Question Number 158843 by mnjuly1970 last updated on 09/Nov/21 Commented by mr W last updated on 09/Nov/21 $$\left(\mathrm{1}\right) \\ $$$${not}\:{true}! \\ $$$${example}:\:{x}=\mathrm{4},\:{y}=\mathrm{6} \\ $$$$\mathrm{6}{x}+\mathrm{11}{y}=\mathrm{24}+\mathrm{66}=\mathrm{90}\:\equiv\mathrm{0}\:{mod}\left(\mathrm{30}\right) \\…
Question Number 93296 by student work last updated on 12/May/20 Commented by student work last updated on 12/May/20 $$\mathrm{how}\:\mathrm{many}\:\mathrm{triangles}? \\ $$ Answered by Ritu Jain…
Question Number 27761 by shiv15031973@gmail.com last updated on 14/Jan/18 $$\mathrm{4}\left(\mathrm{2a}+\mathrm{b}\right)^{\mathrm{2}} −\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} \\ $$ Answered by Rasheed.Sindhi last updated on 14/Jan/18 $$\:\:\:\mathrm{4}\left(\mathrm{2a}+\mathrm{b}\right)^{\mathrm{2}} −\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} \\ $$$$=\mathrm{4}\left(\mathrm{4a}^{\mathrm{2}} +\mathrm{4ab}+\mathrm{b}^{\mathrm{2}}…
Question Number 158823 by amin96 last updated on 09/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158816 by HongKing last updated on 09/Nov/21 $$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{2017}^{\mathrm{2017}} \:\:\mathrm{and}\:\:\:\mathrm{2017}^{\mathrm{2018}} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{perfect}\:\mathrm{squares}. \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 158812 by amin96 last updated on 09/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158813 by HongKing last updated on 09/Nov/21 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{value}\:\:\boldsymbol{\beta}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:+\infty} {\int}}\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2021}\boldsymbol{\beta}} \:+\:\mathrm{ln}\centerdot\left(\mathrm{1}\:+\:\beta\mathrm{x}\right)}\:\mathrm{dx}\:<\:+\infty \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158814 by HongKing last updated on 09/Nov/21 $$\mathrm{Compare}\:\mathrm{it}: \\ $$$$\left(\mathrm{log}_{\mathrm{4}} \mathrm{20}\right)^{\mathrm{2}} \:\:\:\mathrm{and}\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{320} \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 158781 by HongKing last updated on 08/Nov/21 Answered by MJS_new last updated on 09/Nov/21 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}{x}\right)\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{1}+{a}\mathrm{sin}^{\mathrm{2}} \:{x}}{dx}=\mathrm{2}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\frac{\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}{x}\right)\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{1}+{a}\mathrm{sin}^{\mathrm{2}} \:{x}}…
Question Number 158775 by HongKing last updated on 08/Nov/21 $$\mathrm{Find}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\left(\mathrm{1}\:+\:\mathrm{ax}\right)}\:\mathrm{dx}\:\:;\:\:\mathrm{a}>\mathrm{0} \\ $$$$ \\ $$$$\mathrm{Answer}: \\ $$$$\frac{-\pi\sqrt{\mathrm{3}}\centerdot\left(\mathrm{a}-\mathrm{2}\right)+\mathrm{9a}\centerdot\mathrm{ln}\left(\mathrm{a}\right)}{\mathrm{9}\centerdot\left(\mathrm{a}^{\mathrm{2}} -\mathrm{a}+\mathrm{1}\right)} \\ $$ Answered…