Question Number 172613 by cortano1 last updated on 29/Jun/22 $$\:\:\:{min}\:{y}=\mathrm{9}\:\mathrm{sin}\:^{\mathrm{2}} {x}+\:\mathrm{4}\:{csc}^{\mathrm{2}} {x}\:+\:\mathrm{3} \\ $$ Answered by Rasheed.Sindhi last updated on 29/Jun/22 $${y}=\left(\mathrm{3sin}\:{x}+\mathrm{2}\:\mathrm{csc}\:{x}\right)^{\mathrm{2}} −\mathrm{12}+\mathrm{3} \\ $$$${y}=\left(\mathrm{3sin}\:{x}+\mathrm{2}\:\mathrm{csc}\:{x}\right)^{\mathrm{2}}…
Question Number 172526 by mnjuly1970 last updated on 28/Jun/22 $$ \\ $$$$\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{dx}}{\left(\mathrm{4}−\mathrm{2}{x}+{x}^{\:\mathrm{2}} \right)^{\:\mathrm{3}} }\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{64}}\:+\frac{\pi}{\mathrm{36}\sqrt{\mathrm{3}}} \\ $$ Answered by MJS_new last updated on…
Question Number 172359 by mnjuly1970 last updated on 25/Jun/22 Answered by Mathspace last updated on 26/Jun/22 $${J}=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{−\frac{\mathrm{1}}{\mathrm{2}}} \left(\mathrm{1}−{x}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} {ln}^{\mathrm{2}} {xdx} \\ $$$${let}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 106787 by bemath last updated on 07/Aug/20 $$\:\:\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\:\:\mathrm{y}\:=\:\left(\mathrm{cos}\:\mathrm{2x}\right)^{\mathrm{sin}\:\mathrm{x}} \:,\:\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 07/Aug/20 $${logy}={sinxlog}\left({cos}\mathrm{2}{x}\right)…
Question Number 106779 by bobhans last updated on 07/Aug/20 $$\:\:\:\:\:\:\:\:\:^{\succ\mathrm{bobhans}\prec} \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{closest}\:\mathrm{to}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{0},\mathrm{18}\right)\:? \\ $$ Answered by john santu last updated on 07/Aug/20 $$\:\:\:\:\:\:\:^{@\mathrm{JS}@}…
Question Number 172253 by cortano1 last updated on 25/Jun/22 $$\:\:{Max}\:{and}\:{min}\:{P}=\sqrt{\mathrm{2}}\:{x}+\:\sqrt{\mathrm{3}}\:{y} \\ $$$${subject}\:{to}\:{constraint}\: \\ $$$$\:\frac{{x}^{\mathrm{2}} }{\mathrm{9}}\:+\frac{{y}^{\mathrm{2}} }{\mathrm{25}}\:\leqslant\:\mathrm{1}\:\leqslant\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$ Answered by mr W last updated…
Question Number 41157 by ajfour last updated on 02/Aug/18 Commented by ajfour last updated on 02/Aug/18 $${If}\:{arc}\:{length}\:{is}\:{constant},\:{equal} \\ $$$${to}\:\boldsymbol{{l}},\:{and}\:{segment}\:{area}\:{a}\:{maximum}, \\ $$$${find}\:{the}\:{radius}. \\ $$ Commented by…
Question Number 41151 by rahul 19 last updated on 02/Aug/18 $$\mathrm{Proof}\:\mathrm{that}\::\:\frac{\mathrm{d}^{\mathrm{n}} }{\mathrm{d}{x}^{{n}} }\left(\mathrm{cos}\:{x}\right)\:=\:\mathrm{cos}\:\left({x}+\frac{{n}\pi}{\mathrm{2}}\right) \\ $$$$\frac{\mathrm{d}^{\mathrm{n}} }{\mathrm{d}{x}^{{n}} }\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{sin}\:\left({x}+\frac{{n}\pi}{\mathrm{2}}\right) \\ $$$$\mathrm{where}\:\mathrm{n}\in\mathbb{Z}. \\ $$ Commented by prof Abdo…
Question Number 41139 by ajfour last updated on 02/Aug/18 Commented by ajfour last updated on 02/Aug/18 $${Q}.\mathrm{41117}\:\:{alternate}\:{solution} \\ $$ Answered by ajfour last updated on…
Question Number 41117 by ajfour last updated on 02/Aug/18 Answered by MJS last updated on 02/Aug/18 $${r}=\mathrm{1} \\ $$$${P}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix}\:\:{A}=\begin{pmatrix}{\mathrm{cos}\:\alpha}\\{\mathrm{1}+\mathrm{sin}\:\alpha}\end{pmatrix}\:\:{F}=\begin{pmatrix}{\mathrm{cos}\:\alpha}\\{\mathrm{0}}\end{pmatrix} \\ $$$$\mid{AP}\mid=\sqrt{\mathrm{2}\left(\mathrm{1}+\mathrm{sin}\:\alpha\right)} \\ $$$$\mid{AF}\mid=\mathrm{1}+\mathrm{sin}\:\alpha \\ $$$$\mid{FP}\mid=\mathrm{cos}\:\alpha…