Question Number 86063 by john santu last updated on 26/Mar/20 Answered by mr W last updated on 26/Mar/20 $$\left(\frac{\mathrm{1}}{{R}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{6}}−\frac{\mathrm{1}}{\mathrm{9}}\right)^{\mathrm{2}} =\mathrm{2}\left(\frac{\mathrm{1}}{{R}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{9}^{\mathrm{2}} }\right) \\…
Question Number 20511 by dioph last updated on 27/Aug/17 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{unit}\:\mathrm{radius}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circular} \\ $$$$\mathrm{spot}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sphere}'\mathrm{s}\:\mathrm{surface}\:\mathrm{given} \\ $$$$\mathrm{the}\:\mathrm{latitude}\:\beta\:\mathrm{and}\:\mathrm{the}\:\mathrm{longitude}\:\lambda \\ $$$$\mathrm{of}\:\mathrm{its}\:\mathrm{center}\:\mathrm{and}\:\mathrm{its}\:\mathrm{angular}\:\mathrm{radius}\:{r}. \\ $$ Terms of Service Privacy Policy…
Question Number 151513 by pete last updated on 21/Aug/21 $$\mathrm{Find}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{p}\:\mathrm{if}\:\mathrm{the}\:\mathrm{lines} \\ $$$${px}−{y}=\mathrm{0}\:\mathrm{and}\:\mathrm{3}{x}+{y}+\mathrm{1}=\mathrm{0}\:\mathrm{intersect}\:\mathrm{at}\:\mathrm{45}° \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\Delta_{\mathrm{1}} \::\:{px}−{y}\:=\:\mathrm{0} \\ $$$$\Delta_{\mathrm{2}}…
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Question Number 151164 by puissant last updated on 18/Aug/21 Commented by puissant last updated on 18/Aug/21 $${solve}\:{in}\:\mathbb{R} \\ $$ Answered by MJS_new last updated on…
Question Number 150977 by aupo14 last updated on 17/Aug/21 Answered by talminator2856791 last updated on 17/Aug/21 $$\:\sqrt{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 19884 by ajfour last updated on 17/Aug/17 Commented by ajfour last updated on 17/Aug/17 $$\:\:{A}\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} \right)\:;\:\:{B}\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right)\:\:;\:{C}\left({x}_{\mathrm{3}} ,{y}_{\mathrm{3}} \right)\:\:; \\ $$$$\:\:{D}\left({x}_{\mathrm{4}}…
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Question Number 150864 by puissant last updated on 16/Aug/21 Answered by ajfour last updated on 16/Aug/21 $$\mathrm{70}°=\theta,\:\mathrm{30}°=\alpha,\:\mathrm{40}°=\beta,\:\mathrm{6}{cm}={r} \\ $$$${A}_{\mathrm{1}} =\left({r}−\mathrm{2}{r}\mathrm{cos}\:\theta\right){r}\mathrm{sin}\:\beta \\ $$$${A}_{\mathrm{2}} =\frac{{r}\left(\mathrm{1}−\mathrm{2cos}\:\theta\right)\left\{{r}\mathrm{sin}\:\theta−{r}\mathrm{sin}\:\beta\right\}}{\mathrm{2}} \\ $$$${A}_{\mathrm{3}}…