Question Number 7969 by tawakalitu last updated on 26/Sep/16 $${During}\:{one}\:{year}\:{in}\:{a}\:{school},\:\frac{\mathrm{5}}{\mathrm{8}}\:{of}\:{the}\:{students} \\ $$$${had}\:{measiles}.\:\frac{\mathrm{1}}{\mathrm{2}}\:{had}\:{chickenpox},\:{and}\:\frac{\mathrm{1}}{\mathrm{8}}\:{had} \\ $$$${Neither}.\:{What}\:{fraction}\:{of}\:{the}\:{school}\:{had}\:{both} \\ $$$${measiles}\:{and}\:{chickenpox}. \\ $$ Answered by Rasheed Soomro last updated on…
Question Number 139036 by mnjuly1970 last updated on 21/Apr/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:{prove}\::: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{\sqrt{{x}}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}{dx}=\frac{\pi}{\mathrm{2}\sqrt{\varphi}} \\ $$$$\:\:\:\:\:\:\varphi:=\:{golden}\:{ratio}\:… \\ $$ Answered by Dwaipayan Shikari…
Question Number 73503 by ajfour last updated on 13/Nov/19 Commented by ajfour last updated on 13/Nov/19 $${Find}\:{the}\:{illuminated}\:{curved} \\ $$$${area}\:{of}\:{cone}\:{with}\:{radius}\:{a},\:{and} \\ $$$${altitude}\:{a}\sqrt{\mathrm{3}}\:.\:{Only}\:{the}\:{right}\:{half} \\ $$$${of}\:{cone}\:{is}\:{there}\:{with}\:{left}\:{half} \\ $$$${covered}\:{but}\:{with}\:{a}\:{largest}\:{circular}…
Question Number 139032 by bramlexs22 last updated on 21/Apr/21 Answered by EDWIN88 last updated on 21/Apr/21 $$\:\ell\mathrm{et}\:\mathrm{y}=\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\:\Rightarrow\mathrm{xy}+\mathrm{y}=\mathrm{1}−\mathrm{x}\: \\ $$$$\:\mathrm{xy}+\mathrm{x}=\mathrm{1}−\mathrm{y}\:\Rightarrow\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{y}}{\mathrm{1}+\mathrm{x}} \\ $$$$\:\left(\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\right)^{\mathrm{2}} .\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\:\ldots\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\right).\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} \:=\:\mathrm{x}\:\ldots\left(\mathrm{2}\right)…
Question Number 73499 by TawaTawa last updated on 13/Nov/19 Commented by MJS last updated on 13/Nov/19 $$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{unique}\:\mathrm{if}\:\mathrm{we}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mid{OP}\mid=\mathrm{2}{r} \\ $$ Commented by TawaTawa last updated on…
Question Number 7962 by upendrakishor99@gmail.com last updated on 25/Sep/16 $${prove}\:{that}\:\:\:{tanx}<\frac{\mathrm{4}{x}}{\pi}\:{for}\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{4}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7961 by tawakalitu last updated on 25/Sep/16 $$\int\frac{\mathrm{5}\:−\:{x}}{\mathrm{1}\:+\:\sqrt{{x}\:−\:\mathrm{4}}}\:{dx} \\ $$ Answered by Yozzia last updated on 25/Sep/16 $${I}=\int\frac{\mathrm{5}−{x}}{\mathrm{1}+\sqrt{{x}−\mathrm{4}}}{dx} \\ $$$${Let}\:{t}=\sqrt{{x}−\mathrm{4}}\Rightarrow{dt}=\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{4}\right)^{−\mathrm{1}/\mathrm{2}} {dx} \\ $$$${dx}=\mathrm{2}\left({x}−\mathrm{4}\right)^{\mathrm{1}/\mathrm{2}}…
Question Number 7960 by tawakalitu last updated on 25/Sep/16 $$\int\frac{\mathrm{4}\:−\:{x}}{\mathrm{4}\:+\:{x}}\:{dx} \\ $$ Commented by Yozzia last updated on 25/Sep/16 $$\int\frac{\mathrm{4}−{x}}{\mathrm{4}+{x}}{dx}=\int\left(\frac{\mathrm{8}}{\mathrm{4}+{x}}−\mathrm{1}\right){dx}=\mathrm{8}{ln}\left({x}+\mathrm{4}\right)−{x}+{c} \\ $$ Commented by tawakalitu…
Question Number 139029 by bramlexs22 last updated on 21/Apr/21 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)=\:\frac{\mathrm{x}}{\mathrm{x}+\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$ Answered by EDWIN88 last updated on 21/Apr/21 $$\:\:\:\:\:\:\:\:\:\mathrm{u}=\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} } \\…
Question Number 7959 by tawakalitu last updated on 25/Sep/16 $$\int\frac{{sin}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by nick last updated on 26/Sep/16 $${do}\:{you}\:{mean}\:\int\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\…