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Question-168388

Question Number 168388 by leicianocosta last updated on 09/Apr/22 Answered by Tibo last updated on 09/Apr/22 $$\left.{a}\right)\:\:\pi{r}^{\mathrm{2}} =\pi×\mathrm{9}\approx\mathrm{28}.\mathrm{26}{cm}^{\mathrm{2}} \\ $$$$\left.{b}\right)\:\:\mathrm{2}\pi{rh}=\mathrm{2}×\pi×\mathrm{3}×\mathrm{8}\approx\mathrm{150}.\mathrm{72}{cm}^{\mathrm{2}} \\ $$$$\left.{c}\right)\:\:\mathrm{2}\left(\mathrm{28}.\mathrm{26}\right)+\mathrm{150}.\mathrm{72}=\mathrm{297}.\mathrm{24}{cm}^{\mathrm{2}} \\ $$$$\left.{d}\right)\:\:\pi{r}^{\mathrm{2}} {h}=\pi×\mathrm{9}×\mathrm{8}\approx\mathrm{226}.\mathrm{08}{cm}^{\mathrm{3}}…

Question-168361

Question Number 168361 by leicianocosta last updated on 08/Apr/22 Answered by som(math1967) last updated on 09/Apr/22 $$\boldsymbol{{x}}=−\boldsymbol{{kz}}−\mathrm{5} \\ $$$$\:\boldsymbol{{x}}+\mathrm{5}=−\boldsymbol{{kz}} \\ $$$$\:\frac{\boldsymbol{{x}}+\mathrm{5}}{−\boldsymbol{{k}}}=\boldsymbol{{z}} \\ $$$$\boldsymbol{{y}}\:=−\mathrm{3}\boldsymbol{{z}}\Rightarrow\frac{{y}}{−\mathrm{3}}=\boldsymbol{{z}} \\ $$$$\boldsymbol{{equn}}.\boldsymbol{{of}}\:\boldsymbol{{r}}\:\:\frac{\boldsymbol{{x}}+\mathrm{5}}{−\boldsymbol{{k}}}=\frac{\boldsymbol{{y}}}{−\mathrm{3}}=\frac{\boldsymbol{{z}}}{\mathrm{1}}…

Hi-MrW-is-back-I-m-sorry-for-having-been-absent-for-months-without-giving-you-a-message-It-s-alright-with-me-The-last-few-months-I-was-very-very-busy-with-our-new-house-and-I-had-no-time-for-othe

Question Number 37221 by MrW3 last updated on 11/Jun/18 $${Hi}!\:{MrW}\:{is}\:{back}! \\ $$$${I}'{m}\:{sorry}\:{for}\:{having}\:{been}\:{absent}\:{for} \\ $$$${months}\:{without}\:{giving}\:{you}\:{a}\:{message}. \\ $$$${It}'{s}\:{alright}\:{with}\:{me}.\: \\ $$$${The}\:{last}\:{few}\:{months}\:{I}\:{was}\:{very}\:{very} \\ $$$${busy}\:{with}\:{our}\:{new}\:{house}\:{and}\:{I}\:{had}\:{no} \\ $$$${time}\:{for}\:{other}\:{things}.\:{I}\:{changed}\:{my} \\ $$$${smartphone}\:{and}\:{lost}\:{my}\:{old}\:{ID}. \\…

Prove-that-sin-3pi-5-sin-4pi-5-1-5-2-

Question Number 168277 by Eulerian last updated on 07/Apr/22 $$\:\mathrm{Prove}\:\mathrm{that}\:\frac{\mathrm{sin}\left(\frac{\mathrm{3}\pi}{\mathrm{5}}\right)}{\mathrm{sin}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)}\:=\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\: \\ $$ Commented by cortano1 last updated on 07/Apr/22 $$\:\:\frac{\mathrm{sin}\:\mathrm{108}°}{\mathrm{sin}\:\mathrm{144}°}\:=\:\frac{\mathrm{sin}\:\left(\mathrm{90}°+\mathrm{18}°\right)}{\mathrm{sin}\:\left(\mathrm{180}°−\mathrm{36}°\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{cos}\:\mathrm{18}°}{\mathrm{sin}\:\mathrm{36}°}\:=\:\frac{\mathrm{cos}\:\mathrm{18}°}{\mathrm{2sin}\:\mathrm{18}°\:\mathrm{cos}\:\mathrm{18}°} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{2sin}\:\mathrm{18}°}\:=\:\frac{\mathrm{1}}{\mathrm{2}\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}\right)} \\…

A-stone-is-thrown-into-a-circular-pond-of-radius-1m-Suppose-the-stone-falls-uniformly-at-random-on-the-area-of-the-pond-What-will-be-the-expected-distance-od-the-stone-from-the-centre-of-the-pond-a-

Question Number 37168 by NECx last updated on 10/Jun/18 $${A}\:{stone}\:{is}\:{thrown}\:{into}\:{a}\:{circular} \\ $$$${pond}\:{of}\:{radius}\:\mathrm{1}{m}.{Suppose}\:{the} \\ $$$${stone}\:{falls}\:{uniformly}\:{at}\:{random} \\ $$$${on}\:{the}\:{area}\:{of}\:{the}\:{pond}.{What} \\ $$$${will}\:{be}\:{the}\:{expected}\:{distance}\:{od} \\ $$$${the}\:{stone}\:{from}\:{the}\:{centre}\:{of}\:{the} \\ $$$${pond}. \\ $$$$ \\…