Question Number 225756 by ajfour last updated on 09/Nov/25 Commented by mr W last updated on 11/Nov/25 $${applying}\:{descartes}\:{theorem}\:{twice}: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{{r}}}=\frac{\mathrm{1}}{\:\sqrt{{R}}}+\frac{\mathrm{1}}{\:\sqrt{{R}}}=\frac{\mathrm{2}}{\:\sqrt{{R}}}\:\Rightarrow{r}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{{a}}}=\frac{\mathrm{1}}{\:\sqrt{{r}}}+\frac{\mathrm{1}}{\:\sqrt{{R}}}=\frac{\mathrm{3}}{\:\sqrt{{R}}} \\ $$$$\Rightarrow{a}=\frac{{R}}{\mathrm{9}} \\…
Question Number 225703 by ajfour last updated on 07/Nov/25 Answered by mahdipoor last updated on 07/Nov/25 $$\mathrm{2}×\left(\mathrm{R}−\mathrm{r}\right)^{\mathrm{2}} =\left(\mathrm{R}+\mathrm{r}\right)^{\mathrm{2}} \Rightarrow\mathrm{r}=\mathrm{R}\left(\mathrm{3}−\sqrt{\mathrm{8}}\right) \\ $$$$\mathrm{center}\:\mathrm{of}\:\mathrm{balls}\:\left(\mathrm{r}\right)\:\mathrm{in}\:\mathrm{R}_{\mathrm{c}} =\mathrm{R}−\mathrm{r}\:\: \\ $$$$\theta_{\mathrm{each}\:\mathrm{ball}} =\mathrm{2tan}^{−\mathrm{1}}…
Question Number 225656 by Jubr last updated on 05/Nov/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 225657 by Jubr last updated on 05/Nov/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 225658 by Jubr last updated on 05/Nov/25 Answered by ajfour last updated on 06/Nov/25 $${p}={R}\mathrm{sin}\:\alpha \\ $$$$\pi−\alpha=\frac{\mathrm{5}}{\mathrm{2}}\:\:\Rightarrow\:\:\mathrm{2}\alpha=\mathrm{2}\pi−\mathrm{5} \\ $$$$\angle{AOC}=\mathrm{2}\left(\frac{\pi}{\mathrm{2}}−\alpha\right)=\pi−\mathrm{2}\alpha \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\pi−\left(\mathrm{2}\pi−\mathrm{5}\right)=\mathrm{5}−\pi \\ $$$${A}_{{shade}}…
Question Number 225666 by mr W last updated on 05/Nov/25 Commented by mr W last updated on 05/Nov/25 $${an}\:{alternative}\:{solution} \\ $$ Commented by ajfour last…
Question Number 225416 by cherokeesay last updated on 25/Oct/25 Commented by Ghisom_ last updated on 25/Oct/25 $${x}=\mathrm{9}={AD} \\ $$ Commented by cherokeesay last updated on…
Question Number 225407 by mr W last updated on 25/Oct/25 Commented by mr W last updated on 25/Oct/25 $${the}\:{frustum}\:{of}\:{a}\:{cone}\:{is}\:{cut}\:{into} \\ $$$${two}\:{parts}\:{as}\:{shown}.\:{find}\:{the}\:{volume} \\ $$$${of}\:{each}\:{part}\:{and}\:{the}\:{area}\:{of}\:{the}\:{cut} \\ $$$${section}.…
Question Number 225354 by ajfour last updated on 22/Oct/25 Commented by ajfour last updated on 22/Oct/25 $${If}\:{P}\left(\mathrm{0},{q}\right)\:{while}\:{origin}\:{centered} \\ $$$${circle}\:{has}\:{radius}\:{R},\:{then}\:{find} \\ $$$${eq}.\:{of}\:{blue}\:{semicircle}\:{and}\:{hence}\: \\ $$$$\:{r},\:{C},\:{B}. \\ $$$${example}:\:{R}=\mathrm{5},\:{q}=\mathrm{3}…
Question Number 224927 by behi834171 last updated on 12/Oct/25 Commented by behi834171 last updated on 12/Oct/25 $$\boldsymbol{{s}}_{\mathrm{1}} =\mathrm{1};\boldsymbol{{s}}_{\mathrm{2}} =\mathrm{2};\boldsymbol{{s}}_{\mathrm{3}} =\mathrm{3}\left(\boldsymbol{{unit}}\right)^{\mathrm{2}} \\ $$$$\boldsymbol{{S}}_{\bigtriangleup} =?\:\left(\boldsymbol{{unit}}\right)^{\mathrm{2}} \\ $$…