Question Number 81734 by jagoll last updated on 15/Feb/20 $${The}\:{vertices}\:{of}\:{quadrilateral} \\ $$$${lie}\:{on}\:{the}\:{graph}\:{of}\:{y}\:=\:{lnx}\:{and}\: \\ $$$${the}\:{x}−{coordinates}\:{of}\:{these}\:{vertices} \\ $$$${are}\:{consecutive}\:{positive}\:{integer} \\ $$$$.\:{The}\:{area}\:{of}\:{the}\:{quadrilateral} \\ $$$${is}\:{ln}\:\left(\frac{\mathrm{91}}{\mathrm{90}}\right).\:{what}\:{is}\:{the}\:{x}−{coordinate} \\ $$$${of}\:{the}\:{leftmost}\:{vertex} \\ $$ Commented…
Question Number 15993 by ajfour last updated on 16/Jun/17 Commented by ajfour last updated on 16/Jun/17 $$\:{answer}\:{to}\:{Q}.\mathrm{15969}\: \\ $$ Answered by ajfour last updated on…
Question Number 81485 by ajfour last updated on 13/Feb/20 Commented by ajfour last updated on 13/Feb/20 $${If}\:{area}\:{of}\:{region}\:{A}\:{is}\:{equal}\:{to} \\ $$$${that}\:{of}\:{B},\:{find}\:{eq}.\:{of}\:{parabola}. \\ $$ Commented by jagoll last…
Question Number 81470 by ajfour last updated on 13/Feb/20 $${Prove}\:{that}\:{the}\:{locus}\:{of}\:{the}\:{point} \\ $$$${of}\:{intersection}\:{of}\:{perpendicular} \\ $$$${tangents}\:{to}\:{an}\:{ellipse}\:{is}\:{another} \\ $$$${ellipse}. \\ $$ Answered by mr W last updated on…
Question Number 15868 by tawa tawa last updated on 14/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumcircle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{formed}\:\mathrm{by}\: \\ $$$$\mathrm{the}\:\mathrm{three}\:\mathrm{line}: \\ $$$$\mathrm{2y}\:−\:\mathrm{9x}\:+\:\mathrm{26}\:=\:\mathrm{0} \\ $$$$\mathrm{9y}\:+\:\mathrm{2x}\:+\:\mathrm{32}\:=\:\mathrm{0} \\ $$$$\mathrm{11y}\:−\:\mathrm{7x}\:−\:\mathrm{27}\:=\:\mathrm{0} \\ $$ Answered by Tinkutara last…
Question Number 81393 by ajfour last updated on 12/Feb/20 Commented by ajfour last updated on 12/Feb/20 $${Q}.\mathrm{81331}\:{reposted} \\ $$ Answered by ajfour last updated on…
Question Number 146840 by bramlexs22 last updated on 16/Jul/21 Answered by nimnim last updated on 16/Jul/21 $$ \\ $$ Commented by bobhans last updated on…
Question Number 15736 by ajfour last updated on 13/Jun/17 $${From}\:{a}\:{point}\:{A}\:{on}\:{the}\:{circum}- \\ $$$${ference}\:{of}\:{a}\:{circle}\:{of}\:{radius}\:\boldsymbol{{r}},\:{a} \\ $$$${perpendicular}\:{AF}\:\:{is}\:{dropped}\:{on} \\ $$$${a}\:{tangent}\:{to}\:{the}\:{circle}\:{at}\:{P}. \\ $$$${Find}\:{the}\:\:{maximum}\:{possible}\: \\ $$$${area}\:{of}\:\Delta{APF}\:. \\ $$ Answered by mrW1…
Question Number 146775 by Willson last updated on 15/Jul/21 $$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\:\underset{\:\mathrm{0}} {\int}^{\:\boldsymbol{\pi}} \boldsymbol{{tln}}\left(\boldsymbol{{sint}}\right)\boldsymbol{{dt}}=\:−\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{2}}\boldsymbol{{ln}}\left(\mathrm{2}\right) \\ $$ Answered by ArielVyny last updated on 15/Jul/21 $$\int_{\mathrm{0}}…
Question Number 81135 by ajfour last updated on 09/Feb/20 Commented by ajfour last updated on 09/Feb/20 $${Find}\:{radii}\:{of}\:{both}\:{circles}. \\ $$ Answered by mr W last updated…