Question Number 144875 by lapache last updated on 30/Jun/21 Answered by Dwaipayan Shikari last updated on 30/Jun/21 $$\frac{\mathrm{1}}{{n}!}\int_{\mathrm{0}} ^{\infty} {x}^{{n}} \mathrm{sin}\:\left({x}\right){e}^{−{x}} {dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{in}!}\int_{\mathrm{0}} ^{\infty}…
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Question Number 79290 by 21042009 last updated on 24/Jan/20 $${What}\:{is}\:{the}\:{area}\:{of}\:{one}\:{petal}\:{of} \\ $$$${r}=\mathrm{2cos}\left(\mathrm{3}\theta\right) \\ $$ Answered by mr W last updated on 24/Jan/20 $${A}=\int_{−\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{6}}} \frac{{r}^{\mathrm{2}}…
Question Number 79289 by 21042009 last updated on 24/Jan/20 $${m}^{\mathrm{2}} +{n}^{\mathrm{2}} =\mathrm{2}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$$${What}\:{is}\:\mathrm{2}\left({a}+{b}\right)\:{in}\:{terms}\:{of}\:{m}\:{and}\:{n} \\ $$ Commented by mr W last updated on…
Question Number 144801 by mohammad17 last updated on 29/Jun/21 $${if}\:{you}\:{know}\:{that}\:{the}\:{probability}\:{of}\:{a}\:{picture} \\ $$$${appearing}\:{when}\:{acoin}\:{is}\:{tossed}\:{is}\:\mathrm{2}/\mathrm{5} \\ $$$${then}\:{the}\:{probability}\:{of}\:{getting}\:{writings}\: \\ $$$${when}\:{this}\:{coin}\:{is}\:{tossed}\:\mathrm{6}\:{times}\:? \\ $$ Commented by mohammad17 last updated on 29/Jun/21…
Question Number 79266 by Maclaurin Stickker last updated on 24/Jan/20 $${let}\:{ABC}\:{be}\:{a}\:{escalene}\:{triangle}\:{of} \\ $$$${area}\:\mathrm{7}.\:{Let}\:{A}_{\mathrm{1}} \:{be}\:{a}\:{point}\:{on}\:{the}\:{side} \\ $$$${BC},\:{and}\:{let}\:{B}_{\mathrm{1}} \:{and}\:{C}_{\mathrm{1}} \:{be}\:{points}\:{on} \\ $$$${the}\:{sides}\:{AC}\:{and}\:{AB},\:{such}\:{that} \\ $$$${AA}_{\mathrm{1}} ,\:{BB}_{\mathrm{1}} \:{and}\:{CC}_{\mathrm{1}} \:{are}\:{parallel}.\:{Find}…
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