Question Number 98192 by behi83417@gmail.com last updated on 12/Jun/20 Commented by bemath last updated on 12/Jun/20 $$\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} −\mathrm{xy}=\mathrm{133}\: \\ $$$$\mathrm{set}\:\sqrt{\mathrm{xy}}\:=\:\mathrm{u}\:\&\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{v} \\ $$$$\Leftrightarrow\mathrm{v}^{\mathrm{2}} −\mathrm{u}^{\mathrm{2}} \:=\:\mathrm{133}\:\&\:\mathrm{v}+\mathrm{u}\:=\:\mathrm{19} \\…
Question Number 163730 by HongKing last updated on 09/Jan/22 $$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\:\int\:\frac{\mathrm{sin}\left(\mathrm{x}\right)\:+\:\sqrt{\mathrm{3}}\:\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{sin}\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$ Answered by cortano1 last updated on 10/Jan/22 $$\:=\mathrm{2}\int\:\frac{\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{3}}\right)}{\mathrm{sin}\:\left(\mathrm{3}{x}\right)}\:{dx} \\ $$$$\:=\:\mathrm{2}\int\:\frac{{d}\left(\mathrm{tan}\:\theta\right)}{\mathrm{3}−\mathrm{tan}\:^{\mathrm{2}} \theta}\:;\:\theta={x}+\frac{\pi}{\mathrm{6}} \\ $$$$\:=\:\frac{\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{3}}\:\mathrm{tanh}\:^{−\mathrm{1}}…
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Question Number 32650 by keklou last updated on 30/Mar/18 $${f}\left({x}\right)=\mathrm{8}{x}−\mathrm{34}\sqrt{\mathrm{25}−\mathrm{4}\:\frac{\mathrm{3}}{\mathrm{2}}} \\ $$ Answered by MJS last updated on 30/Mar/18 $${f}\left({x}\right)=\mathrm{8}{x}−\mathrm{17}\sqrt{\mathrm{78}} \\ $$ Answered by Rio…
Question Number 32648 by jasno91 last updated on 30/Mar/18 Answered by Joel578 last updated on 30/Mar/18 $$\mathrm{157}\frac{\mathrm{1}}{\mathrm{4}}\::\:\mathrm{18}\frac{\mathrm{1}}{\mathrm{2}}\:=\:\frac{\mathrm{629}}{\mathrm{4}}\::\:\frac{\mathrm{37}}{\mathrm{2}}\:=\:\frac{\mathrm{629}}{\mathrm{4}}\:×\:\frac{\mathrm{2}}{\mathrm{37}}\:=\:\frac{\mathrm{17}}{\mathrm{2}}\:\mathrm{kg} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 32647 by jasno91 last updated on 30/Mar/18 Answered by Joel578 last updated on 30/Mar/18 $$\mathrm{15}\frac{\mathrm{5}}{\mathrm{6}}\::\:\mathrm{6}\frac{\mathrm{1}}{\mathrm{3}}\:=\:\frac{\mathrm{95}}{\mathrm{6}}\::\:\frac{\mathrm{19}}{\mathrm{3}}\:=\:\frac{\mathrm{95}}{\mathrm{6}}\:×\:\frac{\mathrm{3}}{\mathrm{19}}\:=\:\frac{\mathrm{5}}{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 163718 by HongKing last updated on 09/Jan/22 $$\mathrm{let}\:\:\mathrm{m}\in\mathbb{N}\:\:\mathrm{and}\:\:\mathrm{0}<\mathrm{x}<\mathrm{m} \\ $$$$\mathrm{if}\:\:\:\boldsymbol{\mathrm{i}}\:=\:\left[\frac{\left(\mathrm{m}\:+\:\mathrm{1}\right)\mathrm{x}}{\mathrm{x}\:+\:\mathrm{1}}\right] \\ $$$$\mathrm{prove}\:\mathrm{that}\:\:\:\mathrm{2}\begin{pmatrix}{\mathrm{m}}\\{\:\:\mathrm{i}}\end{pmatrix}\:\geqslant\:\mathrm{x}^{\boldsymbol{\mathrm{m}}-\boldsymbol{\mathrm{i}}} \\ $$$$\mathrm{where}\:\left[\boldsymbol{\mathrm{x}}\right]\:\mathrm{is}\:\mathrm{integer}\:\mathrm{part}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}\:\mathrm{and}\:\begin{pmatrix}{\mathrm{m}}\\{\:\:\mathrm{i}}\end{pmatrix} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{binomial}\:\mathrm{coefficient} \\ $$ Terms of Service Privacy Policy…
Question Number 163719 by HongKing last updated on 09/Jan/22 $$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{limit}: \\ $$$$\Phi\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:-\:\frac{\mathrm{1}}{\mathrm{n}!}\:\centerdot\:\frac{\mathrm{d}^{\boldsymbol{\mathrm{n}}} }{\mathrm{dx}^{\boldsymbol{\mathrm{n}}} }\:\left(\frac{\mathrm{e}^{\boldsymbol{\mathrm{x}}-\mathrm{1}} }{\mathrm{x}\:-\:\mathrm{1}}\right)\mid_{\boldsymbol{\mathrm{x}}=\mathrm{0}} \\ $$ Answered by Mathspace last updated on 09/Jan/22…
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Question Number 32632 by Tinkutara last updated on 29/Mar/18 Commented by mrW2 last updated on 30/Mar/18 $$\left(\mathrm{1}+{x}^{\mathrm{12}} +{x}^{\mathrm{24}} +{x}^{\mathrm{36}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{12}} \\ $$$${C}_{\mathrm{10}} ^{\mathrm{12}} +{C}_{\mathrm{4}}…