Question Number 203389 by sonukgindia last updated on 18/Jan/24 Answered by mr W last updated on 18/Jan/24 Commented by mr W last updated on 18/Jan/24…
Question Number 203416 by Spillover last updated on 18/Jan/24 Answered by a.lgnaoui last updated on 19/Jan/24 $$\:\: \\ $$$$\:\:\:\boldsymbol{\mathrm{R}}=\mathrm{2}\boldsymbol{\mathrm{r}}+\boldsymbol{\mathrm{BM}}\mathrm{cos}\:\boldsymbol{\alpha}\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\boldsymbol{\mathrm{BM}}\mathrm{sin}\:\boldsymbol{\alpha}=\boldsymbol{\mathrm{r}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\: \\ $$$$\Rightarrow\:\:\begin{cases}{\mathrm{cos}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{R}}−\mathrm{2}\boldsymbol{\mathrm{r}}}{\boldsymbol{\mathrm{BM}}}}\\{\mathrm{sin}\:\boldsymbol{\alpha}=\frac{\boldsymbol{\mathrm{r}}}{\:\boldsymbol{\mathrm{BM}}}}\end{cases}…
Question Number 203417 by hardmath last updated on 18/Jan/24 $$\mathrm{If} \\ $$$$\mid\overline {−\mathrm{z}\:+\:\boldsymbol{\mathrm{i}}\mathrm{z}}\mid\:=\:\mathrm{2}\:\sqrt{\mathrm{13}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}\:=\:\mathrm{1}\:+\:\left(\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\boldsymbol{\mathrm{i}} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{mun}\left(\mathrm{x}\right)\:=\:? \\ $$ Commented by hardmath last updated on…
Question Number 203385 by patrice last updated on 18/Jan/24 Answered by Mathspace last updated on 18/Jan/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\mathrm{1}+{x}^{\mathrm{3}} }\:\Rightarrow{I}=\int_{\mathrm{0}} ^{\mathrm{1}} \sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{3}{n}}…
Question Number 203419 by essaad last updated on 18/Jan/24 Commented by mr W last updated on 18/Jan/24 $${question}\:{is}\:{wrong}!\:{you}\:{can}\:{not} \\ $$$${determine}\:\alpha\:{uniquely}. \\ $$ Commented by essaad…
Question Number 203387 by Noorzai last updated on 18/Jan/24 Answered by Rasheed.Sindhi last updated on 18/Jan/24 $$\mathrm{S}=\frac{\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}+\sqrt{{n}}}\:}{\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\sqrt{\mathrm{10}−\sqrt{{n}}}\:} \\ $$$$\mathrm{S}=\frac{\underset{{n}=\mathrm{1}} {\overset{\mathrm{99}} {\sum}}\frac{\sqrt{\mathrm{100}−{n}}\:}{\:\sqrt{\mathrm{10}−\sqrt{{n}}}}}{\underset{{n}=\mathrm{1}}…
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Question Number 203379 by York12 last updated on 18/Jan/24 $$\mathrm{If}\:{a},{b},{c}\:\in\mathbb{R}^{+} \:\mathrm{with}\:{a}+{b}+{c}=\mathrm{3}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{6}} +{b}^{\mathrm{6}} +\mathrm{3}{c}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{b}^{\mathrm{6}} +{c}^{\mathrm{6}} +\mathrm{3}{a}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{c}^{\mathrm{6}} +{a}^{\mathrm{6}} +\mathrm{3}{b}^{\mathrm{3}} +\mathrm{4}}\leqslant\frac{\mathrm{3}}{\mathrm{3}+\mathrm{2}\left(\sqrt{{ab}}+\sqrt{{bc}}+\sqrt{{ac}}\right)} \\ $$ Terms…
Question Number 203401 by cherokeesay last updated on 18/Jan/24 Answered by MM42 last updated on 18/Jan/24 $$<{B}=\mathrm{30}^{{o}} \\ $$$${AB}=\mathrm{2}\sqrt{\mathrm{3}}×{cos}\mathrm{30}=\mathrm{3} \\ $$$${R}=\sqrt{\mathrm{21}} \\ $$$${EC}=\mathrm{2}\sqrt{\mathrm{3}}×{cos}\mathrm{60}=\sqrt{\mathrm{3}} \\ $$$${r}=\sqrt{\mathrm{3}}×{tan}\mathrm{30}\Rightarrow{r}=\mathrm{1}…