Question Number 116452 by zakirullah last updated on 04/Oct/20 Answered by bobhans last updated on 04/Oct/20 $$\Rightarrow\mathrm{the}\:\mathrm{number}\:\begin{cases}{\mathrm{x}}\\{\mathrm{9x}}\end{cases}\:\Leftrightarrow\:\mathrm{9x}^{\mathrm{2}} =\mathrm{15},\mathrm{876} \\ $$$$\mathrm{x}\:=\:\sqrt{\frac{\mathrm{15},\mathrm{876}}{\mathrm{9}}}\:=\:\frac{\mathrm{126}}{\mathrm{3}}\:=\:\mathrm{42} \\ $$ Answered by nimnim…
Question Number 50908 by Smail last updated on 22/Dec/18 $${Given}\:{f}\left({x}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\:^{{n}} {C}_{{k}} {sin}\left({kx}\right){cos}\left(\left({n}−{k}\right){x}\right) \\ $$$${Find}\:{a}\:{simple}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left({Your}\:{answer}\:{should}\:{be}\:{written}\:{like}\:{c}\left({n}\right).{g}\left({nx}\right)\right)\: \\ $$ Answered by Smail last updated…
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Question Number 181923 by manxsol last updated on 02/Dec/22 Answered by SEKRET last updated on 02/Dec/22 $$\:\:\:\boldsymbol{\mathrm{xlog}}\mathrm{2}\left(\boldsymbol{\mathrm{y}}\right)=\mathrm{6}\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{y}}=\mathrm{2}^{\frac{\mathrm{6}}{\boldsymbol{\mathrm{x}}}} \\ $$$$\:\left(\frac{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}\right)\boldsymbol{\mathrm{log}}\mathrm{2}\left(\boldsymbol{\mathrm{y}}\right)=\mathrm{4} \\ $$$$\:\:\frac{\mathrm{6}}{\boldsymbol{\mathrm{x}}}=\:\frac{\mathrm{4}\boldsymbol{\mathrm{x}}−\mathrm{4}\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}\:\:\:\:\:\:\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{6}\boldsymbol{\mathrm{y}}=\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{xy}} \\ $$$$\:\:\boldsymbol{\mathrm{y}}\left(\mathrm{6}+\mathrm{4}\boldsymbol{\mathrm{x}}\right)=\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{\mathrm{x}}\:\:\:\:\:\boldsymbol{\mathrm{y}}=\:\frac{\boldsymbol{\mathrm{x}}\left(\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\right)}{\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}\right)}…
Question Number 181903 by Shrinava last updated on 01/Dec/22 Answered by mr W last updated on 02/Dec/22 $${at}\:{z}: \\ $$$${the}\:{cross}−{section}\:{is} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}}…
Question Number 181902 by Acem last updated on 01/Dec/22 Answered by Rasheed.Sindhi last updated on 02/Dec/22 $$\left({x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:=\mathrm{185}….\left({i}\right) \\ $$$$\left({x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}}…
Question Number 181897 by Acem last updated on 01/Dec/22 Answered by mr W last updated on 02/Dec/22 $${T}_{{k}} =\frac{{k}^{\mathrm{2}} }{{k}^{\mathrm{2}} −\mathrm{10}{k}+\mathrm{50}}=\frac{{k}^{\mathrm{2}} }{\left({k}−\mathrm{5}\right)^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} } \\…
Question Number 50825 by behi83417@gmail.com last updated on 20/Dec/18 $$\boldsymbol{\mathrm{x}}^{\mathrm{4}} =\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\boldsymbol{\mathrm{by}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{y}}^{\mathrm{4}} =\boldsymbol{\mathrm{bx}}^{\mathrm{2}} +\boldsymbol{\mathrm{ay}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}},\:\boldsymbol{\mathrm{y}}.\:\left[\boldsymbol{\mathrm{a}}\:,\boldsymbol{\mathrm{b}}\in\:\boldsymbol{\mathrm{R}};\:\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\neq\mathrm{0}\right] \\ $$ Answered by mr W last…
Question Number 116358 by bemath last updated on 03/Oct/20 $$\mathrm{Given}\:\mathrm{that}\:\sqrt[{\mathrm{3}\:}]{\mathrm{17}−\frac{\mathrm{27}}{\mathrm{4}}\sqrt{\mathrm{6}}}\:\mathrm{and}\:\sqrt[{\mathrm{3}\:}]{\mathrm{17}+\frac{\mathrm{27}}{\mathrm{4}}\sqrt{\mathrm{6}}} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{ax}+\mathrm{b}\:=\:\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{ab}. \\ $$ Answered by MJS_new last updated on 03/Oct/20 $$\sqrt[{\mathrm{3}}]{\mathrm{17}\pm\frac{\mathrm{27}\sqrt{\mathrm{6}}}{\mathrm{4}}}=\mathrm{2}\pm\frac{\sqrt{\mathrm{6}}}{\mathrm{2}}…
Question Number 116323 by bobhans last updated on 03/Oct/20 $$\left(\mathrm{1}\right)\mathrm{Let}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{ab}}{\mathrm{a}+\mathrm{b}}\:=\:\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{bc}}{\mathrm{b}+\mathrm{c}}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{and}\:\frac{\mathrm{ac}}{\mathrm{a}+\mathrm{c}}\:=\:\frac{\mathrm{1}}{\mathrm{5}}.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{24abc}}{\mathrm{ab}+\mathrm{ac}+\mathrm{bc}}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Let}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{be}\:\mathrm{two}\:\mathrm{real}\:\mathrm{number}\:\mathrm{that} \\ $$$$\mathrm{satisfy}\:\mathrm{p}.\mathrm{q}=\mathrm{2013}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\left(\mathrm{p}+\mathrm{q}\right)^{\mathrm{2}} \:? \\ $$ Answered by…