Question Number 95106 by bobhans last updated on 23/May/20 $$\begin{cases}{{x}+{y}+{z}\:=\:\mathrm{7}}\\{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:=\:\mathrm{49}}\\{{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \:=\:\mathrm{7}}\end{cases} \\ $$$${find}\:{x};\:\mathrm{y}\:;\:{z}\: \\ $$ Answered by john santu last…
Question Number 95093 by I want to learn more last updated on 22/May/20 $$\mathrm{Solve}: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{y}^{\mathrm{2}} \:\:=\:\:\mathrm{13}\:\:\:\:\:\:\:\:\:\:…….\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{2x}^{\mathrm{2}} \:\:+\:\:\mathrm{3y}\:\:=\:\:\mathrm{2xy}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:…….\:\left(\mathrm{ii}\right) \\ $$ Answered…
Question Number 95062 by mr W last updated on 22/May/20 $${solve}\:{for}\:{x},\:{y},\:{z}\:\in\mathbb{C}\:{such}\:{that} \\ $$$$\mid{x}\mid=\mid{y}\mid=\mid{z}\mid=\mathrm{1} \\ $$$${x}+{y}+{z}=\mathrm{1} \\ $$$${xyz}=\mathrm{1} \\ $$ Commented by EmericGent last updated on…
Question Number 29520 by bbbbbb last updated on 09/Feb/18 $$\mathrm{to}\:\mathrm{make}\:\mathrm{an}\:\mathrm{open}\:\mathrm{fish}\:\mathrm{tank}\:\mathrm{a}\:\mathrm{glass}\:\mathrm{sheet}\:\mathrm{of}\: \\ $$$$\mathrm{2mm}\:\mathrm{gauge}\:\mathrm{is}\:\mathrm{used}\:.\mathrm{the}\:\mathrm{outer}\:\mathrm{length} \\ $$$$,\mathrm{breadth}\:\mathrm{and}\:\mathrm{height}\:\mathrm{are}\:\mathrm{60}.\mathrm{4}\:,\:\mathrm{40}.\mathrm{4},\: \\ $$$$\mathrm{40}.\mathrm{2}\:\mathrm{respectively}\:.\mathrm{how}\:\mathrm{much}\:\mathrm{maximum} \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{water}\:\mathrm{will}\:\mathrm{be}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{it}\:? \\ $$$$ \\ $$ Answered by Rasheed.Sindhi…
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Question Number 95048 by Tony Lin last updated on 22/May/20 $${a}_{\mathrm{1}} =−\frac{\mathrm{1}}{\mathrm{30}} \\ $$$${a}_{\mathrm{2}} =−\frac{\mathrm{1}}{\mathrm{12}} \\ $$$${a}_{\mathrm{3}} =−\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${a}_{\mathrm{4}} =−\frac{\mathrm{7}}{\mathrm{24}} \\ $$$${a}_{\mathrm{5}} =−\frac{\mathrm{7}}{\mathrm{15}} \\…
Question Number 160564 by Avijit007 last updated on 02/Dec/21 $${if}\:{the}\:{roots}\:{of}\:{th}\mathrm{e}\:{equation}\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0} \\ $$$${are}\:{in}\:{the}\:{ratio}\:\mathrm{3}:\mathrm{4},{then}\:{show}\:{that}\: \\ $$$$\mathrm{12b}^{\mathrm{2}} =\mathrm{49ac}. \\ $$ Commented by otchereabdullai@gmail.com last updated on 02/Dec/21…
Question Number 160560 by HongKing last updated on 01/Dec/21 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on…
Question Number 95014 by I want to learn more last updated on 22/May/20 $$\boldsymbol{\mathrm{If}}\:\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:−\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \:\:\:=\:\:\:\mathrm{6},\:\:\:\:\:\:\:\boldsymbol{\mathrm{and}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\mathrm{0}} \:\:=\:\:\:\mathrm{7} \\ $$$$\boldsymbol{\mathrm{Find}}\:\:\:\:\:\boldsymbol{\mathrm{y}}_{\boldsymbol{\mathrm{n}}} \\ $$ Commented by prakash jain…
Question Number 160550 by HongKing last updated on 01/Dec/21 $$\mathrm{if}\:\:\:\mathrm{x};\mathrm{y}\in\left(\mathrm{0};\frac{\pi}{\mathrm{2}}\right)\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{sin}\boldsymbol{\mathrm{x}}\:+\:\mathrm{sin}\boldsymbol{\mathrm{y}}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\boldsymbol{\mathrm{x}}\:+\:\mathrm{cos}\boldsymbol{\mathrm{y}}}}\:\leqslant\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$ Answered by mr W last updated on 02/Dec/21 $${LHS} \\ $$$$\leqslant\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{sin}\:{x}\:\mathrm{sin}\:{y}}}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{cos}\:{x}\:\mathrm{cos}\:{y}}}}…