Question Number 165226 by Neils last updated on 27/Jan/22 $${make}\:{x}\:{the}\:{subject}\:{of}\:{the}\:{formula}; \\ $$$${a}^{{x}} +{bx}+{c}=\mathrm{0} \\ $$ Answered by mr W last updated on 28/Jan/22 $${a}^{{x}} =−\left({bx}+{c}\right)…
Question Number 165215 by HongKing last updated on 27/Jan/22 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{tan}^{−\mathrm{1}} \:\left(\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\right) \\ $$ Answered by mindispower last updated on 27/Jan/22 $${S}=\Sigma\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{n}^{\mathrm{2}}…
Question Number 165209 by HongKing last updated on 27/Jan/22 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{k}}} {\sum}}\:\frac{\mathrm{n}^{\mathrm{2}} \:\mathrm{sin}^{\mathrm{2}} \:\frac{\mathrm{n}\pi}{\mathrm{2}}}{\mathrm{n}^{\mathrm{4}} \:\pi^{\mathrm{4}} \:+\:\mathrm{n}^{\mathrm{2}} \:\pi^{\mathrm{2}} \:\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$ Terms of Service Privacy Policy…
Question Number 34139 by NECx last updated on 01/May/18 $${What}\:{is}\:{the}\:{remainder}\:{when} \\ $$$$\mathrm{17}^{\mathrm{200}} \:{is}\:{divided}\:{by}\:\mathrm{18} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 01/May/18 $${letn}=\mathrm{200} \\ $$$${so}\:{problem}\:{is}\:\left(\mathrm{18}−\mathrm{1}\right)^{{n}}…
Question Number 99655 by bemath last updated on 22/Jun/20 Commented by bramlex last updated on 22/Jun/20 $${approximation}\:{x}=\mathrm{7}.\mathrm{464} \\ $$$$\Leftrightarrow\:{x}−\mathrm{2}\sqrt{{x}}\:=\:\mathrm{7}.\mathrm{464}−\mathrm{2}\sqrt{\mathrm{7}.\mathrm{464}}\:\approx\:\mathrm{1}.\mathrm{9999355}…\: \\ $$ Answered by Farruxjano last…
Question Number 99645 by bramlex last updated on 22/Jun/20 $${If}\:{x},{y}\:>\:\mathrm{0}\:{then}\:\mid\sqrt{{xy}}−\frac{{x}+{y}}{\mathrm{2}}\mid\:+\:\mid\frac{{x}+{y}}{\mathrm{2}}\:+\:\sqrt{{xy}}\:\mid\:= \\ $$ Commented by bemath last updated on 22/Jun/20 $$\mathrm{since}\:\sqrt{\mathrm{xy}}\:>\:\mathrm{0}\:\&\:\frac{\mathrm{x}+\mathrm{y}}{\mathrm{2}}\:>\:\mathrm{0} \\ $$$$\mathrm{so}\:\frac{\mathrm{x}+\mathrm{y}}{\mathrm{2}}\:+\:\sqrt{\mathrm{xy}}\:>\:\mathrm{0} \\ $$$$\mathrm{case}\left(\mathrm{1}\right)\:\mathrm{if}\:\sqrt{\mathrm{xy}}−\frac{\mathrm{x}+\mathrm{y}}{\mathrm{2}}\:>\:\mathrm{0} \\…
Question Number 165157 by mathlove last updated on 26/Jan/22 $$\underset{{k}=\mathrm{6}} {\overset{{n}+\mathrm{6}} {\sum}}\left({k}−\mathrm{4}\right)=\frac{{an}^{\mathrm{2}} +{bn}+{c}}{\mathrm{2}} \\ $$$${a}+{b}+{c}=? \\ $$ Commented by bobhans last updated on 30/Jan/22 $$\:\underset{\mathrm{k}=\mathrm{6}}…
Question Number 99621 by student work last updated on 22/Jun/20 $$\mathrm{6}^{\mathrm{x}} =\mathrm{x}^{\mathrm{5}\:\:\:\:\:\:\:} \mathrm{x}=?\:\:\:\:\:\:\:\mathrm{help}\:\mathrm{me} \\ $$ Commented by Dwaipayan Shikari last updated on 22/Jun/20 $$\frac{{x}}{{logx}}=\frac{\mathrm{5}}{{log}\mathrm{6}} \\…
Question Number 165153 by mathlove last updated on 26/Jan/22 $${f}\left({x}\right)=\mathrm{3}{e}^{\mathrm{2}{x}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by mahdipoor last updated on 26/Jan/22 $$\Rightarrow{x}=\mathrm{3}{e}^{\mathrm{2}{y}} \Rightarrow\frac{\mathrm{1}}{\mathrm{2}}{ln}\frac{{x}}{\mathrm{3}}={y}={f}^{−\mathrm{1}} \left({x}\right)…
Question Number 34081 by Aditya 879 last updated on 30/Apr/18 $$\mathrm{2}^{{n}} −\mathrm{2}^{{n}−\mathrm{1}} =\mathrm{4}\:.{find}\:{n}^{{n}.} \\ $$ Answered by math1967 last updated on 30/Apr/18 $$\mathrm{2}^{{n}} \left(\mathrm{1}−\mathrm{2}^{−\mathrm{1}} \right)=\mathrm{4}…