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 $$\left(\mathrm{1}+{x}^{\mathrm{12}} +{x}^{\mathrm{24}} +{x}^{\mathrm{36}} \right)\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{12}} \\ $$$${C}_{\mathrm{10}} ^{\mathrm{12}} +{C}_{\mathrm{4}}…
Question Number 32629 by rahul 19 last updated on 29/Mar/18 $$\boldsymbol{{I}}{f}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{9}\:,\:\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} =\mathrm{16}, \\ $$$${then}\:\boldsymbol{{maximum}}\:{value}\:{of}\: \\ $$$$\mathrm{4}{a}^{\mathrm{2}} {x}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{12}{abxy}\:{is}\:? \\ $$…
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Question Number 32584 by Tinkutara last updated on 28/Mar/18 Answered by Joel578 last updated on 28/Mar/18 $$\mathrm{10}! \\ $$ Commented by Tinkutara last updated on…
Question Number 163651 by mathlove last updated on 09/Jan/22 $${if}\:\:\left({a}−\mathrm{2}{b}\right)^{\mathrm{2}} +\left({b}−\mathrm{2}{c}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$${find}\:\:{volve}\:\:\frac{\left({b}+{c}−{a}\right)^{\mathrm{3}} }{{abc}}=? \\ $$ Commented by cortano1 last updated on 09/Jan/22 $$\left.\begin{matrix}{{a}=\mathrm{2}{b}\Rightarrow{b}=\frac{\mathrm{1}}{\mathrm{2}}{a}}\\{{b}=\mathrm{2}{c}\Rightarrow{c}=\frac{\mathrm{1}}{\mathrm{4}}{a}}\end{matrix}\right\}\:\Rightarrow\frac{−\frac{\mathrm{1}}{\mathrm{64}}{a}^{\mathrm{3}}…
Question Number 32563 by rahul 19 last updated on 27/Mar/18 $$\boldsymbol{{T}}{he}\:{set}\:{of}\:{values}\:{of}\:'{a}'\:{for}\:{which}\: \\ $$$${all}\:{the}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{4sin}\:^{\mathrm{4}} {x}+{a}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{3}=\mathrm{0}\:{are}\:{real}\:{and}\: \\ $$$${distinct}\:{is}\:? \\ $$ Commented by rahul 19…