Question Number 215540 by MrGaster last updated on 10/Jan/25 $$\int_{\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \leq\mathrm{1}} \left(\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \right)^{{m}} \left(\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{a}_{{i}} {x}_{{i}} \right)^{\mathrm{2}{k}} \underset{\mathrm{1}\leq{i}\leq{n}} {\prod}{dx}_{{i}} \\ $$…
Question Number 215564 by Wuji last updated on 10/Jan/25 $$\boldsymbol{\mathrm{given}};\:\:\boldsymbol{\mathrm{x}}\sqrt{\boldsymbol{\mathrm{y}}}+\boldsymbol{\mathrm{y}}\sqrt{\boldsymbol{\mathrm{x}}}=\mathrm{630} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{y}}\sqrt{\boldsymbol{\mathrm{y}}}+\boldsymbol{\mathrm{x}}\sqrt{\boldsymbol{\mathrm{x}}}=\mathrm{604} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}} \\ $$ Answered by Frix last updated on 10/Jan/25 $$\sqrt{{x}}={a}+{b}\mathrm{i}\wedge\sqrt{{y}}={a}−{b}\mathrm{i};\:{b}\geqslant\mathrm{0} \\…
Question Number 215535 by MrGaster last updated on 10/Jan/25 $$\int_{\underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} ^{\mathrm{2}} \leq{R}^{\mathrm{2}} } \underset{\mathrm{1}\leq{i}\leq{n}} {\sum}{x}_{{i}} \frac{\partial{f}}{\partial{x}_{{i}} }\underset{\mathrm{1}\leq{i}\leq{n}} {\prod}{dx}_{{i}} =? \\ $$ Answered by MrGaster…
Question Number 215559 by hardmath last updated on 10/Jan/25 $$\sqrt{\mathrm{y}}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{5} \\ $$$$\sqrt{\mathrm{x}}\:\centerdot\:\sqrt{\mathrm{y}}\:=\:\mathrm{8} \\ $$$$\frac{\sqrt{\mathrm{x}}\:\mathrm{y}\:−\:\mathrm{x}\:\sqrt{\mathrm{y}}}{\mathrm{y}\:−\:\mathrm{x}}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 10/Jan/25 $$\sqrt{\mathrm{y}}\:+\sqrt{\mathrm{x}}\:=\mathrm{5}\:;\:\sqrt{\mathrm{x}}\:\sqrt{\mathrm{y}}\:=\mathrm{8} \\…
Question Number 215516 by MrGaster last updated on 09/Jan/25 $$\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\pi^{\mathrm{2}} {n}^{\mathrm{2}} +\mathrm{1}}=\frac{\mathrm{1}}{{e}^{\mathrm{2}} −\mathrm{1}} \\ $$ Answered by mr W last updated…
Question Number 215519 by walterpieuler last updated on 09/Jan/25 $$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{Find}}\:\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)^{\boldsymbol{\mathrm{log}}_{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{y}}}} \frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\:} \boldsymbol{\mathrm{below}}: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{xy}}\:−\:\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$ \\…
Question Number 215528 by alephnull last updated on 09/Jan/25 Commented by mr W last updated on 10/Jan/25 $${this}\:{is}\:{not}\:{a}\:{question},\:{actually}\:{pure} \\ $$$${non}−{sense}\:{with}\:{a}\:{lot}\:{of} \\ $$$${mathematical}\:{symbols}\:{stacked} \\ $$$${together}. \\…
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Question Number 215525 by zetamaths last updated on 09/Jan/25 $$\Phi\::\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R}^{\mathrm{2}} \: \\ $$$$\:\:\:\left({x}.;{y}\right)\mid\rightarrow\left(\mathrm{2}{x}+\mathrm{3}{y}:\mathrm{3}{y}\right) \\ $$$${find} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\Phi\in\mathscr{L}\left(\mathbb{R}^{\mathrm{2}} \right)…
t-33-ab-t-00-ab-Clearing-up-defintions-t-33-a-a-36-3-t-00-a-a-36-0-t-a-a-36-t-a-transformation-of-a-
Question Number 215527 by alephnull last updated on 09/Jan/25 $${t}_{\mathrm{33}} '{ab}+{t}_{\mathrm{00}} '{ab}=? \\ $$$$ \\ $$$$\mathrm{Clearing}\:\mathrm{up}\:\mathrm{defintions}: \\ $$$${t}_{\mathrm{33}} '{a}=\left({a}−\sqrt{\mathrm{36}}\right)×\mathrm{3} \\ $$$${t}_{\mathrm{00}} '{a}=\left({a}−\sqrt{\mathrm{36}}\right)×\mathrm{0} \\ $$$${t}'{a}={a}−\sqrt{\mathrm{36}} \\…