Question Number 87418 by liki last updated on 04/Apr/20 Answered by Rio Michael last updated on 04/Apr/20 $$\left(\mathrm{a}\right)\:\mathrm{since}\:\mathrm{we}\:\mathrm{have}\:\mathrm{3}\:\mathrm{match}\:\mathrm{pairs}\:\mathrm{in}\:\mathrm{the}\:\mathrm{box},\:\mathrm{then} \\ $$$$\mathrm{P}\left(\mathrm{match}\:\mathrm{pair}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}}. \\ $$$$\:\left(\mathrm{b}\right)\:\mathrm{we}\:\mathrm{have}\:\mathrm{six}\:\mathrm{socks}\:\mathrm{in}\:\mathrm{that}\:\mathrm{box},\:\mathrm{3}\:\mathrm{left}\:\mathrm{feet}\:\mathrm{and}\:\mathrm{3}\:\mathrm{right}\:\mathrm{fit} \\ $$$$\:\:\:\:\:\:\:\mathrm{P}\left(\mathrm{left}\:\mathrm{feet}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{and}\:\mathrm{P}\left(\mathrm{right}\:\mathrm{feet}\right)\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\…
Question Number 87409 by redmiiuser last updated on 04/Apr/20 $$\int\left({sinx}\right)^{\frac{\mathrm{1}}{\mathrm{5}}} {dx} \\ $$ Commented by Prithwish Sen 1 last updated on 04/Apr/20 $$\int\frac{\mathrm{sin}^{\frac{\mathrm{1}}{\mathrm{5}}} \mathrm{x}\:\mathrm{cosx}}{\mathrm{cosx}}\:\mathrm{dx}\:\:\:\mathrm{put}\:\mathrm{sinx}\:=\:\mathrm{u}^{\mathrm{5}} \:\:\mathrm{cosxdx}\:=\:\mathrm{5u}^{\mathrm{4}}…
Question Number 152942 by mathlove last updated on 03/Sep/21 Commented by mathdanisur last updated on 03/Sep/21 $$\mathrm{8}\:=\:\mathrm{8}^{\boldsymbol{\mathrm{x}}} \:\Rightarrow\:\mathrm{x}\:=\:\mathrm{1} \\ $$ Answered by puissant last updated…
Question Number 152918 by ZiYangLee last updated on 03/Sep/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{derivative}\:\mathrm{of}\: \\ $$$${y}={x}\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }+\mathrm{16sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{4}} \\ $$ Answered by puissant last updated on 03/Sep/21 $${y}={x}\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }+\mathrm{16}{arcsin}\left(\frac{{x}}{\mathrm{4}}\right)…
Question Number 87376 by naka3546 last updated on 04/Apr/20 Answered by john santu last updated on 04/Apr/20 $$\mathrm{A}^{\mathrm{3}} \:=\:\begin{pmatrix}{\mathrm{3}\:\:\:\:−\mathrm{2}}\\{\:\mathrm{3}\:\:\:\:−\mathrm{4}}\end{pmatrix}\:−\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:−\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{A}^{\mathrm{3}} \:=\:\begin{pmatrix}{\mathrm{1}\:\:\:\:−\mathrm{1}}\\{\mathrm{2}\:\:\:\:−\mathrm{3}}\end{pmatrix} \\ $$$$\mathrm{det}\:\left(\mathrm{A}\right)\:=\:\sqrt[{\mathrm{3}\:\:}]{−\mathrm{3}+\mathrm{2}}\:=\:−\mathrm{1} \\…
Question Number 152900 by SANOGO last updated on 03/Sep/21 Answered by mindispower last updated on 03/Sep/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}.\frac{\mathrm{1}}{{n}}.\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{{k}}{{n}+\mathrm{1}}\right)^{{a}} }{{n}^{\mathrm{2}} {a}+\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}}…
Question Number 152889 by SANOGO last updated on 02/Sep/21 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\alpha} }{\left({n}+\mathrm{1}\right)^{\alpha} \:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\mathrm{1}+{n}\alpha\right)}=\frac{\mathrm{1}}{\mathrm{6}{o}}\: \\ $$$$\alpha=? \\ $$$$\alpha=?{q} \\ $$ Commented…
Question Number 152887 by otchereabdullai@gmail.com last updated on 02/Sep/21 $$\int_{\mathrm{1}} ^{\:\mathrm{2}} \:\:\frac{\mathrm{3}}{\:\sqrt{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{3}} }} \\ $$ Answered by Ar Brandon last updated on 02/Sep/21 $${I}=\int_{\mathrm{1}}…
Question Number 152879 by SANOGO last updated on 02/Sep/21 $$\underset{{x}\rightarrow+{oo}} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{\alpha} \:\:\:}{\left({n}+\mathrm{1}\right)^{\alpha} \:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left({n}\alpha+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{6}{o}}\:\:.\alpha=? \\ $$ Commented by talminator2856791 last updated on…
Question Number 87335 by naka3546 last updated on 04/Apr/20 Answered by TANMAY PANACEA. last updated on 04/Apr/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{sin}^{{a}} {x}}{{sin}^{{a}} {x}+{cos}^{{a}} {x}}{dx}=\frac{{I}\pi}{\mathrm{4}} \\ $$$${using}\:\int_{\mathrm{0}}…