Question Number 23644 by Tinkutara last updated on 03/Nov/17 $${Prove}\:{that}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}{r}.^{{n}} {C}_{{r}} \:{z}^{{r}} \:=\:{nz}\left(\mathrm{1}\:+\:{z}\right)^{{n}−\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89178 by necxxx last updated on 15/Apr/20 $${If}\:{z}\left({z}^{\mathrm{2}} +\mathrm{3}{x}\right)+\mathrm{3}{y}=\mathrm{0}\:{prove}\:{that}\: \\ $$$$\frac{\partial^{\mathrm{2}} {z}}{\partial{x}^{\mathrm{2}} }\:+\:\frac{\partial^{\mathrm{2}} {z}}{\partial{y}^{\mathrm{2}} }=\:\frac{\mathrm{2}{z}\left({x}−\mathrm{1}\right)}{\left({z}^{\mathrm{2}} +{x}\right)^{\mathrm{3}} } \\ $$$$ \\ $$$$ \\ $$$${please}\:{help}.…
Question Number 89172 by M±th+et£s last updated on 15/Apr/20 Answered by mahdi last updated on 15/Apr/20 $$\left(\frac{\mathrm{x}^{\mathrm{1}} .\mathrm{x}^{\frac{−\mathrm{b}}{\mathrm{a}}} .\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{a}}} .\mathrm{x}^{\frac{\mathrm{b}}{\mathrm{a}^{\mathrm{2}} }} }{\mathrm{x}^{\frac{\mathrm{b}}{\mathrm{a}^{\mathrm{2}} }} .\mathrm{x}^{\frac{\mathrm{a}}{\mathrm{a}}} }\right)^{\frac{\mathrm{1}}{\mathrm{b}−\mathrm{1}}}…
Question Number 154710 by mathdanisur last updated on 20/Sep/21 $$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} }{\:\sqrt[{\boldsymbol{\mathrm{n}}+\mathrm{1}}]{\mathrm{2}\left(\mathrm{n}+\mathrm{1}\right)!}}\:-\:\frac{\mathrm{n}^{\mathrm{2}} }{\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{2n}!}}\right)\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 23632 by ajfour last updated on 02/Nov/17 Commented by mrW1 last updated on 03/Nov/17 $$\alpha_{\mathrm{A}} =\frac{\mathrm{d}\omega_{\mathrm{A}} }{\mathrm{dt}}=\frac{\mathrm{d}\omega_{\mathrm{A}} }{\mathrm{d}\theta}×\frac{\mathrm{d}\theta}{\mathrm{dt}}=\frac{\mathrm{d}\omega_{\mathrm{A}} }{\mathrm{d}\theta}×\omega\neq\frac{\mathrm{d}\omega_{\mathrm{A}} }{\mathrm{d}\theta}×\omega_{\mathrm{A}} \\ $$ Commented…
Question Number 89161 by M±th+et£s last updated on 15/Apr/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}\left({sin}\left({x}\right)\right){dx} \\ $$ Commented by niroj last updated on 15/Apr/20 $$\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{log}\:\mathrm{sin}\:\mathrm{x}\:\mathrm{dx}…..\left(\mathrm{i}\right) \\…
Question Number 23617 by Tinkutara last updated on 02/Nov/17 $$\mathrm{The}\:\mathrm{system}\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{rest}.\:\mathrm{All} \\ $$$$\mathrm{surfaces}\:\mathrm{are}\:\mathrm{smooth}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\theta\:\mathrm{at} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{wedge}\:\mathrm{is} \\ $$$$\mathrm{maximum}.\:\left(\mathrm{given}\:\frac{{M}}{{m}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Commented by Tinkutara last updated on 02/Nov/17…
Question Number 89153 by Jidda28 last updated on 15/Apr/20 $$\mathrm{If}\:\mathrm{P}=\frac{\mathrm{RE}^{\mathrm{2}} }{\left(\mathrm{R}+\mathrm{B}\right)^{\mathrm{2}} }\:\mathrm{make}\:\mathrm{R}\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formula}. \\ $$ Answered by MJS last updated on 15/Apr/20 $${p}\left({r}+{b}\right)^{\mathrm{2}} ={re}^{\mathrm{2}} \\ $$$$\left({r}+{b}\right)^{\mathrm{2}}…
Question Number 23612 by Joel577 last updated on 02/Nov/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{2}\:\mathrm{digits}\:\mathrm{from} \\ $$$$\mathrm{20}^{\mathrm{17}} \:+\:\mathrm{17}^{\mathrm{20}} \\ $$ Commented by Rasheed.Sindhi last updated on 02/Nov/17 $$\mathrm{20}^{\mathrm{17}} =\left(\mathrm{2}×\mathrm{10}\right)^{\mathrm{17}} =\mathrm{2}^{\mathrm{17}}…
Question Number 89146 by M±th+et£s last updated on 15/Apr/20 $$\left.\mathrm{1}\right)\int{x}\sqrt{\frac{{x}−\mathrm{2}}{{x}+\mathrm{1}}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$$$\left.\mathrm{3}\right)\int\sqrt{−{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}\:{dx} \\ $$ Commented by mathmax by abdo last updated…