Question Number 9141 by tawakalitu last updated on 20/Nov/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{if} \\ $$$$\left(\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{3}}}\right)^{\mathrm{x}} \:+\:\left(\sqrt{\mathrm{2}\:−\:\sqrt{\mathrm{3}}}\right)^{\mathrm{x}} \:=\:\mathrm{4} \\ $$ Commented by tawakalitu last updated on 20/Nov/16 $$\mathrm{please}\:\mathrm{help}. \\…
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Question Number 140205 by EnterUsername last updated on 05/May/21 $${ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{rhombus}.\:\mathrm{Its}\:\mathrm{diagonals}\:{AC}\:\mathrm{and}\:{BD}\:\mathrm{inter}- \\ $$$$\mathrm{sect}\:\mathrm{at}\:{M}\:\mathrm{and}\:\mathrm{satisfy}\:{BD}=\mathrm{2}{AC}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{points}\:{D}\:\mathrm{and} \\ $$$${M}\:\mathrm{are}\:\mathrm{represented}\:\mathrm{by}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{1}+{i}\:\mathrm{and} \\ $$$$\mathrm{2}−{i},\:\mathrm{respectively},\:\mathrm{then}\:{A}\:\mathrm{is}\:\mathrm{represented}\:\mathrm{by} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{3}−{i}/\mathrm{2}\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{3}+{i}/\mathrm{2}\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{1}+\mathrm{3}{i}/\mathrm{2}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{1}−\mathrm{3}{i}/\mathrm{2} \\ $$ Answered by mr W last…
Question Number 140207 by mathlove last updated on 05/May/21 Answered by liberty last updated on 06/May/21 $$\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}+\mathrm{m}} .\mathrm{e}^{\bigtriangleup\mathrm{x}} −\mathrm{e}^{\mathrm{x}+\mathrm{m}} }{\bigtriangleup\mathrm{x}}\:= \\ $$$$\mathrm{e}^{\mathrm{x}+\mathrm{m}} \:.\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\bigtriangleup\mathrm{x}}…
Question Number 140206 by rs4089 last updated on 05/May/21 $${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…