Question Number 102980 by ajfour last updated on 12/Jul/20 Commented by ajfour last updated on 12/Jul/20 $${Find}\:\:{a}/{b}\:\:{if}\:{regions}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5} \\ $$$${have}\:{equal}\:{areas}. \\ $$ Commented by mr W…
Question Number 102910 by bramlex last updated on 11/Jul/20 $$\left(\mathrm{1}\right)\underset{\mathrm{m}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{m}\pi}{\mathrm{2n}+\mathrm{1}}\right) \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{m}\:=\:\mathrm{1}} {\overset{\mathrm{n}} {\prod}}\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{m}\pi}{\mathrm{2n}+\mathrm{1}}\right)\: \\ $$ Answered by floor(10²Eta[1]) last updated…
Question Number 168233 by alcohol last updated on 06/Apr/22 $$\begin{cases}{{u}_{\mathrm{0}} \:=\:\mathrm{3}\::\:{u}_{\mathrm{1}} \:=\:\mathrm{4}}\\{{u}_{{n}+\mathrm{1}} \:=\:{u}_{{n}} \:+\:\mathrm{6}{u}_{{n}−\mathrm{1}} }\end{cases} \\ $$$${Express}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n} \\ $$ Answered by mr W last…
Question Number 167520 by MikeH last updated on 18/Mar/22 $$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)\:=\:\int_{{x}} ^{\mathrm{2}{x}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{t}^{\mathrm{4}} }}{dt} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{state}\:\mathrm{its}\:\mathrm{domain} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{is}\:{f}\left({x}\right)\:\mathrm{even}\:\mathrm{or}\:\mathrm{odd}? \\ $$ Answered by aleks041103 last updated on…
Question Number 101851 by bemath last updated on 05/Jul/20 Answered by bobhans last updated on 05/Jul/20 $${OA}\:=\:{OB}\:=\:{radius} \\ $$$$\angle{CAO}\:=\:\angle{OBA}\:=\:\beta\:\rightarrow\angle{AOP}\:=\:\mathrm{2}\beta \\ $$$${PA}\:{is}\:{tangent}\:\rightarrow\angle{OAP}\:=\:\mathrm{90}^{{o}} \\ $$$${then}\:\angle{APO}\:=\:\mathrm{90}^{{o}} −\mathrm{2}\beta\: \\…
Question Number 101686 by bemath last updated on 04/Jul/20 Commented by bemath last updated on 05/Jul/20 $$\mathrm{R}\:=\:\frac{\mathrm{abc}}{\mathrm{4L}_{\Delta\mathrm{ABC}} }\:,\:\mathrm{s}\:=\frac{\mathrm{13}+\mathrm{14}+\mathrm{15}}{\mathrm{2}}\:=\:\frac{\mathrm{42}}{\mathrm{2}}\:=\mathrm{21} \\ $$$$\mathrm{area}\:\Delta\mathrm{ABC}\:=\:\sqrt{\mathrm{21}×\mathrm{8}×\mathrm{7}×\mathrm{6}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{7}×\mathrm{3}×\mathrm{4}\:=\:\mathrm{84} \\ $$$$\mathrm{R}\:=\:\frac{\mathrm{13}×\mathrm{14}×\mathrm{15}}{\mathrm{4}×\mathrm{84}}\:=\:\frac{\mathrm{13}×\mathrm{15}}{\mathrm{24}} \\…
Question Number 36030 by kami last updated on 27/May/18 $$\mathrm{Q}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{for}\:\mathrm{area}\:\mathrm{of}\:\mathrm{sphere}?\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{4}\pi\mathrm{r}^{\mathrm{2}} .\:\mathrm{And}\:\mathrm{all}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{cube}\:\mathrm{touches}\:\mathrm{the}\:\mathrm{sphere}. \\ $$ Commented by Rasheed.Sindhi last updated on 28/May/18 $$\mathrm{What}\:\mathrm{does}\:\mathrm{r}\:\mathrm{represent}\:\mathrm{to}?\:\mathrm{Is}\:\mathrm{it}\:\mathrm{radius}\:\mathrm{of} \\ $$$$\mathrm{sphere}?…
Question Number 35968 by RoachDN last updated on 26/May/18 Commented by Joel579 last updated on 26/May/18 $$\mathrm{Would}\:\mathrm{you}\:\mathrm{mind}\:\mathrm{to}\:\mathrm{translate}\:\mathrm{the}\:\mathrm{question}\:\mathrm{into}\:\mathrm{english}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 101110 by bemath last updated on 30/Jun/20 Answered by bramlex last updated on 30/Jun/20 $${v}_{{simon}} \:=\:\mathrm{3}×{v}_{{Ian}} \\ $$$$\Rightarrow\frac{\mathrm{6}×\mathrm{50}}{{v}_{{Ian}} }\:=\:\frac{\mathrm{5}\left(\mathrm{100}+\mathrm{2}{x}\right)}{\mathrm{3}×{v}_{{Ian}} } \\ $$$$\mathrm{180}\:=\:\mathrm{100}+\mathrm{2}{x}\:\Rightarrow{x}\:=\:\mathrm{40}\:{m}\:\leftarrow{wide}\:{is}\:{the}\:{pool} \\…
Question Number 100528 by bemath last updated on 27/Jun/20 Commented by bemath last updated on 27/Jun/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{shaded}\:\mathrm{area}\:\mathrm{region} \\ $$ Commented by Dwaipayan Shikari last updated…