Question Number 140206 by rs4089 last updated on 05/May/21 $${Evaluate}\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}!} \\ $$$${here}\:{H}_{{n}} \:{is}\:{the}\:{nth}\:{harmonic}\:{number} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 140200 by qaz last updated on 05/May/21 $$\int_{\mathrm{0}} ^{\infty} \left(\frac{{lnx}}{{x}−\mathrm{1}}\right)^{\mathrm{3}} {dx}=\pi^{\mathrm{2}} \\ $$ Commented by Ar Brandon last updated on 05/May/21 $$\Phi=\int_{\mathrm{0}} ^{\infty}…
Question Number 140202 by qaz last updated on 05/May/21 $$\int_{\mathrm{0}} ^{\infty} \left(\frac{{lnx}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} {dx}=\frac{\mathrm{2}}{\mathrm{3}}\pi^{\mathrm{2}} \\ $$ Answered by mathmax by abdo last updated on 05/May/21 $$\Phi\:=\int_{\mathrm{0}}…
Question Number 9128 by tawakalitu last updated on 20/Nov/16 Commented by tawakalitu last updated on 20/Nov/16 $$\mathrm{Note}:\:\:#\:\mathrm{means}\:\:\mathrm{Naira}\:\mathrm{in}\:\mathrm{Nigeria}. \\ $$$$\mathrm{while}:\:\:\mathrm{K}\:\mathrm{means}\:\:\mathrm{Kobo}\:\mathrm{in}\:\mathrm{Nigeria} \\ $$$$\mathrm{and} \\ $$$$\mathrm{100}\:\mathrm{kobo}\:=\:\mathrm{1}\:\mathrm{Naira}\:\:\:\:\left(\mathrm{100k}\:=\:#\mathrm{1}\right) \\ $$…
Question Number 140196 by mathdanisur last updated on 05/May/21 $${Calculate}:\:\sqrt{\mathrm{3}}\:{cosec}\:\mathrm{20}°−{sec}\:\mathrm{20}° \\ $$ Answered by liberty last updated on 05/May/21 $$\:\frac{\sqrt{\mathrm{3}}}{\mathrm{sin}\:\mathrm{20}°}−\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}°}\:=\: \\ $$$$\frac{\mathrm{2}\left(\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{20}°−\mathrm{sin}\:\mathrm{20}°\right)}{\mathrm{sin}\:\mathrm{40}°}\:= \\ $$$$\frac{\mathrm{4}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{cos}\:\mathrm{20}°−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{20}°\right)}{\mathrm{sin}\:\mathrm{40}°}\:= \\…
Question Number 74663 by TawaTawa last updated on 28/Nov/19 $$\mathrm{If}\:\:\:\:\mathrm{x}^{\mathrm{x}} \:\mathrm{y}^{\mathrm{y}} \:\mathrm{z}^{\mathrm{z}} \:\:\:=\:\:\:\mathrm{c}\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{at}\:\:\:\:\:\mathrm{x}\:\:=\:\:\mathrm{y}\:\:=\:\:\mathrm{z} \\ $$$$\:\:\:\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}\partial\mathrm{y}}\:\:\:=\:\:\:−\:\left(\mathrm{x}\:\mathrm{log}\:\mathrm{ex}\right)^{−\mathrm{1}} \\ $$ Answered by mind is power last updated…
Question Number 9125 by tawakalitu last updated on 20/Nov/16 $$\mathrm{A}\:\mathrm{polygon}\:\mathrm{has}\:\mathrm{two}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{120}°\:\mathrm{each} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{others}\:\mathrm{are}\:\mathrm{each}\:\mathrm{150}°.\:\mathrm{calculate} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}\:. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{angles}. \\ $$ Answered by mrW last updated on 20/Nov/16…
Question Number 140198 by EnterUsername last updated on 05/May/21 $$\mathrm{Let}\:{a}>\mathrm{0}\:\mathrm{and}\:\mid{z}+\left(\mathrm{1}/{z}\right)\mid={a}\:\left({z}\neq\mathrm{0}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\right). \\ $$$$\mathrm{Then}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum}\:\mathrm{values}\:\mathrm{of}\:\mid{z}\mid\:\mathrm{are} \\ $$$$\left(\mathrm{A}\right)\:\frac{{a}+\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\frac{\mathrm{2}{a}+\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}}{\mathrm{2}} \\ $$$$\left(\mathrm{C}\right)\:\frac{\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}−{a}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\frac{\sqrt{{a}^{\mathrm{2}} +\mathrm{4}}−\mathrm{2}{a}}{\mathrm{2}} \\ $$ Answered by Dwaipayan…
Question Number 140193 by mathdanisur last updated on 05/May/21 $${Solve}\:{for}\:{real}\:{numbers} \\ $$$$\mathrm{4}{sin}\frac{\pi}{\mathrm{26}}\:+\:\mathrm{4}{xsin}\frac{\mathrm{3}\pi}{\mathrm{26}}\:+\:\mathrm{4}{sin}\frac{\mathrm{9}\pi}{\mathrm{26}}\:=\:{x}+\sqrt{\mathrm{13}} \\ $$ Answered by Dwaipayan Shikari last updated on 05/May/21 $${x}\left(\mathrm{1}−\mathrm{4}{sin}\frac{\mathrm{3}\pi}{\mathrm{26}}\right)=\mathrm{4}\left({sin}\frac{\mathrm{9}\pi}{\mathrm{26}}+{sin}\frac{\pi}{\mathrm{26}}\right)−\sqrt{\mathrm{13}} \\ $$$${x}=\frac{\mathrm{4}\left({sin}\frac{\mathrm{9}\pi}{\mathrm{26}}+{sin}\frac{\pi}{\mathrm{16}}\right)−\sqrt{\mathrm{13}}}{\left(\mathrm{1}−\mathrm{4}{sin}\frac{\mathrm{3}\pi}{\mathrm{26}}\right)}…
Question Number 9123 by j.masanja06@gmail.com last updated on 20/Nov/16 $$\mathrm{simplify} \\ $$$$\left(\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)^{−\mathrm{1}/\mathrm{2}} −\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} \right)/\mathrm{x}^{\mathrm{2}} \\ $$ Commented by tawakalitu last updated on 20/Nov/16 $$\frac{\mathrm{x}^{\mathrm{2}}…