Question Number 62850 by ajfour last updated on 25/Jun/19 Commented by ajfour last updated on 25/Jun/19 $${Find}\:{possible}\:{values}\:{of}\:{side}\:\boldsymbol{{s}}\:{of} \\ $$$${equilateral}\:\bigtriangleup{PQR}\:{in}\:{terms}\:{of} \\ $$$${a}\:{and}\:{b}.\left({for}\:{example}\:{let}\:{a}=\mathrm{4},\:{b}=\mathrm{3}\right). \\ $$ Answered by…
Question Number 128385 by n0y0n last updated on 06/Jan/21 $$\int_{\mathrm{1}} ^{\:\pi} \begin{vmatrix}{\mathrm{x}^{\mathrm{3}} }&{\mathrm{lnx}}&{\mathrm{sinx}}\\{\mathrm{3x}^{\mathrm{2}} }&{\frac{\mathrm{1}}{\mathrm{x}}}&{\mathrm{cosx}}\\{\mathrm{6}}&{\mathrm{2x}^{−\mathrm{3}} }&{−\mathrm{cosx}}\end{vmatrix}\mathrm{dx}\:=?\: \\ $$ Answered by mathmax by abdo last updated on…
Question Number 128382 by arash sharifi last updated on 06/Jan/21 $${y}={x}^{{x}^{\mathrm{2}} } \\ $$ Commented by hknkrc46 last updated on 06/Jan/21 $$\bullet\:\boldsymbol{{x}}\:\in\:\mathbb{R}\:\Rightarrow\:\boldsymbol{{y}}\:\in\:\mathbb{R} \\ $$$$\bullet\:\boldsymbol{{x}}\:=\:\mp\mathrm{1}\:\Rightarrow\:\boldsymbol{{y}}\:=\:\mathrm{1} \\…
Question Number 62844 by alphaprime last updated on 25/Jun/19 $${Let}\:{p}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:\:{be}\:{such}\:{that}\:{p}\left({x}\right)\:{takes}\:{real}\:{values} \\ $$$${for}\:{real}\:{values}\:{of}\:{x}\:{and}\:{non}−{real}\:{values}\:{for}\:{non}−{real} \\ $$$${values}\:{of}\:{x}\:.\:{Prove}\:{that}\:{a}\:=\:\mathrm{0}\:{and}\:{find}\:{all} \\ $$$${possible}\:{values}\:{of}\:{c}. \\ $$ Answered by ajfour last updated on…
Question Number 62839 by ajfour last updated on 25/Jun/19 Commented by ajfour last updated on 25/Jun/19 $${let}\:\theta\:{be}\:{angle}\:{between}\:{b}\:{and}\: \\ $$$${extended}\:{c}\:. \\ $$$$\left({c}+{b}\mathrm{cos}\:\theta\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \theta={r}^{\mathrm{2}} \\…
Question Number 128373 by BHOOPENDRA last updated on 06/Jan/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\frac{\mathrm{3}}{\mathrm{2}}} \left(\mathrm{1}−{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 06/Jan/21 $$\int_{\mathrm{0}}…
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Question Number 128370 by mathocean1 last updated on 06/Jan/21 $$\left.{f}\left({x}\right)=\left({x}−\mathrm{1}\right)\sqrt{{x}−\mathrm{1}}\:{on}\:\:\right]\mathrm{1};+\infty\left[\right. \\ $$$${F}\left({x}\right)=? \\ $$ Answered by mathmax by abdo last updated on 06/Jan/21 $$\mathrm{if}\:\mathrm{you}\:\mathrm{want}\:\mathrm{derivative}\:\mathrm{f}^{'} \left(\mathrm{x}\right)=\sqrt{\mathrm{x}−\mathrm{1}}+\left(\mathrm{x}−\mathrm{1}\right)×\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}−\mathrm{1}}}…
Question Number 128371 by aliibrahim1 last updated on 06/Jan/21 Commented by MJS_new last updated on 06/Jan/21 $${A}_{{n}} =\frac{\mathrm{752}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{2}{k}−\mathrm{1}}\:−\mathrm{752}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{k}}}{\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}}} \\…
Question Number 128368 by I want to learn more last updated on 06/Jan/21 $$\mathrm{If}\:\:\:\:\mathrm{a}_{\mathrm{1}} \:=\:\:\mathrm{2},\:\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{3},\:\:\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \:\:=\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} \:\:+\:\:\frac{\mathrm{a}}{\mathrm{2}},\:\:\:\:\:\:\mathrm{find}\:\:\mathrm{a}_{\mathrm{n}} \\ $$ Answered by mr W last…