Question Number 5406 by 1771727373 last updated on 14/May/16 $$\int_{−\infty} ^{\infty} \:{e}^{{x}} {dx}=? \\ $$ Commented by FilupSmith last updated on 14/May/16 $${S}=\underset{{k}\rightarrow\infty} {\mathrm{lim}}\:\underset{−{k}} {\overset{{k}}…
Question Number 5405 by sanusihammed last updated on 14/May/16 $${The}\:{angle}\:{of}\:{elevation}\:{of}\:{point}\:{A}\:{and}\:{B}\:{from}\:{P}\:{are}\:\alpha\:{and}\:\beta\: \\ $$$${respectively}.\:{The}\:{bearing}\:{of}\:{A}\:{and}\:{B}\:{from}\:{P}\:{are}\:{S}\mathrm{20}°{W}\:{and} \\ $$$${S}\mathrm{40}°{E}\:{and}\:{their}\:{distance}\:{from}\:{P}\:\:{measured}\:{on}\:{the}\:{map}\:{are} \\ $$$$\mathrm{3}{cm}\:{and}\:\mathrm{1}{cm}\:{respetively}.\:{A}\:{is}\:{higher}\:{than}\:{B}.\:{Prove}\:{that}\:{the}\: \\ $$$${elevation}\:{of}\:{A}\:{from}\:{B}\:{is} \\ $$$$ \\ $$$$\frac{{tan}^{−\mathrm{1}} \left[\mathrm{3}{tan}\alpha\:−\:{tan}\beta\right]}{\:\sqrt{\mathrm{7}}\:} \\ $$$$…
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Question Number 136475 by EDWIN88 last updated on 22/Mar/21 Commented by EDWIN88 last updated on 22/Mar/21 $$\mathrm{Use}\:\mathrm{the}\:\mathrm{fact}\:\mathrm{that}\:\mathrm{csc}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{x}}{\mathrm{6}}+\frac{\mathrm{7x}^{\mathrm{3}} }{\mathrm{360}}+\frac{\mathrm{31x}^{\mathrm{5}} }{\mathrm{15120}}+…\:\mathrm{for}\:\mid\mathrm{x}\mid\:<\:\pi\:\mathrm{to} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{for} \\ $$$$\mathrm{2}\:\mathrm{csc}\:\left(\mathrm{2x}\right)\:\left[\:\mathrm{for}\:\mid\mathrm{x}\mid\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{and}\:\mathrm{thus}\:\mathrm{for}\:\mathrm{ln}\:\left(\mathrm{tan}\:\mathrm{x}\right).\right. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{ln}\:\mid\mathrm{x}\mid\:+\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 5398 by FilupSmith last updated on 13/May/16 $$\mathrm{If}\:\mathrm{we}\:\mathrm{have}\:\mathrm{an}\:{n}−\mathrm{dimensional}\:\mathrm{cube}. \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{we}\:\mathrm{find}\:\mathrm{its}\:'{volume}'? \\ $$ Commented by Rasheed Soomro last updated on 13/May/16 $$\mathrm{Suppose}\:\mathrm{s}\:\:\mathrm{is}\:\mathrm{measure}\:\mathrm{of}\:\mathrm{side}\:\mathrm{of}\: \\ $$$$\mathrm{n}-\mathrm{dimensional}\:\mathrm{cube}.…
Question Number 136466 by aurpeyz last updated on 22/Mar/21 $$\int\frac{\mathrm{4}{dx}}{\mathrm{3}−\mathrm{5}{sin}\:{x}} \\ $$ Answered by mathmax by abdo last updated on 22/Mar/21 $$\Phi=\int\:\:\frac{\mathrm{4dx}}{\mathrm{3}−\mathrm{5sinx}}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{tan}\left(\frac{\mathrm{x}}{\mathrm{2}}\right)=\mathrm{t}\:\Rightarrow \\ $$$$\Phi=\int\:\:\frac{\mathrm{4}}{\left(\mathrm{3}−\mathrm{5}\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\right)}\frac{\mathrm{2dt}}{\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}}…
Question Number 136463 by Plutonic last updated on 22/Mar/21 $${Evaluate}\:\mathrm{4}\sqrt{\mathrm{3}\:}\left(\frac{\mathrm{3}}{\:\sqrt{\mathrm{3}}}+\sqrt{\mathrm{3}}\right) \\ $$ Answered by aurpeyz last updated on 22/Mar/21 $${multiply}\:{through}\:{by}\:\mathrm{4}\sqrt{\mathrm{3}} \\ $$$$\mathrm{12}+\mathrm{12}=\mathrm{24} \\ $$ Terms…
Question Number 136457 by byaw last updated on 22/Mar/21 Commented by mr W last updated on 22/Mar/21 $${A},{B},{C}\:{are}\:{true}. \\ $$$${question}\:{D}\:{is}\:{not}\:{clear}.\:{one}\:{angle} \\ $$$${alone}\:{can}\:{not}\:{be}\:{complementary}. \\ $$$${if}\:{question}\:{D}\:{means}\:{that}\:{the}\:{angle} \\…
Question Number 5386 by sanusihammed last updated on 12/May/16 $${Solve}\:{simultaneously} \\ $$$$ \\ $$$${x}^{{x}} \:+\:\:{y}^{{y}\:} \:=\:\:\mathrm{31} \\ $$$${x}\:\:+\:\:{y}\:\:=\:\:\mathrm{5} \\ $$$$ \\ $$$${Please}\:{i}\:{did}\:{workings}\:… \\ $$$$ \\…