Question Number 199934 by cortano12 last updated on 11/Nov/23 $$\:\:\:\cancel{\underline{\underbrace{ }}\:} \\ $$$$ \\ $$ Answered by mr W last updated on 11/Nov/23 $$\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 199988 by hardmath last updated on 11/Nov/23 $$\mathrm{ABCD}\:-\:\mathrm{trapezium} \\ $$$$\mathrm{EF}\:-\:\mathrm{middle}\:\mathrm{line} \\ $$$$\mathrm{EG}\:=\:\mathrm{2}\:\:,\:\:\mathrm{GF}\:=\:\mathrm{4}\:\:,\:\:\mathrm{DC}\:=\:\mathrm{y}\:\:\mathrm{and}\:\:\mathrm{AB}\:=\:\mathrm{x} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{x}\:-\:\mathrm{y}\:=\:? \\ $$$$\left(\mathrm{Here}\:\mathrm{point}\:\mathrm{G}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{intersection}\right. \\ $$$$\left.\mathrm{of}\:\mathrm{the}\:\mathrm{extension}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{AB}\:\mathrm{and}\:\mathrm{CD}\right) \\ $$ Terms of Service…
Question Number 199921 by Mingma last updated on 11/Nov/23 Answered by des_ last updated on 12/Nov/23 $$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\:{x}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:=\:{I}; \\ $$$${I}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx},\:{a}\:>\mathrm{0};…
Question Number 199986 by Yakubu last updated on 11/Nov/23 $$ \\ $$How do I solve this please? Show that if the sides of a right…
Question Number 199922 by Mingma last updated on 11/Nov/23 Answered by AST last updated on 11/Nov/23 $${WLOG},{let}\:{C}\:{be}\:{the}\:{origin}\:{and}\:{let}\:{AD}\:{coincide} \\ $$$${with}\:{the}\:{real}\:{axis};{then}\:{a}=\overset{−} {{a}};{b}=−\overset{−} {{b}};{d}=\overset{−} {{d}};{e}=−\overset{−} {{e}} \\ $$$$\frac{{b}−{a}}{−{b}−{a}}=\frac{{a}−{e}}{−{e}−{a}}\Rightarrow−{be}+\mathrm{2}{a}^{\mathrm{2}}…
Question Number 199987 by Yakubu last updated on 11/Nov/23 $$\:\boldsymbol{{Use}}\:\boldsymbol{{mathematical}}\:\boldsymbol{{induction}} \\ $$$$\:\boldsymbol{{to}}\:\boldsymbol{{prove}}\:\boldsymbol{{that}}\:\boldsymbol{{the}}\:\boldsymbol{{statement}} \\ $$$$\:\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{d}}\right)+\left(\boldsymbol{\mathrm{a}}+\mathrm{2}\boldsymbol{\mathrm{d}}\right)+…+\left(\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right)=\frac{\boldsymbol{\mathrm{n}}}{\mathrm{2}}\left[\mathrm{2}\boldsymbol{\mathrm{a}}+\left(\boldsymbol{\mathrm{n}}−\mathrm{1}\right)\boldsymbol{\mathrm{d}}\right] \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{true}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{natural}}\:\boldsymbol{\mathrm{numbers}} \\ $$$$\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:\boldsymbol{{please}} \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 199923 by Rupesh123 last updated on 11/Nov/23 Answered by AST last updated on 11/Nov/23 $${a}+\mathrm{1}+\mathrm{1}\geqslant\mathrm{3}\sqrt[{\mathrm{3}}]{{a}}\Rightarrow\Sigma\frac{{a}}{{a}+\mathrm{2}}\leqslant\Sigma\frac{{a}^{\frac{\mathrm{2}}{\mathrm{3}}} }{\mathrm{3}} \\ $$$${Power}\:{mean}\Rightarrow\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }{\mathrm{3}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:\geqslant\left(\frac{{a}^{\frac{\mathrm{2}}{\mathrm{3}}} +{b}^{\frac{\mathrm{2}}{\mathrm{3}}}…
Question Number 199916 by lealiegalendez last updated on 11/Nov/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 199983 by cortano12 last updated on 11/Nov/23 $$\:\:\:\mathrm{find}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\left(\frac{\pi\mathrm{x}}{\mathrm{5}+\mathrm{3x}}\right)\: \\ $$$$\:\:\mathrm{by}\:\mathrm{sequeeze}\:\mathrm{theorem} \\ $$ Answered by tri26112004 last updated on 12/Nov/23 $${We}\:{have}\: \\ $$$$\mid{sin}\left(\:\frac{\pi{x}}{\mathrm{5}+\mathrm{3}{x}}\right)\mid\:\leqslant\:\mathrm{1}…
Question Number 199913 by WaqasShabbir last updated on 11/Nov/23 $$ \\ $$To calculate the mean and median of the distribution, you can follow these steps:…