Category: Mensuration

Question Number 191143 by Mingma last updated on 19/Apr/23 Answered by HeferH last updated on 21/Apr/23 $$\mathrm{Say}\:\mathrm{CD}\:=\:\mathrm{a},\:\mathrm{DE}\:=\:\mathrm{b},\:\mathrm{AC}\:=\:\mathrm{c},\:\mathrm{AE}\:=\:\mathrm{d} \\ $$$$\:\ast\:\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:=\:\frac{\mathrm{1}}{\mathrm{5}}\:\Rightarrow \\ $$$$\:\mathrm{5}\left(\mathrm{b}−\mathrm{a}\right)=\:\mathrm{ab} \\ $$$$\:\ast\:\mathrm{cd}\:=\:\mathrm{ab}+\mathrm{64} \\ $$$$\:\mathrm{Since}\:\mathrm{AD}\:\mathrm{is}\:\mathrm{bisector}:…

Question Number 125593 by shaker last updated on 12/Dec/20 Answered by MJS_new last updated on 12/Dec/20 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }= \\ $$$$\:\:\:\:\:\left[\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}\:\left({search}\:{the}\:{www}\:{for}\:{it}\right)\right] \\ $$$$=\frac{{x}+\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right)}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}=…

Question Number 191076 by Mingma last updated on 17/Apr/23 Answered by mr W last updated on 18/Apr/23 $${touching}\:{point}\:{P}\left({p},\frac{\mathrm{1}}{{p}^{\mathrm{2}} }\right) \\ $$$$\mathrm{tan}\:\theta=−\frac{{dy}}{{dx}}=\frac{\mathrm{2}}{{p}^{\mathrm{3}} } \\ $$$${r}={p}−{r}\:\mathrm{sin}\:\theta={p}−\frac{\mathrm{2}{r}}{\:\sqrt{\mathrm{4}+{p}^{\mathrm{6}} }}…

Question Number 191062 by Mingma last updated on 17/Apr/23 Answered by mr W last updated on 17/Apr/23 Commented by mr W last updated on 17/Apr/23…

Question Number 125444 by ajfour last updated on 11/Dec/20 Commented by ajfour last updated on 11/Dec/20 $${Find}\:{radius}\:{of}\:{the}\:{quarter}\:{circle}. \\ $$ Answered by ajfour last updated on…