Question Number 220764 by Nicholas666 last updated on 18/May/25 $$ \\ $$$$\:\:\boldsymbol{\mathrm{L}}=\:\boldsymbol{\mathrm{lim}}\underset{\:\boldsymbol{{n}}\rightarrow\infty} {\:}\left(\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\:\frac{\boldsymbol{{k}}}{\boldsymbol{{n}}^{\mathrm{2}} +\boldsymbol{{k}}^{\mathrm{2}} }\right).\left(\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \boldsymbol{{e}}^{−\boldsymbol{{x}}^{\mathrm{2}} } \boldsymbol{{dx}}\overset{−\mathrm{1}} {\right)}.\left(\underset{\boldsymbol{{m}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{m}}} }{\left(\mathrm{2}\boldsymbol{{m}}+\mathrm{1}\right)\mathrm{3}^{\boldsymbol{{m}}}…
Question Number 220730 by Nicholas666 last updated on 18/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{{x}\left(\mathrm{1}\:−\:{x}\right)\left(\mathrm{1}\:+\:{kx}\right)}}\:{dx}\:,\:\left(−\mathrm{1}\:<\:{k}\:<\:\mathrm{1}\right)\:\:\: \\ $$$$ \\ $$ Answered by SdC355 last updated on 18/May/25…
Question Number 220726 by mr W last updated on 18/May/25 Commented by mr W last updated on 18/May/25 $${an}\:{other}\:{method}\:{for}\:{Q}\mathrm{220630} \\ $$$${without}\:{trigonometry} \\ $$ Commented by…
Question Number 220755 by SdC355 last updated on 18/May/25 $$ \\ $$$$\mathrm{Hmm}….\mathrm{i}\:\mathrm{need}\:\mathrm{a}\:\mathrm{help}… \\ $$$$\mathrm{generalize}\: \\ $$$$\mathcal{L}_{{z}} ^{−\mathrm{1}} \left\{\frac{\mathrm{1}}{{z}^{{n}} +\mathrm{1}}\right\}=\:\oint_{\:{C}} \:\:\frac{{e}^{{zt}} }{{z}^{{n}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$ Terms…
Question Number 220744 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $${each}\:{match}\:{has}\:{three}\:{possible} \\ $$$${results} \\ $$$$\mathrm{12}\:{matches}\:{have}\:\mathrm{3}^{\mathrm{12}} =\mathrm{531}\:\mathrm{441} \\ $$$$\:{possible}\:{results}…
Question Number 220712 by Nicholas666 last updated on 18/May/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}: \\ $$$$\:\:\frac{\mathrm{2}\:{tan}\:\mathrm{2}{A}\:+\:{tan}\:{A}}{\mathrm{4}\:{tan}\:\mathrm{3}{A}\:−\:{tan}\:\mathrm{2}{A}}\:=\:{sin}^{\mathrm{2}} \:{A} \\ $$$$\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 220745 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $${cosx}+{cosy}={a} \\ $$$$\Rightarrow\mathrm{2}{cos}\left(\frac{{x}+{y}}{\mathrm{2}}\right){cos}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={a}…\left(\mathrm{1}\right) \\ $$$$\:{sinx}+{siny}={b} \\ $$$$\Rightarrow\mathrm{2}{sin}\left(\frac{{x}+{y}}{\mathrm{2}}\right){cos}\left(\frac{{x}−{y}}{\mathrm{2}}\right)={b}\:\:….\left(\mathrm{2}\right) \\ $$$$\therefore\:{tan}\left(\frac{{x}+{y}}{\mathrm{2}}\right)=\frac{{b}}{{a}}\:\:\:\:\:\left[\:\:\left(\mathrm{2}\right)\boldsymbol{\div}\left(\mathrm{1}\right)\:\right]…
Question Number 220715 by Noorzai last updated on 18/May/25 Commented by Noorzai last updated on 18/May/25 $${do}\:{you}\:{help}\:{me} \\ $$$$ \\ $$ Answered by SdC355 last…
Question Number 220740 by Spillover last updated on 18/May/25 Answered by mr W last updated on 18/May/25 $$\mathrm{52}\:{cards}:\:\mathrm{26}\:{red}\:{and}\:\mathrm{26}\:{black} \\ $$$${to}\:{select}\:\mathrm{13}\:{cards}\:{there}\:{are}\:{totally} \\ $$$${C}_{\mathrm{13}} ^{\mathrm{52}} \:{possibilities} \\…
Question Number 220741 by Spillover last updated on 18/May/25 Answered by som(math1967) last updated on 18/May/25 $$\:\:^{\mathrm{9}} {P}_{\mathrm{4}} =\mathrm{3024} \\ $$ Commented by Spillover last…