Question Number 71229 by naka3546 last updated on 13/Oct/19 Commented by naka3546 last updated on 13/Oct/19 $${Difference}\:\:{of}\:\:{red}\:\:{area}\:\:{and}\:\:{blue}\:\:{area}\:\:{is}\:\:… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 5692 by FilupSmith last updated on 24/May/16 $${f}\left({x}\right)={e}^{{x}} \\ $$$${g}\left({x}\right)=\mathrm{ln}\:{x} \\ $$$${h}\left({x}\right)={x} \\ $$$$ \\ $$$$\mathrm{A}\:\mathrm{line}\:{L}\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:{h}\left({x}\right)\:\mathrm{at}\:\mathrm{point} \\ $$$${P}\left({x},{y}\right)\:\mathrm{and}\:\mathrm{extends}\:\mathrm{and}\:\mathrm{disects}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right). \\ $$$$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:{L}\:\mathrm{between}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right) \\ $$$$\mathrm{is}\:{r}.\:\mathrm{When}\:\mathrm{is}\:{r}\:\mathrm{minimum}? \\…
Question Number 136761 by I want to learn more last updated on 25/Mar/21 Commented by I want to learn more last updated on 25/Mar/21 $$\mathrm{I}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}.…
Question Number 136760 by I want to learn more last updated on 25/Mar/21 Answered by mr W last updated on 25/Mar/21 $$\frac{{BC}}{\mathrm{sin}\:\angle{BDC}}=\frac{{CD}}{\mathrm{sin}\:\mathrm{30}°}\:\:\:\:\:…\left({i}\right) \\ $$$$\frac{\mathrm{sin}\:\angle{BDA}}{{AB}}=\frac{\mathrm{sin}\:\mathrm{45}°}{{DA}}\:\:\:…\left({ii}\right) \\…
Question Number 136762 by snipers237 last updated on 25/Mar/21 $$\:{let}\:\:{C}\left({a},{r}\right)=\left\{{z}\in\mathbb{C},\:\:\mid{z}−{a}\mid={r}\:\right\} \\ $$$${Let}\:{u},{v},{w}\:\in{C}\left({a},{r}\right)\:{such}\:{as}\:\:\:{u}+{v}=\mathrm{2}{w} \\ $$$${Prove}\:{that}\:\:\frac{{u}−{a}}{{v}−{a}}\:=\mathrm{1}\:,\:{u}={v}={w} \\ $$$$ \\ $$$${It}\:{shows}\:{that}\:{the}\:{middle}\:{of}\:{a}\:{segment}\: \\ $$$${joining}\:{two}\:{points}\:{in}\:{a}\:{circle}\:\:{is}\:{not}\:{in}\:{that}\:{circle} \\ $$ Terms of Service…
Question Number 136757 by Dwaipayan Shikari last updated on 25/Mar/21 $$\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{2}.\mathrm{1}!}+\left(\frac{\mathrm{1}.\mathrm{3}}{\mathrm{2}^{\mathrm{2}} }\right)^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} .\mathrm{2}!}+\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}^{\mathrm{3}} }\right).\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}!}+….=\left(\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\left(\mathrm{2}\pi^{\mathrm{3}} \right)^{\mathrm{1}/\mathrm{4}} }\right)^{\mathrm{2}} \\ $$ Answered by mindispower last…
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Question Number 5685 by sanusihammed last updated on 24/May/16 $${Find}\:{the}\:{value}\:{of}\:{x}\:. \\ $$$$ \\ $$$$\mathrm{9}^{{x}} \:=\:\mathrm{6}^{{x}} \:+\:\mathrm{4}^{{x}} \\ $$$$ \\ $$$${Please}\:{help}. \\ $$ Answered by prakash…
Question Number 136758 by mathlove last updated on 25/Mar/21 $$\:\:\mathrm{1}==>\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\pi}+\frac{\mathrm{1}}{\pi^{\mathrm{2}} }+\frac{\mathrm{1}}{\pi^{\mathrm{3}} }+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\pi^{{n}} }\right)=? \\ $$$$ \\ $$$$\:\mathrm{2}=>\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\centerdot\centerdot\centerdot\centerdot+{n}^{\mathrm{2}} }{\mathrm{1}−{n}^{\mathrm{3}} }=? \\ $$…
Question Number 5684 by sanusihammed last updated on 24/May/16 $${Find}\:{the}\:{value}\:{of}\:{x}\:.\: \\ $$$$ \\ $$$${x}^{\left({x}\:+\:\mathrm{2}\right)} \:=\:\left({x}\:+\:\mathrm{2}\right)^{{x}} \\ $$$$ \\ $$$${Thanks}\:{for}\:{your}\:{help}. \\ $$ Commented by prakash jain…