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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 $${let}\:{ABC}\:{be}\:{a}\:{escalene}\:{triangle}\:{of} \\ $$$${area}\:\mathrm{7}.\:{Let}\:{A}_{\mathrm{1}} \:{be}\:{a}\:{point}\:{on}\:{the}\:{side} \\ $$$${BC},\:{and}\:{let}\:{B}_{\mathrm{1}} \:{and}\:{C}_{\mathrm{1}} \:{be}\:{points}\:{on} \\ $$$${the}\:{sides}\:{AC}\:{and}\:{AB},\:{such}\:{that} \\ $$$${AA}_{\mathrm{1}} ,\:{BB}_{\mathrm{1}} \:{and}\:{CC}_{\mathrm{1}} \:{are}\:{parallel}.\:{Find}…
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Question Number 144777 by Nhozie last updated on 29/Jun/21 Answered by som(math1967) last updated on 29/Jun/21 $$\:\left({x}+\mathrm{3}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3} \\ $$$${if}\:{x},{y}\in{R}\:{then}\:\left({x}+\mathrm{3}\right)^{\mathrm{2}} \geqslant\mathrm{0}\:,{y}^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$$\therefore\left({x}+\mathrm{3}\right)^{\mathrm{2}}…
Question Number 144772 by phally last updated on 29/Jun/21 Answered by liberty last updated on 29/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{\mathrm{x}} −\mathrm{1}\right)}{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{ln}\:\left(\mathrm{1}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\right)\right.}\: \\ $$$$\mathrm{consider}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{\mathrm{x}} −\mathrm{1}\right)=\mathrm{x}^{\mathrm{x}} \left(\mathrm{ln}\:\mathrm{x}+\mathrm{1}\right) \\…