Question Number 203497 by ajfour last updated on 20/Jan/24 $${x}^{\mathrm{4}} +{cx}+{d}=\mathrm{0} \\ $$$${then}\:\:{find}\:{p}\:\:{from} \\ $$$${p}^{\mathrm{6}} −\mathrm{4}\left(\frac{{d}^{\:\mathrm{3}} }{{c}^{\mathrm{4}} }\right)^{\mathrm{1}/\mathrm{3}} {p}^{\mathrm{2}} −\mathrm{1}=\mathrm{0} \\ $$$${x}=\frac{{c}^{\mathrm{1}/\mathrm{3}} }{\mathrm{2}}\left({p}\pm\sqrt{−{p}^{\mathrm{2}} −\frac{\mathrm{8}}{{p}}}\:\right) \\…
Question Number 203448 by hardmath last updated on 19/Jan/24 $$\mathrm{y}\:=\:\mathrm{sin3x}−\mathrm{ln}\left(\mathrm{3x}+\mathrm{1}\right)+\mathrm{3}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Commented by hardmath last updated on 19/Jan/24 $$ \\ $$find…
Question Number 203445 by mathlove last updated on 19/Jan/24 Commented by mr W last updated on 19/Jan/24 $$\Rightarrow{Q}\mathrm{203387} \\ $$ Terms of Service Privacy Policy…
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 203378 by Calculusboy last updated on 18/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
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 203424 by Calculusboy last updated on 18/Jan/24 Answered by Rasheed.Sindhi last updated on 19/Jan/24 $${x}+{y}=\mathrm{2}^{{x}−{y}} \:…\left({i}\right) \\ $$$$\left({x}+{y}\right)^{{x}−{y}} =\mathrm{2}…\left({ii}\right) \\ $$$$\left({ii}\right)/\left({i}\right):\:\left({x}+{y}\right)^{{x}−{y}−\mathrm{1}} =\mathrm{2}^{\mathrm{1}−{x}+{y}} \\…
Question Number 203357 by Calculusboy last updated on 17/Jan/24 $$\boldsymbol{{For}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\mathrm{5}−\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{4}}−\frac{\mathrm{5}}{\mathrm{8}}+\centerdot\centerdot\centerdot+\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} \mathrm{5}}{\mathrm{2}^{\boldsymbol{{n}}−\mathrm{1}} } \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{an}}\:\boldsymbol{{expression}}\:\boldsymbol{{for}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{first}} \\ $$$$\boldsymbol{{n}}\:\boldsymbol{{terms}}.\:\boldsymbol{{Also}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\boldsymbol{{converges}}, \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{to}}\:\infty. \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 203352 by Mingma last updated on 17/Jan/24 Answered by witcher3 last updated on 17/Jan/24 $$\mathrm{sin}\left(\mathrm{2x}\right)=\mathrm{0}\Rightarrow\mathrm{x}=\frac{\mathrm{k}\pi}{\mathrm{2}},\mathrm{k}\in\mathbb{Z} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{4}=\mathrm{x}^{\mathrm{2}} −\left(\mathrm{1}+\mathrm{4}\right)\mathrm{x}+\left(\mathrm{1}.\mathrm{4}\right)=\mathrm{0}\Rightarrow\mathrm{x}\in\left\{\mathrm{1},\mathrm{4}\:\right\} \\ $$$$\mathrm{X}=\mathbb{R}−\left(\left\{\mathrm{1},\mathrm{4}\right\}\cup\left\{\frac{\mathrm{k}\pi}{\mathrm{2}},\mathrm{k}\in\mathbb{Z}\right\}\right) \\ $$…