Question Number 67461 by mathmax by abdo last updated on 27/Aug/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{p}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{p}} }{\left(\mathrm{2}{p}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 67454 by Aditya789 last updated on 27/Aug/19 Commented by mathmax by abdo last updated on 27/Aug/19 $${here}\:{C}_{{r}} \:{mean}\:{C}_{{n}} ^{{r}} \:\:\:\:\:\:{we}\:{have}\:\:\sum_{{r}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{r}}…
Question Number 132991 by aurpeyz last updated on 17/Feb/21 $${A}\:{convex}\:{lens}\:{of}\:{focal}\:{length}\:\mathrm{10}{cm} \\ $$$${is}\:{used}\:{to}\:{form}\:{a}\:{real}\:{image}\:{which}\:{is} \\ $$$${half}\:{the}\:{size}\:{of}\:{the}\:{object}.\:{how}\:{far} \\ $$$${from}\:{the}\:{object}\:{is}\:{the}\:{image}??? \\ $$ Commented by aurpeyz last updated on 17/Feb/21…
Question Number 132987 by mnjuly1970 last updated on 17/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{mathematical}\:\:{analysis}… \\ $$$$\:{prove}\:\:{that}::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{3}} }{dx}=\frac{\mathrm{3}\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\ast\ast\ast\ast………. \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 132977 by Raxreedoroid last updated on 17/Feb/21 $$\mathrm{Show}\:\mathrm{that}: \\ $$$$\:^{{n}} {C}_{{r}} =\frac{\underset{{k}=\mathrm{0}} {\overset{{r}−\mathrm{1}} {\prod}}{n}−{k}}{{r}!} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132972 by rexford last updated on 17/Feb/21 Answered by Ar Brandon last updated on 17/Feb/21 $$\begin{vmatrix}{\mathrm{i}}&{\mathrm{j}}&{\mathrm{k}}\\{\mathrm{1}}&{−\mathrm{2}}&{\mathrm{3}}\\{\mathrm{1}}&{−\mathrm{1}}&{−\mathrm{2}}\end{vmatrix}=\mathrm{7i}+\mathrm{5j}+\mathrm{k} \\ $$ Commented by rexford last updated…
Question Number 1902 by Rasheed Soomro last updated on 23/Oct/15 $${f}^{\:\mathrm{2}} \left({x}\right)−{f}\left({x}^{\mathrm{2}} \right)=\mathrm{2}\:,\:{f}^{\:\mathrm{2}} \left({x}\right)\:{stands}\:{for}\:\left[{f}\left({x}\right)\right]^{\mathrm{2}} \\ $$$${f}\left({x}\right)=? \\ $$$$\left({If}\:{possible}\:{solve}\:{stepwise}\right) \\ $$ Commented by 123456 last updated…
Question Number 1899 by Yozzy last updated on 22/Oct/15 $${Consider}\:{the}\:{system}\:{of}\:{equations} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{yz}+{zx}−\mathrm{5}{xy}=\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{yz}−{zx}+\mathrm{2}{xy}=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{yz}−\mathrm{2}{zx}+\mathrm{6}{xy}=\mathrm{3}. \\ $$$${Show}\:{that}\:{xyz}=\pm\mathrm{6}\: \\ $$$${and}\:{find}\:{the}\:{possible}\:{values} \\ $$$${of}\:{x},{y}\:{and}\:{z}. \\ $$ Commented…
Question Number 1898 by 123456 last updated on 22/Oct/15 $$\frac{{df}}{{dt}}=\alpha{f}+\beta{t}+\gamma \\ $$$${f}\left({t}\right)=?? \\ $$ Answered by Yozzy last updated on 22/Oct/15 $$\frac{{df}}{{dt}}=\alpha{f}+\beta{t}+\gamma\:\:\:{where}\:{I}\:{assume}\:{that}\:\alpha,\beta,\gamma\:{are}\:{constants}.\:{This}\:{equation}\:{may}\:{be} \\ $$$${rewritten}\:{as}\:\:\:\:\:\frac{{df}}{{dt}}−\alpha{f}=\beta{t}+\gamma\:\:\left(\ast\right).\:{The}\:{equation}\:{is}\:{a}\:{first}\:{order}\:{linear}\:{non}−{homogeneous} \\…
Question Number 132971 by metamorfose last updated on 17/Feb/21 $$\:\:{Lim}_{{x}\rightarrow\left(\frac{\pi}{\mathrm{2}}\right)^{−\:\:\:} } \frac{\lfloor{sin}\left({x}\right)\rfloor}{{cos}\left({x}\lfloor{x}\rfloor\right)} \\ $$ Answered by mnjuly1970 last updated on 18/Feb/21 $${ans}:\frac{\mathrm{0}}{\mathrm{0}^{+} }=\mathrm{0} \\ $$…