Question Number 145718 by mathdanisur last updated on 07/Jul/21 $${F}_{\mathrm{1}} \:=\:\mathrm{3}\:{N}\:\:;\:\:{F}_{\mathrm{2}} \:=\:\mathrm{4}\:{N}\:\:;\:{F}_{\mathrm{3}} \:=\:\mathrm{6}\:{N} \\ $$$${F}_{\boldsymbol{{max}}} \:\:-\:\:{F}_{\boldsymbol{{min}}} =\:? \\ $$ Commented by mathdanisur last updated on…
Question Number 80160 by peter frank last updated on 31/Jan/20 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{3}} }{{e}^{\mathrm{2}{x}} −{e}^{{x}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 80161 by peter frank last updated on 01/Feb/20 $${Find}\:{the}\:{relation}\:{between} \\ $$$${q}\:{and}\:{r}\:\:{so}\:\:{that} \\ $$$${x}^{\mathrm{3}} +\mathrm{3}{px}^{\mathrm{2}} +{qx}+{r}\:{is}\:{a}\:{perfect} \\ $$$${cube}\:{for}\:{all}\:\:{value}\:{of}\:{x} \\ $$ Commented by peter frank…
Question Number 145687 by mathdanisur last updated on 07/Jul/21 $${if}\:\:{q}\geqslant\mathrm{3}\:;\:{a}>-\mathrm{1}\:\:{then}: \\ $$$$\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+\mathrm{2}{a}\right)\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}-\mathrm{2}} \:\geqslant\:\mathrm{1}+{qa} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 80144 by behi83417@gmail.com last updated on 31/Jan/20 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}: \\ $$$$\frac{\sqrt{\boldsymbol{\mathrm{x}}}+\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{x}}+\mathrm{1}}}+\boldsymbol{\mathrm{ax}}^{\mathrm{2}} =\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\mathrm{1}\right)\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right] \\ $$ Commented by john santu last updated on 31/Jan/20 $${let}\:\sqrt{{x}+\mathrm{1}}\:=\:\mathrm{sec}\:{t}…
Question Number 145683 by imjagoll last updated on 07/Jul/21 $$\:\frac{\mathrm{3}\:\sqrt[{\sqrt{\mathrm{4}}}]{\mathrm{360}}\:−\mathrm{2}\:\sqrt[{!\mathrm{3}}]{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}\:=? \\ $$ Answered by puissant last updated on 07/Jul/21 $$\sqrt{\mathrm{4}}=\mathrm{2}\:\:;\:\:!\mathrm{3}=\:\:\mathrm{3}!\mid\frac{\mathrm{1}!}{\mathrm{0}!}−\frac{\mathrm{1}!}{\mathrm{1}!}−\frac{\mathrm{1}!}{\mathrm{2}!}+\frac{\mathrm{1}!}{\mathrm{3}!}\mid \\ $$$$\Rightarrow\frac{\mathrm{3}\sqrt{\mathrm{360}}−\mathrm{2}\sqrt{\mathrm{162}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}}=\frac{\mathrm{18}\sqrt{\mathrm{10}}−\mathrm{18}\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}} \\ $$$$=\frac{\mathrm{18}\left(\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}\right)}{\left(\sqrt{\mathrm{10}}−\sqrt{\mathrm{2}}\right)}\:=\:\mathrm{18}.. \\…
Question Number 80142 by behi83417@gmail.com last updated on 31/Jan/20 $$\mathrm{a}.\:\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\left(\frac{\boldsymbol{\mathrm{k}}^{\mathrm{3}} }{\mathrm{2}^{\boldsymbol{\mathrm{k}}} }\right)=? \\ $$$$\boldsymbol{\mathrm{b}}.\:\:\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:\left(\frac{\boldsymbol{\mathrm{k}}^{\mathrm{3}} +\boldsymbol{\mathrm{k}}^{\mathrm{2}} +\boldsymbol{\mathrm{k}}+\mathrm{1}}{\mathrm{7}^{\boldsymbol{\mathrm{k}}} }\right)=? \\ $$ Answered by…
Question Number 80145 by behi83417@gmail.com last updated on 31/Jan/20 $$\begin{cases}{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}+\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}=\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} }\\{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\in\boldsymbol{\mathrm{R}}\right]}\\{\boldsymbol{\mathrm{ab}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{y}}^{\mathrm{2}} \right)=\boldsymbol{\mathrm{xy}}\left(\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} \right)}\end{cases} \\ $$ Commented by john santu last updated on…
Question Number 80139 by M±th+et£s last updated on 31/Jan/20 Commented by M±th+et£s last updated on 31/Jan/20 $$\left[{Q}\mathrm{80131}\:{Reposted}\right] \\ $$ Commented by mr W last updated…
Question Number 145668 by mathdanisur last updated on 07/Jul/21 $${Compare}: \\ $$$${sin}\left(\mathrm{43}°\right)\:\:{and}\:\:{sin}\left(\mathrm{40}°\right)+{sin}\left(\mathrm{3}°\right) \\ $$ Answered by mr W last updated on 07/Jul/21 $$\mathrm{sin}\:\mathrm{43}°=\mathrm{sin}\:\left(\mathrm{40}+\mathrm{3}\right) \\ $$$$=\mathrm{cos}\:\mathrm{3}×\mathrm{sin}\:\mathrm{40}+\mathrm{cos}\:\mathrm{40}×\mathrm{sin}\:\mathrm{3}…