Question Number 157884 by HongKing last updated on 29/Oct/21 $$\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{10}°\right)}\:-\:\mathrm{4}\:\mathrm{sin}\left(\mathrm{70}°\right)\:=\:? \\ $$ Answered by tounghoungko last updated on 29/Oct/21 $$\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}−\mathrm{4}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{cos}\:\mathrm{10}°+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{10}°\right) \\ $$$$=\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{10}°}−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{10}°−\mathrm{2sin}\:\mathrm{10}° \\ $$$$=\frac{\mathrm{1}−\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{10}°\:\mathrm{cos}\:\mathrm{10}°−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{10}°}{\mathrm{sin}\:\mathrm{10}°}…
Question Number 157891 by HongKing last updated on 29/Oct/21 Answered by TheSupreme last updated on 29/Oct/21 $$\left(\frac{\mathrm{3}}{\mathrm{4}}+\frac{\mathrm{5}}{\mathrm{36}}+\frac{\mathrm{7}}{\mathrm{144}}+\frac{\mathrm{9}}{\mathrm{400}}+\frac{\mathrm{11}}{\mathrm{900}}\right){x}<\mathrm{70} \\ $$$$\left(\frac{\mathrm{2400}+\mathrm{500}+\mathrm{175}+\mathrm{81}+\mathrm{44}}{\mathrm{3600}}\right){x}<\mathrm{70} \\ $$$$\left(\frac{\mathrm{8}}{\mathrm{9}}\right){x}<\mathrm{70} \\ $$$${x}<\frac{\mathrm{630}}{\mathrm{8}}=\mathrm{78}.\mathrm{75} \\ $$$${largest}\:{x}\:=\:\mathrm{78}…
Question Number 92346 by M±th+et+s last updated on 06/May/20 $${solve} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{1}+\sqrt{{x}}}+\sqrt[{\mathrm{3}}]{\mathrm{1}−\sqrt{{x}}}=\sqrt[{\mathrm{3}}]{\mathrm{5}} \\ $$ Commented by jagoll last updated on 06/May/20 $$\mathrm{x}\:\approx\:.\mathrm{79999999722742} \\ $$ Commented…
Question Number 157880 by Engr_Jidda last updated on 29/Oct/21 Commented by mr W last updated on 29/Oct/21 $${i}\:{may}\:{understand}\:{that}\:{you}\:{need}\:{help} \\ $$$${for}\:{questions}\:{about}\:\:{taylor}\:{series} \\ $$$${and}\:{fourier}\:{transform},\:{and}\:{we}\:{take} \\ $$$${those}\:{questions}\:{serious}.\:{but}\:{i}\:{can} \\…
Question Number 157883 by HongKing last updated on 29/Oct/21 $$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}\:+\:\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}\:+\:…\:+\:\frac{\mathrm{n}-\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}\right)\:=\:? \\ $$ Answered by puissant last updated on 29/Oct/21 $${S}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
Question Number 157873 by HongKing last updated on 29/Oct/21 $$\mathrm{if}:\:\boldsymbol{\alpha}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}}}{\mathrm{1}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}}}\:\:\mathrm{e}^{-\boldsymbol{\pi\mathrm{y}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)} \:\mathrm{dydx} \\ $$$$\mathrm{find}:\:\sqrt{\mathrm{19683}\boldsymbol{\alpha}^{\mathrm{6}} \:-\:\mathrm{94041}\boldsymbol{\alpha}^{\mathrm{4}} \:+\:\mathrm{105786}\boldsymbol{\alpha}^{\mathrm{2}} } \\ $$$$ \\…
Question Number 157871 by HongKing last updated on 29/Oct/21 $$\mathrm{if}\:\:\:\mathrm{x};\mathrm{y}>\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} -\mathrm{x}+\mathrm{1}}\:+\:\frac{\mathrm{y}}{\mathrm{y}^{\mathrm{2}} -\mathrm{y}+\mathrm{1}}\:+\:\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} -\mathrm{xy}+\mathrm{1}}\:\leqslant \\ $$$$\leqslant\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} -\mathrm{x}+\mathrm{1}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} -\mathrm{y}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} -\mathrm{xy}+\mathrm{1}} \\…
Question Number 92335 by jagoll last updated on 06/May/20 $$\sqrt{\left\{\mathrm{x}\right\}}\:=\:\mathrm{1}+\:\mathrm{ln}\left(\mathrm{x}\right)\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92324 by I want to learn more last updated on 06/May/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}\:\:\mathrm{for}\:\mathrm{which}\:\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{0}} {\overset{\mathrm{n}\:\:=\:\:\infty} {\sum}}\:\mathrm{16}\left(\frac{\mathrm{3}}{\mathrm{4}}\mathrm{x}\:\:+\:\:\mathrm{1}\right)^{\mathrm{n}} \\ $$$$\left(\mathrm{a}\right)\:\:\:\mathrm{Is}\:\mathrm{convergent} \\ $$$$\left(\mathrm{b}\right)\:\:\:\mathrm{Is}\:\mathrm{equal}\:\mathrm{to}\:\:\mathrm{10}\frac{\mathrm{2}}{\mathrm{3}} \\ $$ Answered by mr…
Question Number 157855 by HongKing last updated on 28/Oct/21 Commented by Rasheed.Sindhi last updated on 30/Oct/21 $${x},{y},{z}\:{are}\:{measures}\:{of}\:{sides}\:{of}\:\bigtriangleup\mathrm{ABC}? \\ $$ Commented by HongKing last updated on…