Question Number 37462 by bholachaudhary211@gamil.com last updated on 13/Jun/18 $$\mathrm{If}\:{x}+\mathrm{3}\:\mathrm{is}\:\mathrm{the}\:\mathrm{common}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{expressions}\:{ax}^{\mathrm{2}} +{bx}+\mathrm{1}\:\mathrm{and}\: \\ $$$${px}^{\mathrm{2}} +{qx}−\mathrm{3},\:\mathrm{then}\:\frac{−\left(\mathrm{9}{a}+\mathrm{3}{p}\right)}{\mathrm{3}{b}+{q}}\:=\:\_\_\_\_. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 13/Jun/18…
Question Number 102796 by saorey0202 last updated on 11/Jul/20 $$\mathrm{The}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\:\mathrm{vectors} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{i}}+\mathrm{3}\boldsymbol{\mathrm{j}}+\boldsymbol{\mathrm{k}}\:\:\mathrm{and}\:\:\mathrm{2}\boldsymbol{\mathrm{i}}−\boldsymbol{\mathrm{j}}−\boldsymbol{\mathrm{k}}\:\:\mathrm{is} \\ $$ Answered by bramlex last updated on 11/Jul/20 $$\mathrm{cos}\:\beta\:=\:\frac{\overset{\rightarrow} {{a}}.\overset{\rightarrow} {{b}}}{\mid\overset{\rightarrow} {{a}}\mid\:\mid\overset{\rightarrow}…
Question Number 102795 by saorey0202 last updated on 11/Jul/20 $$\mathrm{Points}\:{D},\:{E}\:\mathrm{are}\:\mathrm{taken}\:\mathrm{on}\:\mathrm{the}\:\mathrm{side}\:{BC} \\ $$$$\mathrm{of}\:\mathrm{a}\:\bigtriangleup\:{ABC},\:\mathrm{such}\:\mathrm{that}\:{BD}={DE}={EC}. \\ $$$$\mathrm{If}\:\:\angle{BAD}={x},\:\angle{DAE}={y},\:\angle{EAC}={z}, \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\frac{\mathrm{sin}\:\left({x}+{y}\right)\:\mathrm{sin}\left({y}+{z}\right)}{\mathrm{sin}\:{x}\:\mathrm{sin}\:{z}} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$ Terms of Service Privacy Policy…
Question Number 37189 by rahul 19 last updated on 10/Jun/18 $$\mathrm{If}\:\int\:\:\frac{\mathrm{cos}\:\mathrm{4}{x}+\mathrm{1}}{\mathrm{cot}\:{x}−\mathrm{tan}\:{x}}\:{dx}={A}\:\mathrm{cos}\:\mathrm{4}{x}+{B},\:\mathrm{then}\: \\ $$$$\mathrm{find}\:\mathrm{A},\mathrm{B}? \\ $$ Answered by math1967 last updated on 10/Jun/18 $$\int\frac{\mathrm{2}{cos}^{\mathrm{2}} \mathrm{2}{x}}{\frac{{cos}^{\mathrm{2}} {x}−{sin}^{\mathrm{2}}…
Question Number 37188 by rahul 19 last updated on 10/Jun/18 $$\int\:\sqrt{\frac{\mathrm{cos}\:{x}−\mathrm{cos}^{\mathrm{3}} {x}}{\mathrm{1}−\mathrm{cos}^{\mathrm{3}} {x}}}\:{dx}\:= \\ $$ Answered by ajfour last updated on 10/Jun/18 $${I}=\int\sqrt{\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:^{\mathrm{3}} {x}\left(\mathrm{sec}\:^{\mathrm{3}}…
Question Number 36246 by pappukumarraynp078666@gmail.co last updated on 30/May/18 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{absolute}\:\mathrm{value}\:\mathrm{of}\:\left(\:−\mathrm{10}\right)? \\ $$ Answered by MJS last updated on 30/May/18 $$\mathrm{10} \\ $$ Terms of Service…
Question Number 101582 by Rohit@Thakur last updated on 03/Jul/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{r}\:{e}^{{r}/{n}} \:= \\ $$ Answered by mathmax by abdo last updated on…
Question Number 35877 by 0123456789 last updated on 25/May/18 $$\mathrm{If}\:\:\mathrm{cos}\:{A}=\frac{\mathrm{3}}{\mathrm{4}}\:,\:\mathrm{then}\:\mathrm{32}\:\mathrm{sin}\:\left(\frac{{A}}{\mathrm{2}}\right)\:\mathrm{sin}\:\left(\frac{\mathrm{5}{A}}{\mathrm{2}}\right)= \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 25/May/18 $$\mathrm{32}{sin}\left(\frac{{A}}{\mathrm{2}}\right){sin}\left(\frac{\mathrm{5}{A}}{\mathrm{2}}\right) \\ $$$$=\mathrm{16}×\left({cos}\mathrm{2}{A}−{cos}\mathrm{3}{A}\right) \\ $$$$=\mathrm{16}×\left\{\left(\mathrm{2}{cos}^{\mathrm{2}} {A}−\mathrm{1}\right)−\left(\mathrm{4}{cos}^{\mathrm{3}}…
Question Number 35791 by spherecity@gmail.com last updated on 23/May/18 $$\mathrm{A}\:\mathrm{5100}\:\mathrm{cm}^{\mathrm{2}} \:\mathrm{trapezium}\:\mathrm{has}\:\mathrm{the}\:\mathrm{perpendicular} \\ $$$$\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{two}\:\mathrm{parallel}\:\mathrm{sides} \\ $$$$\mathrm{60}\:\mathrm{m}.\:\mathrm{If}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{sides}\:\mathrm{be}\:\mathrm{40}\:\mathrm{m}\: \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{parallel}\:\mathrm{side}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 101082 by 67549972 last updated on 30/Jun/20 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$${e}^{\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{1}°+\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{2}°+\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{3}°+…+\mathrm{log}_{\mathrm{10}} \:\mathrm{tan}\:\mathrm{89}°} \\ $$$$\mathrm{is} \\ $$ Commented by Dwaipayan Shikari last…