Question Number 98096 by Algoritm last updated on 11/Jun/20 Answered by mathmax by abdo last updated on 11/Jun/20 $$\mathrm{S}\:=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{3n}−\mathrm{1}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\:=_{\mathrm{n}−\mathrm{1}=\mathrm{p}} \:\:\sum_{\mathrm{p}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{3p}+\mathrm{2}}{\mathrm{2}^{\mathrm{p}}…
Question Number 163627 by nurtani last updated on 08/Jan/22 Answered by mr W last updated on 08/Jan/22 $${u}=\frac{\mathrm{1}}{{x}+{y}}\:>\mathrm{0} \\ $$$${v}={xy} \\ $$$$\sqrt{\mathrm{21}{v}}\left(\mathrm{1}−{u}^{\mathrm{2}} \right)=\mathrm{8}\sqrt{\mathrm{2}} \\ $$$${v}=\frac{\mathrm{128}}{\mathrm{21}\left(\mathrm{1}−{u}^{\mathrm{2}}…
Question Number 98087 by Algoritm last updated on 11/Jun/20 Answered by mr W last updated on 11/Jun/20 $${a}_{{k}} =\frac{\mathrm{1}}{\left({k}+\mathrm{2}\right)^{\mathrm{2}} +{k}}=\frac{\mathrm{1}}{\left({k}+\mathrm{1}\right)\left({k}+\mathrm{4}\right)}=\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{1}}{{k}+\mathrm{1}}−\frac{\mathrm{1}}{{k}+\mathrm{4}}\right) \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} =\frac{\mathrm{1}}{\mathrm{3}}\left(\underset{{k}=\mathrm{1}}…
Question Number 163611 by Ramjiane last updated on 08/Jan/22 Answered by ajfour last updated on 08/Jan/22 $$\left(\mathrm{1}\right)\:\:{d}=\frac{{h}}{\mathrm{cot}\:\mathrm{25}°−\mathrm{cot}\:\mathrm{50}°} \\ $$$$\left(\mathrm{2}\right)\:{You}\:{jus}\:{cant}\:{do}\:{without}. \\ $$ Terms of Service Privacy…
Question Number 32535 by naka3546 last updated on 27/Mar/18 $${k}\:\:\leqslant\:\:\mathrm{2018} \\ $$$${f}\:\left({f}\:\left({n}\right)\:\right)\:\:=\:\:\mathrm{2}{n} \\ $$$${f}\:\left({k}\right)\:\:=\:\:\mathrm{2018} \\ $$$${how}\:\:{many}\:\:\:{the}\:{possible}\:{of}\:\:\:\boldsymbol{{k}}\:\:{integers}\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32534 by naka3546 last updated on 27/Mar/18 Answered by MJS last updated on 27/Mar/18 $${m}+\sqrt{{n}}={k} \\ $$$${f}\left({x}\right)={k} \\ $$$${x}^{\mathrm{2}} +{x}−{k}=\mathrm{0} \\ $$$${x}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{4}{k}+\mathrm{1}} \\…
Question Number 163601 by SANOGO last updated on 08/Jan/22 $$\int_{\frac{\mathrm{2}}{\pi}} ^{+{oo}} {ln}\left({cos}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$$${narure}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163580 by mkam last updated on 08/Jan/22 $$\int\:{sin}^{\mathrm{2021}} \left({x}\right)\:.\:{sin}\left(\mathrm{2023}\:{x}\:\right)\:{dx}\: \\ $$ Commented by mkam last updated on 08/Jan/22 $$?????? \\ $$ Answered by…
Question Number 32510 by mondodotto@gmail.com last updated on 26/Mar/18 Commented by abdo imad last updated on 26/Mar/18 $${we}\:{have}\:{y}\:=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{{x}}\:\:}}\:\:\Rightarrow{y}^{\mathrm{2}} \:−\mathrm{1}\:=\left(\mathrm{1}+\sqrt{{x}}\:\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\Rightarrow\mathrm{2}{y}\:{y}^{,} \:=\frac{\mathrm{1}}{\mathrm{2}}\left(\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}\right)^{−\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{2}\:}\sqrt{\sqrt{{x}}}}\:\:\Rightarrow \\ $$$${y}^{'}…
Question Number 98039 by souvik last updated on 11/Jun/20 $$\mathrm{10000}×\frac{\mathrm{10}}{\mathrm{100}}×\frac{\mathrm{20}}{\mathrm{100}}×\frac{\mathrm{30}}{\mathrm{100}}= \\ $$$$ \\ $$ Answered by Ritu Jain last updated on 11/Jun/20 $$\mathrm{60} \\ $$…