Question Number 32569 by naka3546 last updated on 28/Mar/18 $${Compute}\:\:{the}\:\:{number}\:\:{of}\:\:\:{ordered}\:\:{quadruple}\:\:\left({a},\:{b},\:{c},\:{d}\right)\:\:{of}\:\:{distinct}\:\:{positive}\:\:{integers}\:\:\:{so}\:\:{that}\:\:\begin{pmatrix}{\begin{pmatrix}{{a}}\\{{b}}\end{pmatrix}}\\{\begin{pmatrix}{{c}}\\{{d}}\end{pmatrix}}\end{pmatrix}\:\:\:=\:\:\mathrm{21}\:. \\ $$ Commented by MJS last updated on 28/Mar/18 $$\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}=\mathrm{21}\:\Rightarrow\:\left({n};{k}\right)\in\left\{\left(\mathrm{7};\mathrm{2}\right);\left(\mathrm{7};\mathrm{5}\right);\left(\mathrm{21};\mathrm{1}\right);\left(\mathrm{21};\mathrm{20}\right)\right\} \\ $$$$ \\ $$$$\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}=\mathrm{1}\:\Rightarrow\:\left({n};{k}\right)=\left({m};{m}\right)\mid{m}\in\mathbb{N} \\…
Question Number 98104 by bemath last updated on 11/Jun/20 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}\: \\ $$$$\mathrm{if}\:\begin{cases}{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} =\mathrm{1}}\\{\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+\mathrm{1}\right)\left(\mathrm{y}+\mathrm{1}\right)=\mathrm{2}}\end{cases} \\ $$$$ \\ $$ Commented by bemath last updated on 12/Jun/20…
Question Number 163638 by mkam last updated on 08/Jan/22 $$\int\:\frac{\boldsymbol{{dx}}}{\:\sqrt{\mathrm{2}\boldsymbol{{c}}_{\mathrm{1}} +\boldsymbol{{e}}^{−\mathrm{2}\boldsymbol{{x}}} }} \\ $$ Commented by mkam last updated on 09/Jan/22 $$????? \\ $$ Commented…
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