4431	69	3	<	<	X
ejpam-4431	69	4	x	x	X
ejpam-4431	69	5	<	<	X
ejpam-4431	69	6	2	2	NUM
ejpam-4431	69	7	,	,	PUNCT
ejpam-4431	69	8	f	f	PROPN
ejpam-4431	69	9	′(x	′(x	PROPN
ejpam-4431	69	10	)	)	PUNCT
ejpam-4431	69	11	=	=	SYM
ejpam-4431	69	12	0	0	NUM
ejpam-4431	70	1	for	for	ADP
ejpam-4431	70	2	x	x	SYM
ejpam-4431	70	3	=	=	SYM
ejpam-4431	70	4	0	0	NUM
ejpam-4431	70	5	and	and	CCONJ
ejpam-4431	70	6	x	x	SYM
ejpam-4431	70	7	=	=	SYM
ejpam-4431	70	8	2	2	NUM
ejpam-4431	70	9	,	,	PUNCT
ejpam-4431	70	10	f	f	PROPN
ejpam-4431	70	11	′(x	′(x	PROPN
ejpam-4431	70	12	)	)	PUNCT
ejpam-4431	70	13	>	>	X
ejpam-4431	70	14	0	0	PUNCT
ejpam-4431	71	1	for	for	ADP
ejpam-4431	71	2	x	x	PUNCT
ejpam-4431	71	3	<	<	X
ejpam-4431	71	4	0	0	PUNCT
ejpam-4431	71	5	and	and	CCONJ
ejpam-4431	71	6	x	x	ADJ
ejpam-4431	71	7	>	>	X
ejpam-4431	71	8	2	2	NUM
ejpam-4431	71	9	.	.	PUNCT
ejpam-4431	72	1	thus	thus	ADV
ejpam-4431	72	2	,	,	PUNCT
ejpam-4431	72	3	the	the	DET
ejpam-4431	72	4	continuous	continuous	ADJ
ejpam-4431	72	5	function	function	NOUN
ejpam-4431	72	6	y	y	PROPN
ejpam-4431	72	7	=	=	SYM
ejpam-4431	72	8	f(x	f(x	PROPN
ejpam-4431	72	9	)	)	PUNCT
ejpam-4431	72	10	has	have	VERB
ejpam-4431	72	11	a	a	DET
ejpam-4431	72	12	local	local	ADJ
ejpam-4431	72	13	minimum	minimum	NOUN
ejpam-4431	72	14	at	at	ADP
ejpam-4431	72	15	pointx	pointx	VERB
ejpam-4431	72	16	=	=	SYM
ejpam-4431	72	17	2	2	NUM
ejpam-4431	72	18	,	,	PUNCT
ejpam-4431	72	19	and	and	CCONJ
ejpam-4431	72	20	a	a	DET
ejpam-4431	72	21	local	local	ADJ
ejpam-4431	72	22	maximum	maximum	NOUN
ejpam-4431	72	23	at	at	ADP
ejpam-4431	72	24	point	point	NOUN
ejpam-4431	72	25	x	x	PUNCT
ejpam-4431	72	26	=	=	SYM
ejpam-4431	72	27	0	0	NUM
ejpam-4431	72	28	,	,	PUNCT
ejpam-4431	72	29	and	and	CCONJ
ejpam-4431	72	30	f(0	f(0	NOUN
ejpam-4431	72	31	)	)	PUNCT
ejpam-4431	72	32	=	=	SYM
ejpam-4431	72	33	0	0	NUM
ejpam-4431	72	34	,	,	PUNCT
ejpam-4431	72	35	f(2	f(2	PROPN
ejpam-4431	72	36	)	)	PUNCT
ejpam-4431	72	37	=	=	PUNCT
ejpam-4431	72	38	−4	−4	PROPN
ejpam-4431	72	39	,	,	PUNCT
ejpam-4431	72	40	.	.	PUNCT
ejpam-4431	73	1	moreover	moreover	ADV
ejpam-4431	73	2	,	,	PUNCT
ejpam-4431	73	3	the	the	DET
ejpam-4431	73	4	function	function	NOUN
ejpam-4431	73	5	y	y	PROPN
ejpam-4431	73	6	=	=	SYM
ejpam-4431	73	7	f(x	f(x	PROPN
ejpam-4431	73	8	)	)	PUNCT
ejpam-4431	73	9	decreases	decrease	VERB
ejpam-4431	73	10	on	on	ADP
ejpam-4431	73	11	the	the	DET
ejpam-4431	73	12	interval	interval	NOUN
ejpam-4431	73	13	[	[	X
ejpam-4431	73	14	0	0	NUM
ejpam-4431	73	15	,	,	PUNCT
ejpam-4431	73	16	2	2	NUM
ejpam-4431	73	17	]	]	PUNCT
ejpam-4431	73	18	and	and	CCONJ
ejpam-4431	73	19	increases	increase	NOUN
ejpam-4431	73	20	on	on	ADP
ejpam-4431	73	21	the	the	DET
ejpam-4431	73	22	intervals	interval	NOUN
ejpam-4431	73	23	(	(	PUNCT
ejpam-4431	73	24	−∞	−∞	NOUN
ejpam-4431	73	25	,	,	PUNCT
ejpam-4431	73	26	0	0	NUM
ejpam-4431	73	27	]	]	PUNCT
ejpam-4431	73	28	and	and	CCONJ
ejpam-4431	74	1	[	[	X
ejpam-4431	74	2	2,+∞	2,+∞	NUM
ejpam-4431	74	3	)	)	PUNCT
ejpam-4431	74	4	.	.	PUNCT
ejpam-4431	75	1	consequently	consequently	ADV
ejpam-4431	75	2	lim	lim	PROPN
ejpam-4431	75	3	f(x	f(x	PROPN
ejpam-4431	75	4	)	)	PUNCT
ejpam-4431	76	1	x→+∞	x→+∞	PROPN
ejpam-4431	76	2	=	=	PUNCT
ejpam-4431	77	1	+	+	NOUN
ejpam-4431	77	2	∞	∞	NUM
ejpam-4431	77	3	and	and	CCONJ
ejpam-4431	77	4	lim	lim	PROPN
ejpam-4431	77	5	f(x	f(x	PROPN
ejpam-4431	77	6	)	)	PUNCT
ejpam-4431	77	7	x→−∞	x→−∞	PROPN
ejpam-4431	78	1	=	=	PUNCT
ejpam-4431	78	2	−∞	−∞	NOUN
ejpam-4431	78	3	.	.	PUNCT
ejpam-4431	79	1	hence	hence	ADV
ejpam-4431	79	2	it	it	PRON
ejpam-4431	79	3	follows	follow	VERB
ejpam-4431	79	4	that	that	SCONJ
ejpam-4431	79	5	in	in	ADP
ejpam-4431	79	6	order	order	NOUN
ejpam-4431	79	7	to	to	PART
ejpam-4431	79	8	find	find	VERB
ejpam-4431	79	9	out	out	ADP
ejpam-4431	79	10	the	the	DET
ejpam-4431	79	11	dependence	dependence	NOUN
ejpam-4431	79	12	of	of	ADP
ejpam-4431	79	13	the	the	DET
ejpam-4431	79	14	number	number	NOUN
ejpam-4431	79	15	of	of	ADP
ejpam-4431	79	16	roots	root	NOUN
ejpam-4431	79	17	of	of	ADP
ejpam-4431	79	18	the	the	DET
ejpam-4431	79	19	equation	equation	NOUN
ejpam-4431	79	20	on	on	ADP
ejpam-4431	79	21	the	the	DET
ejpam-4431	79	22	possible	possible	ADJ
ejpam-4431	79	23	values	value	NOUN
ejpam-4431	79	24	of	of	ADP
ejpam-4431	79	25	p	p	NOUN
ejpam-4431	79	26	,	,	PUNCT
ejpam-4431	79	27	it	it	PRON
ejpam-4431	79	28	is	be	AUX
ejpam-4431	79	29	necessary	necessary	ADJ
ejpam-4431	79	30	to	to	PART
ejpam-4431	79	31	find	find	VERB
ejpam-4431	79	32	out	out	ADP
ejpam-4431	79	33	the	the	DET
ejpam-4431	79	34	relative	relative	ADJ
ejpam-4431	79	35	position	position	NOUN
ejpam-4431	79	36	of	of	ADP
ejpam-4431	79	37	the	the	DET
ejpam-4431	79	38	graph	graph	NOUN
ejpam-4431	79	39	of	of	ADP
ejpam-4431	79	40	the	the	DET
ejpam-4431	79	41	function	function	NOUN
ejpam-4431	79	42	y	y	PROPN
ejpam-4431	79	43	=	=	SYM
ejpam-4431	79	44	f(x	f(x	PROPN
ejpam-4431	79	45	)	)	PUNCT
ejpam-4431	79	46	and	and	CCONJ
ejpam-4431	79	47	the	the	DET
ejpam-4431	79	48	straight	straight	ADJ
ejpam-4431	79	49	line	line	NOUN
ejpam-4431	79	50	p	p	X
ejpam-4431	79	51	.	.	PUNCT
ejpam-4431	80	1	from	from	ADP
ejpam-4431	80	2	the	the	DET
ejpam-4431	80	3	properties	property	NOUN
ejpam-4431	80	4	of	of	ADP
ejpam-4431	80	5	the	the	DET
ejpam-4431	80	6	function	function	NOUN
ejpam-4431	80	7	y	y	PROPN
ejpam-4431	80	8	=	=	SYM
ejpam-4431	80	9	f(x	f(x	PROPN
ejpam-4431	80	10	)	)	PUNCT
ejpam-4431	80	11	proved	prove	VERB
ejpam-4431	80	12	above	above	ADV
ejpam-4431	80	13	and	and	CCONJ
ejpam-4431	80	14	the	the	DET
ejpam-4431	80	15	fact	fact	NOUN
ejpam-4431	80	16	that	that	SCONJ
ejpam-4431	80	17	the	the	DET
ejpam-4431	80	18	function	function	NOUN
ejpam-4431	80	19	y	y	PROPN
ejpam-4431	80	20	=	=	SYM
ejpam-4431	80	21	f(x	f(x	PROPN
ejpam-4431	80	22	)	)	PUNCT
ejpam-4431	80	23	is	be	AUX
ejpam-4431	80	24	continuous	continuous	ADJ
ejpam-4431	80	25	and	and	CCONJ
ejpam-4431	80	26	is	be	AUX
ejpam-4431	80	27	a	a	DET
ejpam-4431	80	28	polynomial	polynomial	NOUN
ejpam-4431	80	29	of	of	ADP
ejpam-4431	80	30	the	the	DET
ejpam-4431	80	31	third	third	ADJ
ejpam-4431	80	32	degree	degree	NOUN
ejpam-4431	80	33	,	,	PUNCT
ejpam-4431	80	34	we	we	PRON
ejpam-4431	80	35	have	have	VERB
ejpam-4431	80	36	that	that	DET
ejpam-4431	80	37	1	1	NUM
ejpam-4431	80	38	)	)	PUNCT
ejpam-4431	80	39	for	for	ADP
ejpam-4431	80	40	p	p	PROPN
ejpam-4431	80	41	>	>	X
ejpam-4431	80	42	0	0	PUNCT
ejpam-4431	81	1	the	the	DET
ejpam-4431	81	2	equation	equation	NOUN
ejpam-4431	81	3	has	have	VERB
ejpam-4431	81	4	one	one	NUM
ejpam-4431	81	5	root	root	NOUN
ejpam-4431	81	6	;	;	PUNCT
ejpam-4431	81	7	s.	s.	PROPN
ejpam-4431	81	8	j.aliyev	j.aliyev	PROPN
ejpam-4431	81	9	,	,	PUNCT
ejpam-4431	81	10	b.	b.	PROPN
ejpam-4431	81	11	o.tahirov	o.tahirov	PROPN
ejpam-4431	81	12	,	,	PUNCT
ejpam-4431	81	13	t.	t.	PROPN
ejpam-4431	81	14	a.hashimova	a.hashimova	PROPN
ejpam-4431	81	15	/	/	SYM
ejpam-4431	81	16	eur	eur	PROPN
ejpam-4431	81	17	.	.	PUNCT
ejpam-4431	82	1	j.	j.	PROPN
ejpam-4431	82	2	pure	pure	PROPN
ejpam-4431	82	3	appl	appl	PROPN
ejpam-4431	82	4	.	.	PROPN
ejpam-4431	82	5	math	math	PROPN
ejpam-4431	82	6	,	,	PUNCT
ejpam-4431	82	7	15	15	NUM
ejpam-4431	82	8	(	(	PUNCT
ejpam-4431	82	9	3	3	NUM
ejpam-4431	82	10	)	)	PUNCT
ejpam-4431	82	11	(	(	PUNCT
ejpam-4431	82	12	2022	2022	NUM
ejpam-4431	82	13	)	)	PUNCT
ejpam-4431	82	14	,	,	PUNCT
ejpam-4431	82	15	1015	1015	NUM
ejpam-4431	82	16	-	-	SYM
ejpam-4431	82	17	1022	1022	NUM
ejpam-4431	82	18	1019	1019	NUM
ejpam-4431	82	19	2	2	NUM
ejpam-4431	82	20	)	)	PUNCT
ejpam-4431	82	21	for	for	ADP
ejpam-4431	82	22	p	p	NOUN
ejpam-4431	82	23	=	=	NOUN
ejpam-4431	82	24	0	0	NOUN
ejpam-4431	82	25	the	the	DET
ejpam-4431	82	26	equation	equation	NOUN
ejpam-4431	82	27	has	have	VERB
ejpam-4431	82	28	three	three	NUM
ejpam-4431	82	29	roots	root	NOUN
ejpam-4431	82	30	(	(	PUNCT
ejpam-4431	82	31	x1	x1	PROPN
ejpam-4431	82	32	=	=	SYM
ejpam-4431	82	33	x2	x2	PROPN
ejpam-4431	82	34	=	=	PUNCT
ejpam-4431	82	35	0	0	NUM
ejpam-4431	82	36	;	;	PUNCT
ejpam-4431	82	37	x3	x3	ADJ
ejpam-4431	82	38	=	=	SYM
ejpam-4431	82	39	3	3	NUM
ejpam-4431	82	40	)	)	PUNCT
ejpam-4431	82	41	,	,	PUNCT
ejpam-4431	82	42	among	among	ADP
ejpam-4431	82	43	which	which	PRON
ejpam-4431	82	44	there	there	PRON
ejpam-4431	82	45	are	be	VERB
ejpam-4431	82	46	two	two	NUM
ejpam-4431	82	47	coinciding	coincide	VERB
ejpam-4431	82	48	;	;	PUNCT
ejpam-4431	82	49	3	3	X
ejpam-4431	82	50	)	)	PUNCT
ejpam-4431	82	51	for	for	ADP
ejpam-4431	82	52	−4	−4	X
ejpam-4431	82	53	<	<	X
ejpam-4431	82	54	p	p	X
ejpam-4431	82	55	<	<	X
ejpam-4431	82	56	0	0	NUM
ejpam-4431	83	1	the	the	DET
ejpam-4431	83	2	equation	equation	NOUN
ejpam-4431	83	3	has	have	VERB
ejpam-4431	83	4	three	three	NUM
ejpam-4431	83	5	different	different	ADJ
ejpam-4431	83	6	roots	root	NOUN
ejpam-4431	83	7	;	;	PUNCT
ejpam-4431	83	8	4	4	X
ejpam-4431	83	9	)	)	PUNCT
ejpam-4431	83	10	for	for	ADP
ejpam-4431	83	11	p	p	NOUN
ejpam-4431	83	12	=	=	PUNCT
ejpam-4431	83	13	−4	−4	X
ejpam-4431	83	14	the	the	DET
ejpam-4431	83	15	equation	equation	NOUN
ejpam-4431	83	16	has	have	VERB
ejpam-4431	83	17	three	three	NUM
ejpam-4431	83	18	roots	root	NOUN
ejpam-4431	83	19	(	(	PUNCT
ejpam-4431	83	20	x1	x1	PROPN
ejpam-4431	83	21	=	=	SYM
ejpam-4431	83	22	x2	x2	PROPN
ejpam-4431	83	23	=	=	SYM
ejpam-4431	83	24	2	2	NUM
ejpam-4431	83	25	;	;	PUNCT
ejpam-4431	83	26	x3	x3	ADJ
ejpam-4431	83	27	=	=	SYM
ejpam-4431	83	28	−1	−1	NOUN
ejpam-4431	83	29	)	)	PUNCT
ejpam-4431	83	30	,	,	PUNCT
ejpam-4431	83	31	among	among	ADP
ejpam-4431	83	32	which	which	PRON
ejpam-4431	83	33	there	there	PRON
ejpam-4431	83	34	are	be	VERB
ejpam-4431	83	35	two	two	NUM
ejpam-4431	83	36	coinciding	coincide	VERB
ejpam-4431	83	37	;	;	PUNCT
ejpam-4431	83	38	5	5	X
ejpam-4431	83	39	)	)	PUNCT
ejpam-4431	83	40	for	for	ADP
ejpam-4431	83	41	p	p	NOUN
ejpam-4431	83	42	<	<	X
ejpam-4431	83	43	−4	−4	X
ejpam-4431	83	44	the	the	DET
ejpam-4431	83	45	equation	equation	NOUN
ejpam-4431	83	46	has	have	VERB
ejpam-4431	83	47	one	one	NUM
ejpam-4431	83	48	root	root	NOUN
ejpam-4431	83	49	.	.	PUNCT
ejpam-4431	84	1	figure	figure	VERB
ejpam-4431	84	2	6	6	NUM
ejpam-4431	84	3	:	:	PUNCT
ejpam-4431	84	4	y	y	PROPN
ejpam-4431	84	5	=	=	PUNCT
ejpam-4431	84	6	x3	x3	ADJ
ejpam-4431	84	7	−	−	NUM
ejpam-4431	85	1	3x2	3x2	NUM
ejpam-4431	85	2	function	function	NOUN
ejpam-4431	85	3	graph	graph	NOUN
ejpam-4431	85	4	problem	problem	NOUN
ejpam-4431	85	5	5	5	NUM
ejpam-4431	85	6	.	.	PUNCT
ejpam-4431	86	1	let	let	VERB
ejpam-4431	86	2	two	two	NUM
ejpam-4431	86	3	circles	circle	NOUN
ejpam-4431	86	4	lie	lie	VERB
ejpam-4431	86	5	in	in	ADP
ejpam-4431	86	6	an	an	DET
ejpam-4431	86	7	isosceles	isoscele	NOUN
ejpam-4431	86	8	trapezoid	trapezoid	NOUN
ejpam-4431	86	9	.	.	PUNCT
ejpam-4431	87	1	one	one	NUM
ejpam-4431	87	2	of	of	ADP
ejpam-4431	87	3	them	they	PRON
ejpam-4431	87	4	,	,	PUNCT
ejpam-4431	87	5	with	with	ADP
ejpam-4431	87	6	radius	radius	NOUN
ejpam-4431	87	7	1	1	NUM
ejpam-4431	87	8	,	,	PUNCT
ejpam-4431	87	9	is	be	AUX
ejpam-4431	87	10	inscribed	inscribe	VERB
ejpam-4431	87	11	in	in	ADP
ejpam-4431	87	12	this	this	DET
ejpam-4431	87	13	trapezoid	trapezoid	NOUN
ejpam-4431	87	14	,	,	PUNCT
ejpam-4431	87	15	while	while	SCONJ
ejpam-4431	87	16	the	the	DET
ejpam-4431	87	17	other	other	ADJ
ejpam-4431	87	18	touches	touch	VERB
ejpam-4431	87	19	two	two	NUM
ejpam-4431	87	20	sides	side	NOUN
ejpam-4431	87	21	of	of	ADP
ejpam-4431	87	22	trapezoid	trapezoid	NOUN
ejpam-4431	87	23	and	and	CCONJ
ejpam-4431	87	24	the	the	DET
ejpam-4431	87	25	first	first	ADJ
ejpam-4431	87	26	circle	circle	NOUN
ejpam-4431	87	27	.	.	PUNCT
ejpam-4431	88	1	the	the	DET
ejpam-4431	88	2	distance	distance	NOUN
ejpam-4431	88	3	between	between	ADP
ejpam-4431	88	4	the	the	DET
ejpam-4431	88	5	vertex	vertex	NOUN
ejpam-4431	88	6	of	of	ADP
ejpam-4431	88	7	the	the	DET
ejpam-4431	88	8	angle	angle	NOUN
ejpam-4431	88	9	created	create	VERB
ejpam-4431	88	10	by	by	ADP
ejpam-4431	88	11	two	two	NUM
ejpam-4431	88	12	sides	side	NOUN
ejpam-4431	88	13	of	of	ADP
ejpam-4431	88	14	trapezoid	trapezoid	NOUN
ejpam-4431	88	15	touching	touch	VERB
ejpam-4431	88	16	the	the	DET
ejpam-4431	88	17	second	second	ADJ
ejpam-4431	88	18	circle	circle	NOUN
ejpam-4431	88	19	and	and	CCONJ
ejpam-4431	88	20	the	the	DET
ejpam-4431	88	21	tangent	tangent	ADJ
ejpam-4431	88	22	point	point	NOUN
ejpam-4431	88	23	of	of	ADP
ejpam-4431	88	24	two	two	NUM
ejpam-4431	88	25	circles	circle	NOUN
ejpam-4431	88	26	is	be	AUX
ejpam-4431	88	27	twice	twice	ADV
ejpam-4431	88	28	as	as	ADV
ejpam-4431	88	29	much	much	ADJ
ejpam-4431	88	30	as	as	ADP
ejpam-4431	88	31	the	the	DET
ejpam-4431	88	32	diameter	diameter	NOUN
ejpam-4431	88	33	of	of	ADP
ejpam-4431	88	34	the	the	DET
ejpam-4431	88	35	second	second	ADJ
ejpam-4431	88	36	circle	circle	NOUN
ejpam-4431	88	37	.	.	PUNCT
ejpam-4431	89	1	find	find	VERB
ejpam-4431	89	2	the	the	DET
ejpam-4431	89	3	area	area	NOUN
ejpam-4431	89	4	of	of	ADP
ejpam-4431	89	5	the	the	DET
ejpam-4431	89	6	trapezoid	trapezoid	NOUN
ejpam-4431	89	7	.	.	PUNCT
ejpam-4431	90	1	it	it	PRON
ejpam-4431	90	2	is	be	AUX
ejpam-4431	90	3	not	not	PART
ejpam-4431	90	4	clear	clear	ADJ
ejpam-4431	90	5	from	from	ADP
ejpam-4431	90	6	the	the	DET
ejpam-4431	90	7	conditions	condition	NOUN
ejpam-4431	90	8	of	of	ADP
ejpam-4431	90	9	the	the	DET
ejpam-4431	90	10	problem	problem	NOUN
ejpam-4431	90	11	into	into	ADP
ejpam-4431	90	12	which	which	DET
ejpam-4431	90	13	angle	angle	NOUN
ejpam-4431	90	14	of	of	ADP
ejpam-4431	90	15	trapezoid	trapezoid	NOUN
ejpam-4431	90	16	the	the	DET
ejpam-4431	90	17	second	second	ADJ
ejpam-4431	90	18	circle	circle	NOUN
ejpam-4431	90	19	is	be	AUX
ejpam-4431	90	20	inscribed	inscribe	VERB
ejpam-4431	90	21	:	:	PUNCT
ejpam-4431	90	22	obtuse	obtuse	NOUN
ejpam-4431	90	23	or	or	CCONJ
ejpam-4431	90	24	acute	acute	ADJ
ejpam-4431	90	25	?	?	PUNCT
ejpam-4431	91	1	therefore	therefore	ADV
ejpam-4431	91	2	,	,	PUNCT
ejpam-4431	91	3	we	we	PRON
ejpam-4431	91	4	have	have	VERB
ejpam-4431	91	5	to	to	PART
ejpam-4431	91	6	consider	consider	VERB
ejpam-4431	91	7	both	both	DET
ejpam-4431	91	8	variants	variant	NOUN
ejpam-4431	91	9	,	,	PUNCT
ejpam-4431	91	10	and	and	CCONJ
ejpam-4431	91	11	,	,	PUNCT
ejpam-4431	91	12	analyzing	analyze	VERB
ejpam-4431	91	13	two	two	NUM
ejpam-4431	91	14	corresponding	corresponding	ADJ
ejpam-4431	91	15	figures	figure	NOUN
ejpam-4431	91	16	,	,	PUNCT
ejpam-4431	91	17	we	we	PRON
ejpam-4431	91	18	have	have	VERB
ejpam-4431	91	19	to	to	PART
ejpam-4431	91	20	try	try	VERB
ejpam-4431	91	21	to	to	PART
ejpam-4431	91	22	find	find	VERB
ejpam-4431	91	23	out	out	ADP
ejpam-4431	91	24	which	which	PRON
ejpam-4431	91	25	of	of	ADP
ejpam-4431	91	26	them	they	PRON
ejpam-4431	91	27	satisfies	satisfy	VERB
ejpam-4431	91	28	the	the	DET
ejpam-4431	91	29	conditions	condition	NOUN
ejpam-4431	91	30	of	of	ADP
ejpam-4431	91	31	the	the	DET
ejpam-4431	91	32	problem	problem	NOUN
ejpam-4431	91	33	.	.	PUNCT
ejpam-4431	92	1	let	let	VERB
ejpam-4431	92	2	o	o	NOUN
ejpam-4431	92	3	be	be	AUX
ejpam-4431	92	4	a	a	DET
ejpam-4431	92	5	center	center	NOUN
ejpam-4431	92	6	of	of	ADP
ejpam-4431	92	7	the	the	DET
ejpam-4431	92	8	circle	circle	NOUN
ejpam-4431	92	9	inscribed	inscribe	VERB
ejpam-4431	92	10	in	in	ADP
ejpam-4431	92	11	the	the	DET
ejpam-4431	92	12	trapezoid	trapezoid	ADJ
ejpam-4431	92	13	abcd	abcd	NOUN
ejpam-4431	92	14	,	,	PUNCT
ejpam-4431	92	15	and	and	CCONJ
ejpam-4431	92	16	o1	o1	NOUN
ejpam-4431	92	17	be	be	VERB
ejpam-4431	92	18	a	a	DET
ejpam-4431	92	19	center	center	NOUN
ejpam-4431	92	20	of	of	ADP
ejpam-4431	92	21	the	the	DET
ejpam-4431	92	22	second	second	ADJ
ejpam-4431	92	23	circle	circle	NOUN
ejpam-4431	92	24	which	which	PRON
ejpam-4431	92	25	touches	touch	VERB
ejpam-4431	92	26	the	the	DET
ejpam-4431	92	27	first	first	ADJ
ejpam-4431	92	28	circle	circle	NOUN
ejpam-4431	92	29	at	at	ADP
ejpam-4431	92	30	the	the	DET
ejpam-4431	92	31	point	point	NOUN
ejpam-4431	92	32	p	p	NOUN
ejpam-4431	92	33	and	and	CCONJ
ejpam-4431	92	34	two	two	NUM
ejpam-4431	92	35	sides	side	NOUN
ejpam-4431	92	36	of	of	ADP
ejpam-4431	92	37	the	the	DET
ejpam-4431	92	38	trapezoid	trapezoid	NOUN
ejpam-4431	92	39	.	.	PUNCT
ejpam-4431	93	1	denote	denote	VERB
ejpam-4431	93	2	by	by	ADP
ejpam-4431	93	3	r	r	NOUN
ejpam-4431	93	4	the	the	DET
ejpam-4431	93	5	radius	radius	NOUN
ejpam-4431	93	6	of	of	ADP
ejpam-4431	93	7	the	the	DET
ejpam-4431	93	8	second	second	ADJ
ejpam-4431	93	9	circle	circle	NOUN
ejpam-4431	93	10	.	.	PUNCT
ejpam-4431	94	1	let	let	VERB
ejpam-4431	94	2	’s	’s	NOUN
ejpam-4431	94	3	join	join	VERB
ejpam-4431	94	4	the	the	DET
ejpam-4431	94	5	centers	center	NOUN
ejpam-4431	94	6	of	of	ADP
ejpam-4431	94	7	two	two	NUM
ejpam-4431	94	8	circles	circle	NOUN
ejpam-4431	94	9	and	and	CCONJ
ejpam-4431	94	10	the	the	DET
ejpam-4431	94	11	tangent	tangent	NOUN
ejpam-4431	94	12	points	point	VERB
ejpam-4431	94	13	m	m	VERB
ejpam-4431	94	14	and	and	CCONJ
ejpam-4431	94	15	n	n	PROPN
ejpam-4431	94	16	of	of	ADP
ejpam-4431	94	17	the	the	DET
ejpam-4431	94	18	corresponding	corresponding	ADJ
ejpam-4431	94	19	base	base	NOUN
ejpam-4431	94	20	bc	bc	PROPN
ejpam-4431	94	21	(	(	PUNCT
ejpam-4431	94	22	or	or	CCONJ
ejpam-4431	94	23	ad	ad	NOUN
ejpam-4431	94	24	)	)	PUNCT
ejpam-4431	94	25	of	of	ADP
ejpam-4431	94	26	trapezoid	trapezoid	NOUN
ejpam-4431	94	27	.	.	PUNCT
ejpam-4431	95	1	then	then	ADV
ejpam-4431	95	2	we	we	PRON
ejpam-4431	95	3	obtain	obtain	VERB
ejpam-4431	95	4	two	two	NUM
ejpam-4431	95	5	similar	similar	ADJ
ejpam-4431	95	6	right	right	ADJ
ejpam-4431	95	7	triangles	triangle	NOUN
ejpam-4431	95	8	omc	omc	PROPN
ejpam-4431	95	9	and	and	CCONJ
ejpam-4431	95	10	o1nc	o1nc	NUM
ejpam-4431	95	11	(	(	PUNCT
ejpam-4431	95	12	or	or	CCONJ
ejpam-4431	95	13	omd	omd	NOUN
ejpam-4431	95	14	and	and	CCONJ
ejpam-4431	95	15	o1nd	o1nd	NUM
ejpam-4431	95	16	)	)	PUNCT
ejpam-4431	95	17	.	.	PUNCT
ejpam-4431	96	1	as	as	ADP
ejpam-4431	96	2	oc	oc	ADP
ejpam-4431	96	3	=	=	NOUN
ejpam-4431	96	4	op	op	NOUN
ejpam-4431	96	5	+	+	NOUN
ejpam-4431	96	6	pc	pc	NOUN
ejpam-4431	96	7	=	=	SYM
ejpam-4431	96	8	1	1	NUM
ejpam-4431	96	9	+	+	CCONJ
ejpam-4431	96	10	4r	4r	NOUN
ejpam-4431	96	11	,	,	PUNCT
ejpam-4431	96	12	od	od	NOUN
ejpam-4431	96	13	=	=	SYM
ejpam-4431	96	14	op	op	NOUN
ejpam-4431	96	15	+	+	CCONJ
ejpam-4431	96	16	pd	pd	X
ejpam-4431	96	17	=	=	SYM
ejpam-4431	96	18	1	1	NUM
ejpam-4431	96	19	+	+	CCONJ
ejpam-4431	96	20	4r	4r	NOUN
ejpam-4431	96	21	,	,	PUNCT
ejpam-4431	96	22	s.	s.	PROPN
ejpam-4431	96	23	j.aliyev	j.aliyev	PROPN
ejpam-4431	96	24	,	,	PUNCT
ejpam-4431	96	25	b.	b.	PROPN
ejpam-4431	96	26	o.tahirov	o.tahirov	PROPN
ejpam-4431	96	27	,	,	PUNCT
ejpam-4431	96	28	t.	t.	PROPN
ejpam-4431	96	29	a.hashimova	a.hashimova	PROPN
ejpam-4431	96	30	/	/	SYM
ejpam-4431	96	31	eur	eur	PROPN
ejpam-4431	96	32	.	.	PUNCT
ejpam-4431	97	1	j.	j.	PROPN
ejpam-4431	97	2	pure	pure	PROPN
ejpam-4431	97	3	appl	appl	PROPN
ejpam-4431	97	4	.	.	PROPN
ejpam-4431	97	5	math	math	PROPN
ejpam-4431	97	6	,	,	PUNCT
ejpam-4431	97	7	15	15	NUM
ejpam-4431	97	8	(	(	PUNCT
ejpam-4431	97	9	3	3	NUM
ejpam-4431	97	10	)	)	PUNCT
ejpam-4431	97	11	(	(	PUNCT
ejpam-4431	97	12	2022	2022	NUM
ejpam-4431	97	13	)	)	PUNCT
ejpam-4431	97	14	,	,	PUNCT
ejpam-4431	97	15	1015	1015	NUM
ejpam-4431	97	16	-	-	SYM
ejpam-4431	97	17	1022	1022	NUM
ejpam-4431	97	18	1020	1020	NUM
ejpam-4431	97	19	figure	figure	NOUN
ejpam-4431	97	20	7	7	NUM
ejpam-4431	97	21	:	:	PUNCT
ejpam-4431	97	22	second	second	ADJ
ejpam-4431	97	23	circle	circle	NOUN
ejpam-4431	97	24	inscribed	inscribe	VERB
ejpam-4431	97	25	in	in	ADP
ejpam-4431	97	26	the	the	DET
ejpam-4431	97	27	obtuse	obtuse	ADJ
ejpam-4431	97	28	angle	angle	NOUN
ejpam-4431	97	29	of	of	ADP
ejpam-4431	97	30	the	the	DET
ejpam-4431	97	31	trapezoid	trapezoid	ADJ
ejpam-4431	97	32	abcd	abcd	PROPN
ejpam-4431	97	33	figure	figure	NOUN
ejpam-4431	97	34	8	8	NUM
ejpam-4431	97	35	:	:	PUNCT
ejpam-4431	97	36	second	second	ADJ
ejpam-4431	97	37	circle	circle	NOUN
ejpam-4431	97	38	inscribed	inscribe	VERB
ejpam-4431	97	39	in	in	ADP
ejpam-4431	97	40	the	the	DET
ejpam-4431	97	41	acute	acute	ADJ
ejpam-4431	97	42	angle	angle	NOUN
ejpam-4431	97	43	of	of	ADP
ejpam-4431	97	44	the	the	DET
ejpam-4431	97	45	trapezoid	trapezoid	ADJ
ejpam-4431	97	46	abcd	abcd	NOUN
ejpam-4431	97	47	from	from	ADP
ejpam-4431	97	48	the	the	DET
ejpam-4431	97	49	relations	relation	NOUN
ejpam-4431	97	50	om	om	PROPN
ejpam-4431	97	51	o1n	o1n	NOUN
ejpam-4431	97	52	=	=	PUNCT
ejpam-4431	97	53	oc	oc	ADP
ejpam-4431	97	54	o1c	o1c	PROPN
ejpam-4431	97	55	,	,	PUNCT
ejpam-4431	97	56	om	om	PROPN
ejpam-4431	97	57	o1n	o1n	NOUN
ejpam-4431	97	58	=	=	PUNCT
ejpam-4431	97	59	od	od	NUM
ejpam-4431	97	60	o1d	o1d	ADJ
ejpam-4431	97	61	.	.	PUNCT
ejpam-4431	98	1	we	we	PRON
ejpam-4431	98	2	easily	easily	ADV
ejpam-4431	98	3	obtain	obtain	VERB
ejpam-4431	98	4	r	r	NOUN
ejpam-4431	98	5	=	=	SYM
ejpam-4431	98	6	1	1	NUM
ejpam-4431	98	7	2	2	NUM
ejpam-4431	98	8	.	.	PUNCT
ejpam-4431	99	1	but	but	CCONJ
ejpam-4431	99	2	then	then	ADV
ejpam-4431	99	3	,	,	PUNCT
ejpam-4431	99	4	by	by	ADP
ejpam-4431	99	5	pythagoras	pythagoras	PROPN
ejpam-4431	99	6	theorem	theorem	PROPN
ejpam-4431	99	7	,	,	PUNCT
ejpam-4431	99	8	from	from	ADP
ejpam-4431	99	9	the	the	DET
ejpam-4431	99	10	triangles	triangle	NOUN
ejpam-4431	99	11	omc	omc	PROPN
ejpam-4431	99	12	and	and	CCONJ
ejpam-4431	99	13	omd	omd	PROPN
ejpam-4431	99	14	it	it	PRON
ejpam-4431	99	15	follows	follow	VERB
ejpam-4431	99	16	that	that	SCONJ
ejpam-4431	99	17	mc	mc	PROPN
ejpam-4431	100	1	=	=	PUNCT
ejpam-4431	100	2	√	√	PROPN
ejpam-4431	101	1	oc2	oc2	INTJ
ejpam-4431	101	2	−om2	−om2	NOUN
ejpam-4431	102	1	=	=	NOUN
ejpam-4431	102	2	2	2	NUM
ejpam-4431	102	3	√	√	NUM
ejpam-4431	102	4	2	2	NUM
ejpam-4431	102	5	,	,	PUNCT
ejpam-4431	102	6	md	md	PROPN
ejpam-4431	102	7	=	=	NOUN
ejpam-4431	102	8	√	√	ADP
ejpam-4431	102	9	od2	od2	NOUN
ejpam-4431	102	10	−om2	−om2	NOUN
ejpam-4431	102	11	=	=	NOUN
ejpam-4431	102	12	2	2	NUM
ejpam-4431	102	13	√	√	NUM
ejpam-4431	102	14	2	2	NUM
ejpam-4431	102	15	.	.	PUNCT
ejpam-4431	103	1	so	so	ADV
ejpam-4431	103	2	,	,	PUNCT
ejpam-4431	103	3	in	in	ADP
ejpam-4431	103	4	the	the	DET
ejpam-4431	103	5	case	case	NOUN
ejpam-4431	103	6	described	describe	VERB
ejpam-4431	103	7	by	by	ADP
ejpam-4431	103	8	fig.7	fig.7	ADJ
ejpam-4431	103	9	,	,	PUNCT
ejpam-4431	103	10	where	where	SCONJ
ejpam-4431	103	11	the	the	DET
ejpam-4431	103	12	second	second	ADJ
ejpam-4431	103	13	circle	circle	NOUN
ejpam-4431	103	14	touches	touch	VERB
ejpam-4431	103	15	the	the	DET
ejpam-4431	103	16	smaller	small	ADJ
ejpam-4431	103	17	base	base	NOUN
ejpam-4431	103	18	of	of	ADP
ejpam-4431	103	19	trapezoid	trapezoid	NOUN
ejpam-4431	103	20	,	,	PUNCT
ejpam-4431	103	21	the	the	DET
ejpam-4431	103	22	smaller	small	ADJ
ejpam-4431	103	23	base	base	NOUN
ejpam-4431	103	24	must	must	AUX
ejpam-4431	103	25	be	be	AUX
ejpam-4431	103	26	equal	equal	ADJ
ejpam-4431	103	27	to	to	ADP
ejpam-4431	103	28	4	4	NUM
ejpam-4431	103	29	√	√	NUM
ejpam-4431	103	30	2	2	NUM
ejpam-4431	103	31	,	,	PUNCT
ejpam-4431	103	32	and	and	CCONJ
ejpam-4431	103	33	in	in	ADP
ejpam-4431	103	34	the	the	DET
ejpam-4431	103	35	case	case	NOUN
ejpam-4431	103	36	described	describe	VERB
ejpam-4431	103	37	by	by	ADP
ejpam-4431	103	38	fig.8	fig.8	PROPN
ejpam-4431	103	39	,	,	PUNCT
ejpam-4431	103	40	where	where	SCONJ
ejpam-4431	103	41	the	the	DET
ejpam-4431	103	42	second	second	ADJ
ejpam-4431	103	43	circle	circle	NOUN
ejpam-4431	103	44	touches	touch	VERB
ejpam-4431	103	45	the	the	DET
ejpam-4431	103	46	larger	large	ADJ
ejpam-4431	103	47	base	base	NOUN
ejpam-4431	103	48	of	of	ADP
ejpam-4431	103	49	trapezoid	trapezoid	NOUN
ejpam-4431	103	50	,	,	PUNCT
ejpam-4431	103	51	the	the	DET
ejpam-4431	103	52	larger	large	ADJ
ejpam-4431	103	53	base	base	NOUN
ejpam-4431	103	54	must	must	AUX
ejpam-4431	103	55	be	be	AUX
ejpam-4431	103	56	equal	equal	ADJ
ejpam-4431	103	57	to	to	ADP
ejpam-4431	103	58	4	4	NUM
ejpam-4431	103	59	√	√	NUM
ejpam-4431	103	60	2	2	NUM
ejpam-4431	103	61	.	.	PUNCT
ejpam-4431	104	1	but	but	CCONJ
ejpam-4431	104	2	it	it	PRON
ejpam-4431	104	3	is	be	AUX
ejpam-4431	104	4	clear	clear	ADJ
ejpam-4431	104	5	that	that	SCONJ
ejpam-4431	104	6	if	if	SCONJ
ejpam-4431	104	7	a	a	DET
ejpam-4431	104	8	circle	circle	NOUN
ejpam-4431	104	9	is	be	AUX
ejpam-4431	104	10	inscribed	inscribe	VERB
ejpam-4431	104	11	in	in	ADP
ejpam-4431	104	12	an	an	DET
ejpam-4431	104	13	isosceles	isoscele	NOUN
ejpam-4431	104	14	trapezoid	trapezoid	NOUN
ejpam-4431	104	15	,	,	PUNCT
ejpam-4431	104	16	then	then	ADV
ejpam-4431	104	17	the	the	DET
ejpam-4431	104	18	smaller	small	ADJ
ejpam-4431	104	19	base	base	NOUN
ejpam-4431	104	20	of	of	ADP
ejpam-4431	104	21	trapezoid	trapezoid	NOUN
ejpam-4431	104	22	is	be	AUX
ejpam-4431	104	23	less	less	ADJ
ejpam-4431	104	24	than	than	ADP
ejpam-4431	104	25	the	the	DET
ejpam-4431	104	26	diameter	diameter	NOUN
ejpam-4431	104	27	of	of	ADP
ejpam-4431	104	28	the	the	DET
ejpam-4431	104	29	circle	circle	NOUN
ejpam-4431	104	30	,	,	PUNCT
ejpam-4431	104	31	and	and	CCONJ
ejpam-4431	104	32	the	the	DET
ejpam-4431	104	33	larger	large	ADJ
ejpam-4431	104	34	base	base	NOUN
ejpam-4431	104	35	is	be	AUX
ejpam-4431	104	36	greater	great	ADJ
ejpam-4431	104	37	than	than	ADP
ejpam-4431	104	38	the	the	DET
ejpam-4431	104	39	diameter	diameter	NOUN
ejpam-4431	104	40	of	of	ADP
ejpam-4431	104	41	the	the	DET
ejpam-4431	104	42	circle	circle	NOUN
ejpam-4431	104	43	.	.	PUNCT
ejpam-4431	105	1	consequently	consequently	ADV
ejpam-4431	105	2	,	,	PUNCT
ejpam-4431	105	3	only	only	ADV
ejpam-4431	105	4	the	the	DET
ejpam-4431	105	5	larger	large	ADJ
ejpam-4431	105	6	base	base	NOUN
ejpam-4431	105	7	of	of	ADP
ejpam-4431	105	8	trapezoid	trapezoid	NOUN
ejpam-4431	105	9	can	can	AUX
ejpam-4431	105	10	be	be	AUX
ejpam-4431	105	11	equal	equal	ADJ
ejpam-4431	105	12	to	to	ADP
ejpam-4431	105	13	4	4	NUM
ejpam-4431	105	14	√	√	NUM
ejpam-4431	105	15	2	2	NUM
ejpam-4431	105	16	.	.	PUNCT
ejpam-4431	106	1	in	in	ADP
ejpam-4431	106	2	other	other	ADJ
ejpam-4431	106	3	words	word	NOUN
ejpam-4431	106	4	,	,	PUNCT
ejpam-4431	106	5	the	the	DET
ejpam-4431	106	6	variant	variant	NOUN
ejpam-4431	106	7	described	describe	VERB
ejpam-4431	106	8	by	by	ADP
ejpam-4431	106	9	fig	fig	NOUN
ejpam-4431	106	10	.	.	PUNCT
ejpam-4431	106	11	7	7	NUM
ejpam-4431	106	12	contradicts	contradict	VERB
ejpam-4431	106	13	the	the	DET
ejpam-4431	106	14	conditions	condition	NOUN
ejpam-4431	106	15	of	of	ADP
ejpam-4431	106	16	the	the	DET
ejpam-4431	106	17	problem	problem	NOUN
ejpam-4431	106	18	and	and	CCONJ
ejpam-4431	106	19	we	we	PRON
ejpam-4431	106	20	should	should	AUX
ejpam-4431	106	21	consider	consider	VERB
ejpam-4431	106	22	the	the	DET
ejpam-4431	106	23	case	case	NOUN
ejpam-4431	106	24	described	describe	VERB
ejpam-4431	106	25	by	by	ADP
ejpam-4431	106	26	fig.8	fig.8	PROPN
ejpam-4431	106	27	only	only	ADV
ejpam-4431	106	28	.	.	PUNCT
ejpam-4431	107	1	now	now	ADV
ejpam-4431	107	2	it	it	PRON
ejpam-4431	107	3	is	be	AUX
ejpam-4431	107	4	not	not	PART
ejpam-4431	107	5	difficult	difficult	ADJ
ejpam-4431	107	6	to	to	PART
ejpam-4431	107	7	find	find	VERB
ejpam-4431	107	8	the	the	DET
ejpam-4431	107	9	area	area	NOUN
ejpam-4431	107	10	of	of	ADP
ejpam-4431	107	11	the	the	DET
ejpam-4431	107	12	trapezoid	trapezoid	NOUN
ejpam-4431	107	13	.	.	PUNCT
ejpam-4431	108	1	let	let	VERB
ejpam-4431	108	2	’s	’s	NOUN
ejpam-4431	108	3	join	join	VERB
ejpam-4431	108	4	the	the	DET
ejpam-4431	108	5	center	center	NOUN
ejpam-4431	108	6	o	o	NOUN
ejpam-4431	108	7	of	of	ADP
ejpam-4431	108	8	the	the	DET
ejpam-4431	108	9	s.	s.	PROPN
ejpam-4431	108	10	j.aliyev	j.aliyev	PROPN
ejpam-4431	108	11	,	,	PUNCT
ejpam-4431	108	12	b.	b.	PROPN
ejpam-4431	108	13	o.tahirov	o.tahirov	PROPN
ejpam-4431	108	14	,	,	PUNCT
ejpam-4431	108	15	t.	t.	PROPN
ejpam-4431	108	16	a.hashimova	a.hashimova	PROPN
ejpam-4431	108	17	/	/	SYM
ejpam-4431	108	18	eur	eur	PROPN
ejpam-4431	108	19	.	.	PUNCT
ejpam-4431	109	1	j.	j.	PROPN
ejpam-4431	109	2	pure	pure	PROPN
ejpam-4431	109	3	appl	appl	PROPN
ejpam-4431	109	4	.	.	PROPN
ejpam-4431	109	5	math	math	PROPN
ejpam-4431	109	6	,	,	PUNCT
ejpam-4431	109	7	15	15	NUM
ejpam-4431	109	8	(	(	PUNCT
ejpam-4431	109	9	3	3	NUM
ejpam-4431	109	10	)	)	PUNCT
ejpam-4431	109	11	(	(	PUNCT
ejpam-4431	109	12	2022	2022	NUM
ejpam-4431	109	13	)	)	PUNCT
ejpam-4431	109	14	,	,	PUNCT
ejpam-4431	109	15	1015	1015	NUM
ejpam-4431	109	16	-	-	SYM
ejpam-4431	109	17	1022	1022	NUM
ejpam-4431	109	18	1021	1021	NUM
ejpam-4431	109	19	inscribed	inscribe	VERB
ejpam-4431	109	20	circle	circle	NOUN
ejpam-4431	109	21	and	and	CCONJ
ejpam-4431	109	22	the	the	DET
ejpam-4431	109	23	vertex	vertex	NOUN
ejpam-4431	109	24	c.	c.	PROPN
ejpam-4431	110	1	the	the	DET
ejpam-4431	110	2	triangle	triangle	NOUN
ejpam-4431	110	3	cod	cod	NOUN
ejpam-4431	110	4	is	be	AUX
ejpam-4431	110	5	right	right	ADJ
ejpam-4431	110	6	.	.	PUNCT
ejpam-4431	111	1	in	in	ADP
ejpam-4431	111	2	fact	fact	NOUN
ejpam-4431	111	3	,	,	PUNCT
ejpam-4431	111	4	∠ocd	∠ocd	PROPN
ejpam-4431	111	5	+	+	PROPN
ejpam-4431	111	6	∠odc	∠odc	PROPN
ejpam-4431	111	7	=	=	SYM
ejpam-4431	111	8	1	1	NUM
ejpam-4431	111	9	2	2	NUM
ejpam-4431	111	10	∠bcd	∠bcd	PROPN
ejpam-4431	111	11	+	+	NUM
ejpam-4431	111	12	1	1	NUM
ejpam-4431	111	13	2	2	NUM
ejpam-4431	111	14	∠adc	∠adc	NOUN
ejpam-4431	111	15	=	=	SYM
ejpam-4431	111	16	1	1	NUM
ejpam-4431	111	17	2	2	NUM
ejpam-4431	111	18	·	·	SYM
ejpam-4431	111	19	180	180	NUM
ejpam-4431	111	20	◦	◦	NOUN
ejpam-4431	111	21	=	=	SYM
ejpam-4431	111	22	90	90	NUM
ejpam-4431	111	23	◦	◦	NOUN
ejpam-4431	111	24	,	,	PUNCT
ejpam-4431	111	25	i.e.	i.e.	X
ejpam-4431	111	26	∠cod	∠cod	ADJ
ejpam-4431	111	27	=	=	SYM
ejpam-4431	111	28	90	90	NUM
ejpam-4431	111	29	◦	◦	NOUN
ejpam-4431	111	30	.	.	PUNCT
ejpam-4431	112	1	as	as	SCONJ
ejpam-4431	112	2	the	the	DET
ejpam-4431	112	3	radius	radius	NOUN
ejpam-4431	112	4	drawn	draw	VERB
ejpam-4431	112	5	to	to	ADP
ejpam-4431	112	6	the	the	DET
ejpam-4431	112	7	tangent	tangent	NOUN
ejpam-4431	112	8	point	point	NOUN
ejpam-4431	112	9	h	h	NOUN
ejpam-4431	112	10	of	of	ADP
ejpam-4431	112	11	the	the	DET
ejpam-4431	112	12	inscribed	inscribe	VERB
ejpam-4431	112	13	circle	circle	NOUN
ejpam-4431	112	14	and	and	CCONJ
ejpam-4431	112	15	the	the	DET
ejpam-4431	112	16	leg	leg	NOUN
ejpam-4431	112	17	cd	cd	PROPN
ejpam-4431	112	18	is	be	AUX
ejpam-4431	112	19	a	a	DET
ejpam-4431	112	20	height	height	NOUN
ejpam-4431	112	21	of	of	ADP
ejpam-4431	112	22	the	the	DET
ejpam-4431	112	23	triangle	triangle	NOUN
ejpam-4431	112	24	cod	cod	NOUN
ejpam-4431	112	25	,	,	PUNCT
ejpam-4431	112	26	and	and	CCONJ
ejpam-4431	112	27	as	as	ADP
ejpam-4431	112	28	,	,	PUNCT
ejpam-4431	112	29	due	due	ADP
ejpam-4431	112	30	to	to	ADP
ejpam-4431	112	31	tangent	tangent	VERB
ejpam-4431	112	32	property	property	NOUN
ejpam-4431	112	33	,	,	PUNCT
ejpam-4431	112	34	the	the	DET
ejpam-4431	112	35	relations	relation	NOUN
ejpam-4431	112	36	ch	ch	NOUN
ejpam-4431	112	37	=	=	NOUN
ejpam-4431	112	38	1	1	NUM
ejpam-4431	112	39	2	2	NUM
ejpam-4431	112	40	bc	bc	NOUN
ejpam-4431	112	41	and	and	CCONJ
ejpam-4431	112	42	dh	dh	NOUN
ejpam-4431	112	43	=	=	NOUN
ejpam-4431	112	44	1	1	NUM
ejpam-4431	112	45	2	2	NUM
ejpam-4431	112	46	ad	ad	NOUN
ejpam-4431	112	47	hold	hold	NOUN
ejpam-4431	112	48	,	,	PUNCT
ejpam-4431	112	49	we	we	PRON
ejpam-4431	112	50	have	have	VERB
ejpam-4431	112	51	oh2	oh2	NOUN
ejpam-4431	112	52	=	=	NOUN
ejpam-4431	112	53	ch	ch	PROPN
ejpam-4431	112	54	·	·	PUNCT
ejpam-4431	112	55	dh	dh	NOUN
ejpam-4431	112	56	=	=	NOUN
ejpam-4431	112	57	1	1	NUM
ejpam-4431	112	58	4	4	NUM
ejpam-4431	112	59	bc	bc	PROPN
ejpam-4431	112	60	·	·	SYM
ejpam-4431	112	61	ad	ad	NOUN
ejpam-4431	112	62	.	.	PUNCT
ejpam-4431	113	1	but	but	CCONJ
ejpam-4431	113	2	,	,	PUNCT
ejpam-4431	113	3	oh	oh	INTJ
ejpam-4431	113	4	=	=	SYM
ejpam-4431	113	5	1	1	NUM
ejpam-4431	113	6	,	,	PUNCT
ejpam-4431	113	7	ad	ad	NOUN
ejpam-4431	113	8	=	=	SYM
ejpam-4431	113	9	4	4	NUM
ejpam-4431	113	10	√	√	NOUN
ejpam-4431	113	11	2	2	NUM
ejpam-4431	113	12	consequently	consequently	ADV
ejpam-4431	113	13	,	,	PUNCT
ejpam-4431	113	14	bc	bc	PROPN
ejpam-4431	113	15	=	=	PUNCT
ejpam-4431	114	1	√	√	PROPN
ejpam-4431	114	2	2	2	NUM
ejpam-4431	114	3	2	2	NUM
ejpam-4431	114	4	.	.	PUNCT
ejpam-4431	115	1	taking	take	VERB
ejpam-4431	115	2	into	into	ADP
ejpam-4431	115	3	account	account	NOUN
ejpam-4431	115	4	that	that	SCONJ
ejpam-4431	115	5	the	the	DET
ejpam-4431	115	6	height	height	NOUN
ejpam-4431	115	7	of	of	ADP
ejpam-4431	115	8	trapezoid	trapezoid	NOUN
ejpam-4431	115	9	is	be	AUX
ejpam-4431	115	10	equal	equal	ADJ
ejpam-4431	115	11	to	to	ADP
ejpam-4431	115	12	the	the	DET
ejpam-4431	115	13	diameter	diameter	NOUN
ejpam-4431	115	14	of	of	ADP
ejpam-4431	115	15	the	the	DET
ejpam-4431	115	16	inscribed	inscribe	VERB
ejpam-4431	115	17	circle	circle	NOUN
ejpam-4431	115	18	,	,	PUNCT
ejpam-4431	115	19	we	we	PRON
ejpam-4431	115	20	find	find	VERB
ejpam-4431	115	21	that	that	SCONJ
ejpam-4431	115	22	the	the	DET
ejpam-4431	115	23	area	area	NOUN
ejpam-4431	115	24	of	of	ADP
ejpam-4431	115	25	trapezoid	trapezoid	NOUN
ejpam-4431	115	26	is	be	AUX
ejpam-4431	115	27	equal	equal	ADJ
ejpam-4431	115	28	to	to	ADP
ejpam-4431	115	29	9	9	NUM
ejpam-4431	115	30	√	√	NUM
ejpam-4431	115	31	2	2	NUM
ejpam-4431	115	32	2	2	NUM
ejpam-4431	115	33	.	.	PUNCT
ejpam-4431	116	1	sometimes	sometimes	ADV
ejpam-4431	116	2	the	the	DET
ejpam-4431	116	3	conditions	condition	NOUN
ejpam-4431	116	4	of	of	ADP
ejpam-4431	116	5	the	the	DET
ejpam-4431	116	6	problem	problem	NOUN
ejpam-4431	116	7	are	be	AUX
ejpam-4431	116	8	deliberately	deliberately	ADV
ejpam-4431	116	9	stated	state	VERB
ejpam-4431	116	10	somewhat	somewhat	ADV
ejpam-4431	116	11	vaguely	vaguely	ADV
ejpam-4431	116	12	,	,	PUNCT
ejpam-4431	116	13	so	so	SCONJ
ejpam-4431	116	14	that	that	SCONJ
ejpam-4431	116	15	they	they	PRON
ejpam-4431	116	16	geometrically	geometrically	ADV
ejpam-4431	116	17	admit	admit	VERB
ejpam-4431	116	18	very	very	ADV
ejpam-4431	116	19	different	different	ADJ
ejpam-4431	116	20	figures	figure	NOUN
ejpam-4431	116	21	and	and	CCONJ
ejpam-4431	116	22	it	it	PRON
ejpam-4431	116	23	is	be	AUX
ejpam-4431	116	24	not	not	PART
ejpam-4431	116	25	clear	clear	ADJ
ejpam-4431	116	26	which	which	PRON
ejpam-4431	116	27	of	of	ADP
ejpam-4431	116	28	these	these	DET
ejpam-4431	116	29	figures	figure	NOUN
ejpam-4431	116	30	suits	suit	VERB
ejpam-4431	116	31	the	the	DET
ejpam-4431	116	32	problem	problem	NOUN
ejpam-4431	116	33	.	.	PUNCT
ejpam-4431	117	1	in	in	ADP
ejpam-4431	117	2	this	this	DET
ejpam-4431	117	3	case	case	NOUN
ejpam-4431	117	4	,	,	PUNCT
ejpam-4431	117	5	you	you	PRON
ejpam-4431	117	6	first	first	ADV
ejpam-4431	117	7	have	have	VERB
ejpam-4431	117	8	to	to	PART
ejpam-4431	117	9	consider	consider	VERB
ejpam-4431	117	10	all	all	DET
ejpam-4431	117	11	possibilities	possibility	NOUN
ejpam-4431	117	12	which	which	PRON
ejpam-4431	117	13	formally	formally	ADV
ejpam-4431	117	14	correspond	correspond	VERB
ejpam-4431	117	15	to	to	ADP
ejpam-4431	117	16	the	the	DET
ejpam-4431	117	17	conditions	condition	NOUN
ejpam-4431	117	18	of	of	ADP
ejpam-4431	117	19	the	the	DET
ejpam-4431	117	20	problem	problem	NOUN
ejpam-4431	117	21	,	,	PUNCT
ejpam-4431	117	22	and	and	CCONJ
ejpam-4431	117	23	then	then	ADV
ejpam-4431	117	24	to	to	ADP
ejpam-4431	117	25	”	"	PUNCT
ejpam-4431	117	26	decipher	decipher	PROPN
ejpam-4431	117	27	”	"	PUNCT
ejpam-4431	117	28	the	the	DET
ejpam-4431	117	29	only	only	ADJ
ejpam-4431	117	30	true	true	ADJ
ejpam-4431	117	31	geometric	geometric	ADJ
ejpam-4431	117	32	configuration	configuration	NOUN
ejpam-4431	117	33	.	.	PUNCT
ejpam-4431	118	1	let	let	VERB
ejpam-4431	118	2	’s	’s	NOUN
ejpam-4431	118	3	mention	mention	VERB
ejpam-4431	118	4	the	the	DET
ejpam-4431	118	5	conditions	condition	NOUN
ejpam-4431	118	6	which	which	PRON
ejpam-4431	118	7	lead	lead	VERB
ejpam-4431	118	8	to	to	ADP
ejpam-4431	118	9	the	the	DET
ejpam-4431	118	10	ambiguous	ambiguous	ADJ
ejpam-4431	118	11	interpretation	interpretation	NOUN
ejpam-4431	118	12	of	of	ADP
ejpam-4431	118	13	geometric	geometric	ADJ
ejpam-4431	118	14	problem	problem	NOUN
ejpam-4431	118	15	.	.	PUNCT
ejpam-4431	119	1	1	1	X
ejpam-4431	119	2	.	.	X
ejpam-4431	120	1	the	the	DET
ejpam-4431	120	2	conditions	condition	NOUN
ejpam-4431	120	3	of	of	ADP
ejpam-4431	120	4	the	the	DET
ejpam-4431	120	5	problem	problem	NOUN
ejpam-4431	120	6	do	do	AUX
ejpam-4431	120	7	not	not	PART
ejpam-4431	120	8	define	define	VERB
ejpam-4431	120	9	the	the	DET
ejpam-4431	120	10	location	location	NOUN
ejpam-4431	120	11	of	of	ADP
ejpam-4431	120	12	points	point	NOUN
ejpam-4431	120	13	and	and	CCONJ
ejpam-4431	120	14	figures	figure	NOUN
ejpam-4431	120	15	with	with	ADP
ejpam-4431	120	16	respect	respect	NOUN
ejpam-4431	120	17	to	to	ADP
ejpam-4431	120	18	each	each	DET
ejpam-4431	120	19	other	other	ADJ
ejpam-4431	120	20	:	:	PUNCT
ejpam-4431	120	21	a	a	X
ejpam-4431	120	22	)	)	PUNCT
ejpam-4431	120	23	the	the	DET
ejpam-4431	120	24	point	point	NOUN
ejpam-4431	120	25	either	either	CCONJ
ejpam-4431	120	26	belongs	belong	VERB
ejpam-4431	120	27	to	to	ADP
ejpam-4431	120	28	the	the	DET
ejpam-4431	120	29	interval	interval	NOUN
ejpam-4431	120	30	ab	ab	PROPN
ejpam-4431	120	31	or	or	CCONJ
ejpam-4431	120	32	does	do	VERB
ejpam-4431	120	33	not	not	PART
ejpam-4431	120	34	,	,	PUNCT
ejpam-4431	120	35	but	but	CCONJ
ejpam-4431	120	36	lies	lie	VERB
ejpam-4431	120	37	on	on	ADP
ejpam-4431	120	38	the	the	DET
ejpam-4431	120	39	straight	straight	ADJ
ejpam-4431	120	40	line	line	NOUN
ejpam-4431	120	41	ab	ab	PROPN
ejpam-4431	120	42	;	;	PUNCT
ejpam-4431	120	43	b	b	X
ejpam-4431	120	44	)	)	PUNCT
ejpam-4431	120	45	the	the	DET
ejpam-4431	120	46	points	point	NOUN
ejpam-4431	120	47	lie	lie	VERB
ejpam-4431	120	48	either	either	CCONJ
ejpam-4431	120	49	on	on	ADP
ejpam-4431	120	50	the	the	DET
ejpam-4431	120	51	same	same	ADJ
ejpam-4431	120	52	half	half	ADJ
ejpam-4431	120	53	-	-	PUNCT
ejpam-4431	120	54	plane	plane	NOUN
ejpam-4431	120	55	(	(	PUNCT
ejpam-4431	120	56	half	half	ADJ
ejpam-4431	120	57	-	-	PUNCT
ejpam-4431	120	58	space	space	NOUN
ejpam-4431	120	59	)	)	PUNCT
ejpam-4431	120	60	with	with	ADP
ejpam-4431	120	61	respect	respect	NOUN
ejpam-4431	120	62	to	to	ADP
ejpam-4431	120	63	the	the	DET
ejpam-4431	120	64	given	give	VERB
ejpam-4431	120	65	straight	straight	ADJ
ejpam-4431	120	66	line	line	NOUN
ejpam-4431	120	67	or	or	CCONJ
ejpam-4431	120	68	on	on	ADP
ejpam-4431	120	69	different	different	ADJ
ejpam-4431	120	70	ones	one	NOUN
ejpam-4431	120	71	;	;	PUNCT
ejpam-4431	120	72	c	c	X
ejpam-4431	120	73	)	)	PUNCT
ejpam-4431	120	74	different	different	ADJ
ejpam-4431	120	75	locations	location	NOUN
ejpam-4431	120	76	of	of	ADP
ejpam-4431	120	77	the	the	DET
ejpam-4431	120	78	center	center	NOUN
ejpam-4431	120	79	of	of	ADP
ejpam-4431	120	80	inscribed	inscribe	VERB
ejpam-4431	120	81	circle	circle	NOUN
ejpam-4431	120	82	or	or	CCONJ
ejpam-4431	120	83	the	the	DET
ejpam-4431	120	84	orthocenter	orthocenter	NOUN
ejpam-4431	120	85	of	of	ADP
ejpam-4431	120	86	triangle	triangle	NOUN
ejpam-4431	120	87	depending	depend	VERB
ejpam-4431	120	88	on	on	ADP
ejpam-4431	120	89	the	the	DET
ejpam-4431	120	90	type	type	NOUN
ejpam-4431	120	91	of	of	ADP
ejpam-4431	120	92	triangle	triangle	NOUN
ejpam-4431	120	93	.	.	PUNCT
ejpam-4431	121	1	2	2	X
ejpam-4431	121	2	.	.	X
ejpam-4431	121	3	two	two	NUM
ejpam-4431	121	4	tangent	tangent	NOUN
ejpam-4431	121	5	circles	circle	NOUN
ejpam-4431	121	6	appear	appear	VERB
ejpam-4431	121	7	in	in	ADP
ejpam-4431	121	8	the	the	DET
ejpam-4431	121	9	conditions	condition	NOUN
ejpam-4431	121	10	of	of	ADP
ejpam-4431	121	11	the	the	DET
ejpam-4431	121	12	problem	problem	NOUN
ejpam-4431	121	13	,	,	PUNCT
ejpam-4431	121	14	but	but	CCONJ
ejpam-4431	121	15	no	no	DET
ejpam-4431	121	16	information	information	NOUN
ejpam-4431	121	17	about	about	ADP
ejpam-4431	121	18	whether	whether	SCONJ
ejpam-4431	121	19	the	the	DET
ejpam-4431	121	20	tangency	tangency	NOUN
ejpam-4431	121	21	is	be	AUX
ejpam-4431	121	22	internal	internal	ADJ
ejpam-4431	121	23	or	or	CCONJ
ejpam-4431	121	24	external	external	ADJ
ejpam-4431	121	25	.	.	PUNCT
ejpam-4431	122	1	two	two	NUM
ejpam-4431	122	2	points	point	NOUN
ejpam-4431	122	3	are	be	AUX
ejpam-4431	122	4	given	give	VERB
ejpam-4431	122	5	in	in	ADP
ejpam-4431	122	6	the	the	DET
ejpam-4431	122	7	problem	problem	NOUN
ejpam-4431	122	8	which	which	PRON
ejpam-4431	122	9	divide	divide	VERB
ejpam-4431	122	10	the	the	DET
ejpam-4431	122	11	circle	circle	NOUN
ejpam-4431	122	12	into	into	ADP
ejpam-4431	122	13	two	two	NUM
ejpam-4431	122	14	arcs	arc	NOUN
ejpam-4431	122	15	,	,	PUNCT
ejpam-4431	122	16	and	and	CCONJ
ejpam-4431	122	17	some	some	DET
ejpam-4431	122	18	straight	straight	ADJ
ejpam-4431	122	19	line	line	NOUN
ejpam-4431	122	20	touches	touch	VERB
ejpam-4431	122	21	the	the	DET
ejpam-4431	122	22	circle	circle	NOUN
ejpam-4431	122	23	.	.	PUNCT
ejpam-4431	123	1	but	but	CCONJ
ejpam-4431	123	2	no	no	DET
ejpam-4431	123	3	information	information	NOUN
ejpam-4431	123	4	about	about	ADP
ejpam-4431	123	5	which	which	PRON
ejpam-4431	123	6	of	of	ADP
ejpam-4431	123	7	two	two	NUM
ejpam-4431	123	8	arcs	arc	NOUN
ejpam-4431	123	9	the	the	DET
ejpam-4431	123	10	tangent	tangent	NOUN
ejpam-4431	123	11	point	point	NOUN
ejpam-4431	123	12	lies	lie	VERB
ejpam-4431	123	13	on	on	ADP
ejpam-4431	123	14	.	.	PUNCT
ejpam-4431	124	1	3	3	X
ejpam-4431	124	2	.	.	X
ejpam-4431	124	3	the	the	DET
ejpam-4431	124	4	problem	problem	NOUN
ejpam-4431	124	5	includes	include	VERB
ejpam-4431	124	6	objects	object	NOUN
ejpam-4431	124	7	with	with	ADP
ejpam-4431	124	8	some	some	DET
ejpam-4431	124	9	properties	property	NOUN
ejpam-4431	124	10	,	,	PUNCT
ejpam-4431	124	11	but	but	CCONJ
ejpam-4431	124	12	there	there	PRON
ejpam-4431	124	13	is	be	VERB
ejpam-4431	124	14	no	no	DET
ejpam-4431	124	15	information	information	NOUN
ejpam-4431	124	16	about	about	ADP
ejpam-4431	124	17	the	the	DET
ejpam-4431	124	18	relationship	relationship	NOUN
ejpam-4431	124	19	between	between	ADP
ejpam-4431	124	20	these	these	DET
ejpam-4431	124	21	objects	object	NOUN
ejpam-4431	124	22	and	and	CCONJ
ejpam-4431	124	23	their	their	PRON
ejpam-4431	124	24	properties	property	NOUN
ejpam-4431	124	25	:	:	PUNCT
ejpam-4431	124	26	a	a	X
ejpam-4431	124	27	)	)	PUNCT
ejpam-4431	124	28	it	it	PRON
ejpam-4431	124	29	is	be	AUX
ejpam-4431	124	30	stated	state	VERB
ejpam-4431	124	31	that	that	SCONJ
ejpam-4431	124	32	abc	abc	PROPN
ejpam-4431	124	33	is	be	AUX
ejpam-4431	124	34	an	an	DET
ejpam-4431	124	35	isosceles	isoscele	NOUN
ejpam-4431	124	36	triangle	triangle	NOUN
ejpam-4431	124	37	,	,	PUNCT
ejpam-4431	124	38	but	but	CCONJ
ejpam-4431	124	39	no	no	DET
ejpam-4431	124	40	information	information	NOUN
ejpam-4431	124	41	about	about	ADP
ejpam-4431	124	42	which	which	PRON
ejpam-4431	124	43	of	of	ADP
ejpam-4431	124	44	its	its	PRON
ejpam-4431	124	45	sides	side	NOUN
ejpam-4431	124	46	are	be	AUX
ejpam-4431	124	47	equal	equal	ADJ
ejpam-4431	124	48	;	;	PUNCT
ejpam-4431	124	49	b	b	X
ejpam-4431	124	50	)	)	PUNCT
ejpam-4431	124	51	the	the	DET
ejpam-4431	124	52	point	point	NOUN
ejpam-4431	124	53	m	m	VERB
ejpam-4431	124	54	divides	divide	VERB
ejpam-4431	124	55	the	the	DET
ejpam-4431	124	56	interval	interval	NOUN
ejpam-4431	124	57	ab	ab	PROPN
ejpam-4431	124	58	into	into	ADP
ejpam-4431	124	59	the	the	DET
ejpam-4431	124	60	intervals	interval	NOUN
ejpam-4431	124	61	of	of	ADP
ejpam-4431	124	62	lengths	length	NOUN
ejpam-4431	124	63	a	a	PRON
ejpam-4431	124	64	and	and	CCONJ
ejpam-4431	124	65	b	b	NOUN
ejpam-4431	124	66	,	,	PUNCT
ejpam-4431	124	67	but	but	CCONJ
ejpam-4431	124	68	no	no	DET
ejpam-4431	124	69	information	information	NOUN
ejpam-4431	124	70	about	about	ADP
ejpam-4431	124	71	which	which	PRON
ejpam-4431	124	72	of	of	ADP
ejpam-4431	124	73	these	these	DET
ejpam-4431	124	74	intervals	interval	NOUN
ejpam-4431	124	75	is	be	AUX
ejpam-4431	124	76	equal	equal	ADJ
ejpam-4431	124	77	to	to	ADP
ejpam-4431	124	78	a	a	PRON
ejpam-4431	124	79	,	,	PUNCT
ejpam-4431	124	80	and	and	CCONJ
ejpam-4431	124	81	which	which	PRON
ejpam-4431	124	82	of	of	ADP
ejpam-4431	124	83	them	they	PRON
ejpam-4431	124	84	is	be	AUX
ejpam-4431	124	85	equal	equal	ADJ
ejpam-4431	124	86	to	to	ADP
ejpam-4431	124	87	b	b	NOUN
ejpam-4431	124	88	;	;	PUNCT
ejpam-4431	124	89	c	c	X
ejpam-4431	124	90	)	)	PUNCT
ejpam-4431	124	91	the	the	DET
ejpam-4431	124	92	angle	angle	NOUN
ejpam-4431	124	93	between	between	ADP
ejpam-4431	124	94	the	the	DET
ejpam-4431	124	95	straight	straight	ADJ
ejpam-4431	124	96	lines	line	NOUN
ejpam-4431	124	97	ab	ab	PROPN
ejpam-4431	124	98	and	and	CCONJ
ejpam-4431	124	99	cd	cd	PROPN
ejpam-4431	124	100	intersecting	intersecting	NOUN
ejpam-4431	124	101	at	at	ADP
ejpam-4431	124	102	the	the	DET
ejpam-4431	124	103	point	point	NOUN
ejpam-4431	124	104	m	m	VERB
ejpam-4431	124	105	is	be	AUX
ejpam-4431	124	106	equal	equal	ADJ
ejpam-4431	124	107	to	to	ADP
ejpam-4431	124	108	α	α	PRON
ejpam-4431	124	109	,	,	PUNCT
ejpam-4431	124	110	but	but	CCONJ
ejpam-4431	124	111	no	no	DET
ejpam-4431	124	112	information	information	NOUN
ejpam-4431	124	113	about	about	ADP
ejpam-4431	124	114	which	which	PRON
ejpam-4431	124	115	of	of	ADP
ejpam-4431	124	116	the	the	DET
ejpam-4431	124	117	angles	angle	NOUN
ejpam-4431	124	118	amd	amd	PROPN
ejpam-4431	124	119	and	and	CCONJ
ejpam-4431	124	120	amc	amc	PROPN
ejpam-4431	124	121	is	be	AUX
ejpam-4431	124	122	acute	acute	ADJ
ejpam-4431	124	123	.	.	PUNCT
ejpam-4431	125	1	3	3	X
ejpam-4431	125	2	.	.	X
ejpam-4431	125	3	concluding	conclude	VERB
ejpam-4431	125	4	remaks	remak	NOUN
ejpam-4431	125	5	now	now	ADV
ejpam-4431	125	6	let	let	VERB
ejpam-4431	125	7	’s	’s	NOUN
ejpam-4431	125	8	list	list	VERB
ejpam-4431	125	9	the	the	DET
ejpam-4431	125	10	stages	stage	NOUN
ejpam-4431	125	11	of	of	ADP
ejpam-4431	125	12	the	the	DET
ejpam-4431	125	13	methodology	methodology	NOUN
ejpam-4431	125	14	of	of	ADP
ejpam-4431	125	15	using	use	VERB
ejpam-4431	125	16	variative	variative	ADJ
ejpam-4431	125	17	problems	problem	NOUN
ejpam-4431	125	18	.	.	PUNCT
ejpam-4431	126	1	in	in	ADP
ejpam-4431	126	2	the	the	DET
ejpam-4431	126	3	first	first	ADJ
ejpam-4431	126	4	stage	stage	NOUN
ejpam-4431	126	5	,	,	PUNCT
ejpam-4431	126	6	it	it	PRON
ejpam-4431	126	7	’s	’	VERB
ejpam-4431	126	8	best	good	ADJ
ejpam-4431	126	9	to	to	PART
ejpam-4431	126	10	state	state	VERB
ejpam-4431	126	11	a	a	DET
ejpam-4431	126	12	”	"	PUNCT
ejpam-4431	126	13	multiple	multiple	ADJ
ejpam-4431	126	14	choice	choice	NOUN
ejpam-4431	126	15	question	question	NOUN
ejpam-4431	126	16	”	"	PUNCT
ejpam-4431	126	17	problem	problem	NOUN
ejpam-4431	126	18	(	(	PUNCT
ejpam-4431	126	19	the	the	DET
ejpam-4431	126	20	possible	possible	ADJ
ejpam-4431	126	21	cases	case	NOUN
ejpam-4431	126	22	”	"	PUNCT
ejpam-4431	126	23	follow	follow	VERB
ejpam-4431	126	24	”	"	PUNCT
ejpam-4431	126	25	references	reference	NOUN
ejpam-4431	126	26	1022	1022	NUM
ejpam-4431	126	27	from	from	ADP
ejpam-4431	126	28	the	the	DET
ejpam-4431	126	29	conditions	condition	NOUN
ejpam-4431	126	30	of	of	ADP
ejpam-4431	126	31	the	the	DET
ejpam-4431	126	32	problem	problem	NOUN
ejpam-4431	126	33	)	)	PUNCT
ejpam-4431	126	34	.	.	PUNCT
ejpam-4431	127	1	after	after	ADP
ejpam-4431	127	2	having	having	AUX
ejpam-4431	127	3	solved	solve	VERB
ejpam-4431	127	4	this	this	DET
ejpam-4431	127	5	problem	problem	NOUN
ejpam-4431	127	6	,	,	PUNCT
ejpam-4431	127	7	you	you	PRON
ejpam-4431	127	8	have	have	VERB
ejpam-4431	127	9	to	to	PART
ejpam-4431	127	10	consider	consider	VERB
ejpam-4431	127	11	the	the	DET
ejpam-4431	127	12	generalization	generalization	NOUN
ejpam-4431	127	13	of	of	ADP
ejpam-4431	127	14	all	all	DET
ejpam-4431	127	15	cases	case	NOUN
ejpam-4431	127	16	a	a	DET
ejpam-4431	127	17	variative	variative	ADJ
ejpam-4431	127	18	problem	problem	NOUN
ejpam-4431	127	19	.	.	PUNCT
ejpam-4431	128	1	the	the	DET
ejpam-4431	128	2	solution	solution	NOUN
ejpam-4431	128	3	of	of	ADP
ejpam-4431	128	4	every	every	DET
ejpam-4431	128	5	”	"	PUNCT
ejpam-4431	128	6	multiple	multiple	ADJ
ejpam-4431	128	7	choice	choice	NOUN
ejpam-4431	128	8	question	question	NOUN
ejpam-4431	128	9	”	"	PUNCT
ejpam-4431	128	10	problem	problem	NOUN
ejpam-4431	128	11	included	include	VERB
ejpam-4431	128	12	in	in	ADP
ejpam-4431	128	13	school	school	NOUN
ejpam-4431	128	14	manual	manual	NOUN
ejpam-4431	128	15	must	must	AUX
ejpam-4431	128	16	be	be	AUX
ejpam-4431	128	17	concluded	conclude	VERB
ejpam-4431	128	18	with	with	ADP
ejpam-4431	128	19	the	the	DET
ejpam-4431	128	20	statement	statement	NOUN
ejpam-4431	128	21	of	of	ADP
ejpam-4431	128	22	a	a	DET
ejpam-4431	128	23	variative	variative	ADJ
ejpam-4431	128	24	problem	problem	NOUN
ejpam-4431	128	25	.	.	PUNCT
ejpam-4431	129	1	in	in	ADP
ejpam-4431	129	2	the	the	DET
ejpam-4431	129	3	next	next	ADJ
ejpam-4431	129	4	stage	stage	NOUN
ejpam-4431	129	5	,	,	PUNCT
ejpam-4431	129	6	the	the	DET
ejpam-4431	129	7	students	student	NOUN
ejpam-4431	129	8	must	must	AUX
ejpam-4431	129	9	be	be	AUX
ejpam-4431	129	10	taught	teach	VERB
ejpam-4431	129	11	how	how	SCONJ
ejpam-4431	129	12	to	to	PART
ejpam-4431	129	13	derive	derive	VERB
ejpam-4431	129	14	a	a	DET
ejpam-4431	129	15	variative	variative	ADJ
ejpam-4431	129	16	problem	problem	NOUN
ejpam-4431	129	17	from	from	ADP
ejpam-4431	129	18	the	the	DET
ejpam-4431	129	19	standard	standard	ADJ
ejpam-4431	129	20	one	one	NUM
ejpam-4431	129	21	.	.	PUNCT
ejpam-4431	130	1	students	student	NOUN
ejpam-4431	130	2	must	must	AUX
ejpam-4431	130	3	be	be	AUX
ejpam-4431	130	4	offered	offer	VERB
ejpam-4431	130	5	to	to	PART
ejpam-4431	130	6	create	create	VERB
ejpam-4431	130	7	a	a	DET
ejpam-4431	130	8	problem	problem	NOUN
ejpam-4431	130	9	with	with	ADP
ejpam-4431	130	10	an	an	DET
ejpam-4431	130	11	ambiguous	ambiguous	ADJ
ejpam-4431	130	12	answer	answer	NOUN
ejpam-4431	130	13	,	,	PUNCT
ejpam-4431	130	14	to	to	PART
ejpam-4431	130	15	solve	solve	VERB
ejpam-4431	130	16	both	both	CCONJ
ejpam-4431	130	17	definite	definite	ADJ
ejpam-4431	130	18	and	and	CCONJ
ejpam-4431	130	19	variative	variative	ADJ
ejpam-4431	130	20	problems	problem	NOUN
ejpam-4431	130	21	.	.	PUNCT
ejpam-4431	131	1	students	student	NOUN
ejpam-4431	131	2	trying	try	VERB
ejpam-4431	131	3	to	to	PART
ejpam-4431	131	4	create	create	VERB
ejpam-4431	131	5	variative	variative	ADJ
ejpam-4431	131	6	problems	problem	NOUN
ejpam-4431	131	7	on	on	ADP
ejpam-4431	131	8	their	their	PRON
ejpam-4431	131	9	own	own	ADJ
ejpam-4431	131	10	must	must	AUX
ejpam-4431	131	11	be	be	AUX
ejpam-4431	131	12	encouraged	encourage	VERB
ejpam-4431	131	13	.	.	PUNCT
ejpam-4431	132	1	finally	finally	ADV
ejpam-4431	132	2	,	,	PUNCT
ejpam-4431	132	3	the	the	DET
ejpam-4431	132	4	last	last	ADJ
ejpam-4431	132	5	stage	stage	NOUN
ejpam-4431	132	6	assumes	assume	VERB
ejpam-4431	132	7	the	the	DET
ejpam-4431	132	8	inclusion	inclusion	NOUN
ejpam-4431	132	9	of	of	ADP
ejpam-4431	132	10	variative	variative	ADJ
ejpam-4431	132	11	problems	problem	NOUN
ejpam-4431	132	12	in	in	ADP
ejpam-4431	132	13	teaching	teaching	NOUN
ejpam-4431	132	14	process	process	NOUN
ejpam-4431	132	15	as	as	ADP
ejpam-4431	132	16	one	one	NUM
ejpam-4431	132	17	of	of	ADP
ejpam-4431	132	18	effective	effective	ADJ
ejpam-4431	132	19	tools	tool	NOUN
ejpam-4431	132	20	for	for	ADP
ejpam-4431	132	21	the	the	DET
ejpam-4431	132	22	realization	realization	NOUN
ejpam-4431	132	23	of	of	ADP
ejpam-4431	132	24	activity	activity	NOUN
ejpam-4431	132	25	-	-	PUNCT
ejpam-4431	132	26	based	base	VERB
ejpam-4431	132	27	approach	approach	NOUN
ejpam-4431	132	28	.	.	PUNCT
ejpam-4431	133	1	references	reference	NOUN
ejpam-4431	133	2	[	[	X
ejpam-4431	133	3	1	1	NUM
ejpam-4431	133	4	]	]	PUNCT
ejpam-4431	133	5	m.wertheimer	m.wertheimer	NOUN
ejpam-4431	133	6	;	;	PUNCT
ejpam-4431	133	7	productive	productive	ADJ
ejpam-4431	133	8	thinking	thinking	NOUN
ejpam-4431	133	9	,	,	PUNCT
ejpam-4431	133	10	m.	m.	NOUN
ejpam-4431	133	11	;	;	PUNCT
ejpam-4431	133	12	progress	progress	NOUN
ejpam-4431	133	13	(	(	PUNCT
ejpam-4431	133	14	1987	1987	NUM
ejpam-4431	133	15	)	)	PUNCT
ejpam-4431	133	16	.	.	PUNCT
ejpam-4431	134	1	(	(	PUNCT
ejpam-4431	134	2	in	in	ADP
ejpam-4431	134	3	russian	russian	NOUN
ejpam-4431	134	4	)	)	PUNCT
ejpam-4431	135	1	[	[	X
ejpam-4431	135	2	2	2	NUM
ejpam-4431	135	3	]	]	X
ejpam-4431	135	4	p.i.gornshteyn	p.i.gornshteyn	ADJ
ejpam-4431	135	5	,	,	PUNCT
ejpam-4431	135	6	v.b.polonski	v.b.polonski	ADJ
ejpam-4431	135	7	,	,	PUNCT
ejpam-4431	135	8	m.s.yakir	m.s.yakir	PROPN
ejpam-4431	135	9	;	;	PUNCT
ejpam-4431	135	10	problems	problem	NOUN
ejpam-4431	135	11	with	with	ADP
ejpam-4431	135	12	parameters	parameter	NOUN
ejpam-4431	135	13	,	,	PUNCT
ejpam-4431	135	14	m.	m.	NOUN
ejpam-4431	135	15	;	;	PUNCT
ejpam-4431	135	16	ileksa	ileksa	NOUN
ejpam-4431	135	17	(	(	PUNCT
ejpam-4431	135	18	2017	2017	NUM
ejpam-4431	135	19	)	)	PUNCT
ejpam-4431	135	20	.	.	PUNCT
ejpam-4431	136	1	(	(	PUNCT
ejpam-4431	136	2	in	in	ADP
ejpam-4431	136	3	russian	russian	NOUN
ejpam-4431	136	4	)	)	PUNCT
ejpam-4431	137	1	[	[	X
ejpam-4431	137	2	3	3	NUM
ejpam-4431	137	3	]	]	X
ejpam-4431	137	4	v.b.polonski	v.b.polonski	NOUN
ejpam-4431	137	5	et	et	PROPN
ejpam-4431	137	6	al	al	PROPN
ejpam-4431	137	7	.	.	PROPN
ejpam-4431	137	8	;	;	PUNCT
ejpam-4431	137	9	geometry	geometry	NOUN
ejpam-4431	137	10	.	.	PUNCT
ejpam-4431	138	1	school	school	NOUN
ejpam-4431	138	2	taskbook	taskbook	NOUN
ejpam-4431	138	3	,	,	PUNCT
ejpam-4431	138	4	m.	m.	NOUN
ejpam-4431	138	5	;	;	PUNCT
ejpam-4431	138	6	ast	ast	NOUN
ejpam-4431	138	7	-	-	PUNCT
ejpam-4431	138	8	press	press	NOUN
ejpam-4431	138	9	(	(	PUNCT
ejpam-4431	138	10	1988	1988	NUM
ejpam-4431	138	11	)	)	PUNCT
ejpam-4431	138	12	.	.	PUNCT
ejpam-4431	139	1	(	(	PUNCT
ejpam-4431	139	2	in	in	ADP
ejpam-4431	139	3	russian	russian	NOUN
ejpam-4431	139	4	)	)	PUNCT
ejpam-4431	140	1	[	[	X
ejpam-4431	140	2	4	4	NUM
ejpam-4431	140	3	]	]	X
ejpam-4431	140	4	g.v.dorofeyev	g.v.dorofeyev	ADJ
ejpam-4431	140	5	,	,	PUNCT
ejpam-4431	140	6	m.s.potapov	m.s.potapov	NOUN
ejpam-4431	140	7	,	,	PUNCT
ejpam-4431	140	8	n.kh.rozov	n.kh.rozov	NUM
ejpam-4431	140	9	;	;	PUNCT
ejpam-4431	140	10	manual	manual	NOUN
ejpam-4431	140	11	of	of	ADP
ejpam-4431	140	12	mathematics	mathematic	NOUN
ejpam-4431	140	13	,	,	PUNCT
ejpam-4431	140	14	moscow	moscow	PROPN
ejpam-4431	140	15	,	,	PUNCT
ejpam-4431	140	16	nauka	nauka	PROPN
ejpam-4431	140	17	(	(	PUNCT
ejpam-4431	140	18	1976	1976	NUM
ejpam-4431	140	19	)	)	PUNCT
ejpam-4431	140	20	.	.	PUNCT
ejpam-4431	141	1	(	(	PUNCT
ejpam-4431	141	2	in	in	ADP
ejpam-4431	141	3	russian	russian	NOUN
ejpam-4431	141	4	)	)	PUNCT
ejpam-4431	142	1	[	[	X
ejpam-4431	142	2	5	5	NUM
ejpam-4431	142	3	]	]	PUNCT
ejpam-4431	142	4	y.p.ponarin	y.p.ponarin	NOUN
ejpam-4431	142	5	;	;	PUNCT
ejpam-4431	142	6	elementary	elementary	ADJ
ejpam-4431	142	7	geometry	geometry	NOUN
ejpam-4431	142	8	,	,	PUNCT
ejpam-4431	142	9	vol	vol	NOUN
ejpam-4431	142	10	.	.	PROPN
ejpam-4431	142	11	1	1	NUM
ejpam-4431	142	12	,	,	PUNCT
ejpam-4431	142	13	m.	m.	NOUN
ejpam-4431	142	14	;	;	PUNCT
ejpam-4431	142	15	mcnmo	mcnmo	NOUN
ejpam-4431	142	16	(	(	PUNCT
ejpam-4431	142	17	2008	2008	NUM
ejpam-4431	142	18	)	)	PUNCT
ejpam-4431	142	19	.	.	PUNCT
ejpam-4431	143	1	(	(	PUNCT
ejpam-4431	143	2	in	in	ADP
ejpam-4431	143	3	russian	russian	NOUN
ejpam-4431	143	4	)	)	PUNCT
ejpam-4431	144	1	[	[	X
ejpam-4431	144	2	6	6	NUM
ejpam-4431	144	3	]	]	PUNCT
ejpam-4431	144	4	e.g.gotman	e.g.gotman	NOUN
ejpam-4431	144	5	;	;	PUNCT
ejpam-4431	144	6	exercises	exercise	NOUN
ejpam-4431	144	7	on	on	ADP
ejpam-4431	144	8	planimetry	planimetry	NOUN
ejpam-4431	144	9	and	and	CCONJ
ejpam-4431	144	10	methods	method	NOUN
ejpam-4431	144	11	to	to	PART
ejpam-4431	144	12	solve	solve	VERB
ejpam-4431	144	13	them	they	PRON
ejpam-4431	144	14	,	,	PUNCT
ejpam-4431	144	15	prosvesheniye	prosvesheniye	PROPN
ejpam-4431	144	16	(	(	PUNCT
ejpam-4431	144	17	1996	1996	NUM
ejpam-4431	144	18	)	)	PUNCT
ejpam-4431	144	19	.	.	PUNCT
ejpam-4431	145	1	(	(	PUNCT
ejpam-4431	145	2	in	in	ADP
ejpam-4431	145	3	russian	russian	NOUN
ejpam-4431	145	4	)	)	PUNCT
ejpam-4431	146	1	[	[	X
ejpam-4431	146	2	7	7	X
ejpam-4431	146	3	]	]	SYM
ejpam-4431	146	4	s.krackov	s.krackov	NOUN
ejpam-4431	146	5	;	;	PUNCT
ejpam-4431	146	6	multivariate	multivariate	VERB
ejpam-4431	146	7	visual	visual	ADJ
ejpam-4431	146	8	-	-	PUNCT
ejpam-4431	146	9	graphic	graphic	ADJ
ejpam-4431	146	10	representation	representation	NOUN
ejpam-4431	146	11	of	of	ADP
ejpam-4431	146	12	mathematical	mathematical	ADJ
ejpam-4431	146	13	problems	problem	NOUN
ejpam-4431	146	14	,	,	PUNCT
ejpam-4431	146	15	mathematika	mathematika	X
ejpam-4431	146	16	v	v	PROPN
ejpam-4431	146	17	shkole	shkole	PROPN
ejpam-4431	146	18	,	,	PUNCT
ejpam-4431	146	19	no1	no1	PROPN
ejpam-4431	146	20	,	,	PUNCT
ejpam-4431	146	21	(	(	PUNCT
ejpam-4431	146	22	2013	2013	NUM
ejpam-4431	146	23	)	)	PUNCT
ejpam-4431	146	24	.	.	PUNCT
ejpam-4431	147	1	(	(	PUNCT
ejpam-4431	147	2	in	in	ADP
ejpam-4431	147	3	russian	russian	NOUN
ejpam-4431	147	4	)	)	PUNCT
ejpam-4431	148	1	[	[	X
ejpam-4431	148	2	8	8	NUM
ejpam-4431	148	3	]	]	PUNCT
ejpam-4431	148	4	v.a.petrov	v.a.petrov	NOUN
ejpam-4431	148	5	;	;	PUNCT
ejpam-4431	148	6	applied	apply	VERB
ejpam-4431	148	7	problems	problem	NOUN
ejpam-4431	148	8	,	,	PUNCT
ejpam-4431	148	9	m.	m.	NOUN
ejpam-4431	148	10	;	;	PUNCT
ejpam-4431	148	11	drofa	drofa	NOUN
ejpam-4431	148	12	,	,	PUNCT
ejpam-4431	148	13	(	(	PUNCT
ejpam-4431	148	14	2020	2020	NUM
ejpam-4431	148	15	)	)	PUNCT
ejpam-4431	148	16	.	.	PUNCT
ejpam-4431	149	1	(	(	PUNCT
ejpam-4431	149	2	in	in	ADP
ejpam-4431	149	3	russian	russian	NOUN
ejpam-4431	149	4	)	)	PUNCT