Question Number 40321 by faaiz last updated on 19/Jul/18 $$\mathrm{If}\:{abc}=\mathrm{8}\:\mathrm{and}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{ab}+{bc}+{ca}. \\ $$ Commented by math khazana by abdo last updated on 19/Jul/18 $$\Rightarrow{abc}\left(\frac{\mathrm{1}}{{a}}+\:\frac{\mathrm{1}}{{b}}\:+\frac{\mathrm{1}}{{c}}\right)=\frac{\mathrm{3}}{\mathrm{2}}{abc}\Rightarrow…
Question Number 39975 by sanjar last updated on 14/Jul/18 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\underset{\:\mathrm{0}} {\overset{{x}} {\int}}\:\:{e}^{{x}} \:{dx}\right)^{\mathrm{2}} }{\underset{\:\mathrm{0}} {\overset{{x}} {\int}}\:\:{e}^{\mathrm{2}{x}^{\mathrm{2}} } \:{dx}}\:\:= \\ $$ Commented by tanmay.chaudhury50@gmail.com last…
Question Number 104275 by mubarakagulamhusain last updated on 20/Jul/20 $$\mathrm{The}\:\mathrm{HCF}\:\mathrm{of}\:\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{4}\right)\:\mathrm{and}\: \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}+\mathrm{2}\right)\:\:\mathrm{is} \\ $$ Commented by 1549442205PVT last updated on 20/Jul/20 $$\mathrm{you}\:\mathrm{can}\:\mathrm{tell}\:\mathrm{me}\:\mathrm{what}\:\mathrm{is}\:\mathrm{brief}\:\mathrm{word}\:''\mathrm{HCF}''? \\…
Question Number 38222 by sir themes last updated on 23/Jun/18 $$\mathrm{If}\:\mathbb{U}=\left\{−\mathrm{5},\:−\mathrm{4},\:−\mathrm{3},\:−\mathrm{2},\:−\mathrm{1},\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5}\right\} \\ $$$$\mathrm{A}=\left\{{x}/{x}^{\mathrm{2}} =\mathrm{25},\:{x}\:\in\:\mathrm{Z}\right\} \\ $$$$\mathrm{B}=\left\{{x}/{x}^{\mathrm{2}} +\mathrm{5}=\mathrm{9},\:{x}\:\in\:\mathrm{Z}\right\}\:\mathrm{and} \\ $$$$\mathrm{C}=\left\{{x}/−\mathrm{2}\leqslant\:{x}\:\leqslant\:\mathrm{2},\:{x}\:\in\:\mathrm{Z}\right\}\:\mathrm{then} \\ $$$$\left(\mathrm{A}\:\cap\:\mathrm{B}\:\cap\:\mathrm{C}\right)^{\mathrm{c}} \:\cap\:\left(\mathrm{A}\bigtriangleup\mathrm{B}\right)^{\mathrm{c}} =? \\ $$…
Question Number 103155 by 9027201563 last updated on 13/Jul/20 $$\mathrm{If}\:\mathrm{cos}^{−\mathrm{1}} {x}+\mathrm{cos}^{−\mathrm{1}} {y}+\mathrm{cos}^{−\mathrm{1}} {z}+\mathrm{cos}^{−\mathrm{1}} {u}=\mathrm{2}\pi, \\ $$$$\mathrm{then}\:\:{x}^{\mathrm{1999}} +{y}^{\mathrm{2000}} +{z}^{\mathrm{2001}} +{u}^{\mathrm{2002}} = \\ $$ Commented by 9027201563…
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}}…