Question Number 201848 by cortano12 last updated on 14/Dec/23 Answered by dimentri last updated on 14/Dec/23 $$\:\:\mathrm{1820}\:=\:\mathrm{2}^{\mathrm{2}} ×\mathrm{5}×\mathrm{7}×\mathrm{13} \\ $$$$\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{factors} \\ $$$$\:\mathrm{from}\:\mathrm{1820}\:=\:\underset{\mathrm{i}=\mathrm{0}} {\overset{\mathrm{5}} {\sum}}\begin{pmatrix}{\mathrm{5}}\\{\mathrm{i}}\end{pmatrix}\:=\:\mathrm{2}^{\mathrm{5}} =\:\mathrm{32}…
Question Number 201882 by hardmath last updated on 14/Dec/23 Commented by hardmath last updated on 14/Dec/23 $$ \\ $$If angleABC=45°, angleADC=60°,DC = 2BD, then find…
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Question Number 201846 by cortano12 last updated on 14/Dec/23 $$\:\:\: \\ $$ Commented by Frix last updated on 14/Dec/23 $$\mathrm{Seriously}??? \\ $$$$\mathrm{3184}:\mathrm{2}=\mathrm{1592} \\ $$$$\mathrm{1592}:\mathrm{2}=\mathrm{796} \\…
Question Number 201873 by sonukgindia last updated on 14/Dec/23 Answered by witcher3 last updated on 14/Dec/23 $$\mathrm{Re}\left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{e}^{\mathrm{i}\theta} }\right)=\frac{\mathrm{1}+\mathrm{e}^{−\mathrm{i}\theta} }{\left(\mathrm{1}+\mathrm{e}^{\mathrm{i}\theta} \right)\left(\mathrm{1}+\mathrm{e}^{−\mathrm{i}\theta} \right)}=\frac{\mathrm{1}+\mathrm{cos}\left(\theta\right)}{\mathrm{2}+\mathrm{2cos}\left(\theta\right)}=\frac{\mathrm{1}}{\mathrm{2}};\forall\theta\in\mathbb{R}−\left\{\left(\mathrm{1}+\mathrm{2k}\right)\pi\right\} \\ $$$$\mathrm{I}==\frac{\varphi^{\mathrm{3}} −\mathrm{1}}{\mathrm{2}} \\…
Question Number 201839 by depressiveshrek last updated on 14/Dec/23 Commented by depressiveshrek last updated on 14/Dec/23 $${The}\:{last}\:{one}\:{means}: \\ $$$$\underset{{i}=\mathrm{0}} {\overset{{k}} {\sum}}{i}^{\mathrm{2}} \begin{pmatrix}{{k}}\\{{i}}\end{pmatrix}={k}\left({k}+\mathrm{1}\right)\mathrm{2}^{{k}−\mathrm{2}} \\ $$ Terms…
Question Number 201864 by ajfour last updated on 14/Dec/23 $$\left({ct}^{\mathrm{2}} −\frac{\mathrm{1}}{{ct}^{\mathrm{2}} }+\sqrt{\mathrm{2}}\right)^{\mathrm{2}} ={c}^{\mathrm{2}} \left({t}^{\mathrm{4}} +\frac{\mathrm{1}}{{t}^{\mathrm{4}} }\right) \\ $$$${Find}\:\:{t}={f}\left({c}\right). \\ $$ Commented by Frix last updated…
Question Number 201860 by MrGHK last updated on 14/Dec/23 $$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}} }{\boldsymbol{\mathrm{n}}+\mathrm{1}}=?? \\ $$ Answered by mnjuly1970 last updated on 14/Dec/23 $$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 201857 by cortano12 last updated on 14/Dec/23 $$\:\:\mathrm{If}\:{a},{b},{c},{d},{e}\:\mathrm{are}\:\mathrm{thr}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$$\:\:\mathrm{2x}^{\mathrm{5}} −\mathrm{3x}^{\mathrm{3}} +\mathrm{2x}−\mathrm{7}=\mathrm{0}\:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{cyc}} {\prod}\left({a}^{\mathrm{3}} −\mathrm{1}\right)\: \\ $$ Commented by Frix last updated…