Question Number 74527 by Maclaurin Stickker last updated on 25/Nov/19 Commented by Maclaurin Stickker last updated on 25/Nov/19 $${In}\:{the}\:{figure}\:{determine}\:{the}\:{radius} \\ $$$${of}\:{the}\:{smallest}\:{circumference}\:{as}\:{a} \\ $$$${function}\:{of}\:{the}\:{radius}\:\boldsymbol{\mathrm{R}}\:{of}\:{the}\:{quadrant}. \\ $$…
Question Number 8988 by Daily last updated on 10/Nov/16 $${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}\left({k}+\mathrm{1}\right)={k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)/\mathrm{3} \\ $$ Answered by 123456 last updated on 11/Nov/16 $${s}\left({n}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}}…
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Question Number 74522 by necxxx last updated on 25/Nov/19 $${A}\:{rope}\:{inclined}\:{at}\:{angle}\:\mathrm{37}°\:{to}\:{the}\: \\ $$$${horizontal}\:{is}\:{used}\:{to}\:{drag}\:{a}\:\mathrm{50}{kg}\:{block} \\ $$$${along}\:{a}\:{level}\:{floor}\:{with}\:{an}\:{acceleration} \\ $$$${of}\:\mathrm{1}{m}/{s}^{\mathrm{2}} \:.{The}\:{coefficient}\:{of}\:{friction} \\ $$$${between}\:{the}\:{block}\:{and}\:{the}\:{floor}\:{is}\:\mathrm{0}.\mathrm{2}. \\ $$$${What}\:{is}\:{the}\:{tension}\:{in}\:{the}\:{rope}? \\ $$ Commented by…
Question Number 140056 by Ndala last updated on 03/May/21 $$\mathrm{Prove}\:\mathrm{the}\:\mathrm{folowing}\:\mathrm{result}: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{cot}\:\theta\centerdot\left(\mathrm{log}\:\mathrm{sec}\:\theta\right)^{\mathrm{3}} {d}\theta=\frac{\pi^{\mathrm{4}} }{\mathrm{240}} \\ $$$$. \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help},\:\mathrm{if}\:\mathrm{possible}\:\mathrm{please}. \\ $$ Answered by Ar…
Question Number 74520 by chess1 last updated on 25/Nov/19 Answered by MJS last updated on 26/Nov/19 $$\mathrm{0}\leqslant{x}<\mathrm{2}\pi \\ $$$$\mathrm{tan}\:{x}\:>\mathrm{sin}\:{x} \\ $$$$\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}>\mathrm{sin}\:{x} \\ $$$$\mathrm{case}\:\mathrm{1}:\:\mathrm{sin}\:{x}\:>\mathrm{0}\:\Leftrightarrow\:\mathrm{0}<{x}<\pi \\ $$$$\frac{\mathrm{1}}{\mathrm{cos}\:{x}}>\mathrm{1}\:\Leftrightarrow\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{2}}\vee\frac{\mathrm{3}\pi}{\mathrm{2}}<{x}<\mathrm{2}\pi…
Question Number 8985 by j.masanja06@gmail.com last updated on 10/Nov/16 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{log}_{\mathrm{x}} \mathrm{3}=\mathrm{81} \\ $$ Answered by Rasheed Soomro last updated on 10/Nov/16 $$\mathrm{log}_{\mathrm{x}} \mathrm{3}=\mathrm{81}…
Question Number 140053 by ajfour last updated on 03/May/21 Commented by ajfour last updated on 03/May/21 $${Find}\:{radius}\:{of}\:{largest}\:{sphere}\: \\ $$$${within}\:{the}\:{cuboid}\:{and}\:{between} \\ $$$${the}\:{shown}\:{triangular}\:{planes}. \\ $$ Commented by…
Question Number 140055 by mnjuly1970 last updated on 03/May/21 $$\:\:\:\:\:\: \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\Omega:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}−{e}^{−{x}} }{\mathrm{1}+{e}^{\mathrm{2}{x}} }\:.\frac{{dx}}{{x}}\:={ln}\left(\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}}\:\right) \\ $$$$\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}\right)^{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} } \overset{??}…
Question Number 74514 by mathmax by abdo last updated on 25/Nov/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{\left({x}−{sin}\theta\right){d}\theta}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{sin}\theta\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Commented by mathmax by abdo last updated…