Question Number 144736 by mathdanisur last updated on 28/Jun/21 $${P}\left({z}\right)={az}^{\mathrm{3}} +{z}^{\mathrm{2}} −\left({a}+\mathrm{6}\right){z}+{b}−\mathrm{6} \\ $$$${P}\left({z}\right)=\left({z}^{\mathrm{2}} +\mathrm{4}\right)\centerdot{Q}\left({z}\right) \\ $$$${Find}\:\:{a}\centerdot{b}=? \\ $$ Answered by nimnim last updated on…
Question Number 79190 by mr W last updated on 23/Jan/20 $${if}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{50}, \\ $$$${find}\:{the}\:{minimum}\:{and}\:{maximum}\:{of} \\ $$$$\left({x}+{y}\right)^{\mathrm{2}} −\mathrm{8}\left({x}+{y}\right)+\mathrm{20} \\ $$ Commented by jagoll last updated…
Question Number 144716 by mathdanisur last updated on 28/Jun/21 $$\int\left(\frac{{dx}}{{e}^{\mathrm{2}{x}} +\mathrm{1}}\right)=? \\ $$ Answered by imjagoll last updated on 28/Jun/21 $$\:\mathrm{let}\:\mathrm{e}^{\mathrm{x}} \:=\:\mu\:\Rightarrow\mathrm{dx}\:=\:\frac{\mathrm{d}\mu}{\mathrm{e}^{\mathrm{x}} }\:=\:\frac{\mathrm{d}\mu}{\mu} \\ $$$$\mathrm{I}=\int\:\left(\frac{\mathrm{1}}{\mu^{\mathrm{2}}…
Question Number 13647 by chux last updated on 22/May/17 $$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{5}…..\left(\mathrm{1}\right) \\ $$$$\mathrm{3x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} =\mathrm{1}…..\left(\mathrm{2}\right) \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$ Commented…
Question Number 13645 by chux last updated on 21/May/17 $$\mathrm{please}\:\mathrm{is}\:\mathrm{factor}\:\mathrm{theorem}\:\mathrm{and}\:\mathrm{error} \\ $$$$\mathrm{and}\:\mathrm{trial}\:\mathrm{the}\:\mathrm{same}?\:\mathrm{please}\:\mathrm{help}\: \\ $$$$\mathrm{cause}\:\mathrm{i}\:\mathrm{think}\:\mathrm{theres}\:\mathrm{a}\:\mathrm{difference} \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{cant}\:\mathrm{explain}\:\mathrm{it}. \\ $$$$ \\ $$$$\mathrm{Thankz}. \\ $$ Terms of Service…
Question Number 144708 by mathdanisur last updated on 28/Jun/21 $${Simplify}:\:\:\left(\frac{\mathrm{1}}{\left({x}-\mathrm{2}\right)!}\:-\:\frac{\mathrm{1}}{\left({x}-\mathrm{1}\right)!}\right)\centerdot{x}! \\ $$ Answered by MJS_new last updated on 28/Jun/21 $$\left(\frac{\left({x}−\mathrm{1}\right){x}}{{x}!}−\frac{{x}}{{x}!}\right){x}!={x}^{\mathrm{2}} −\mathrm{2}{x}={x}\left({x}−\mathrm{2}\right) \\ $$ Commented by…
Question Number 144693 by mathdanisur last updated on 27/Jun/21 Answered by Rasheed.Sindhi last updated on 28/Jun/21 $${All}\:{natural}\:{numbers}\:{fall}\:{into}\:{the} \\ $$$${following}\:\mathrm{6}\:{catagories}\:{with}\:{respect} \\ $$$${to}\:{modulo}\:\mathrm{6}\:: \\ $$$$\mathrm{6}{k},\mathrm{6}{k}+\mathrm{1},\mathrm{6}{k}+\mathrm{2},\mathrm{6}{k}+\mathrm{3},\mathrm{6}{k}+\mathrm{4},\mathrm{6}{k}+\mathrm{5} \\ $$$${Obviously}\:\underset{=\mathrm{6}{k}}…
Question Number 79147 by jagoll last updated on 23/Jan/20 $$\sqrt{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}+\sqrt{\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:}\leqslant\frac{\mathrm{2}}{\mathrm{x}} \\ $$ Answered by john santu last updated on 23/Jan/20 $$\sqrt{\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}^{\mathrm{2}} }}+\sqrt{\frac{{x}^{\mathrm{3}}…
Question Number 144682 by mathdanisur last updated on 27/Jun/21 $${Compare}:\:\:{x}=\frac{{sin}\left(\mathrm{3}\right)}{{sin}\left(\mathrm{5}\right)}\:\:{and}\:\:{y}=\frac{{cos}\left(\mathrm{3}\right)}{{cos}\left(\mathrm{5}\right)} \\ $$ Answered by mindispower last updated on 27/Jun/21 $$\mathrm{5}\:{degree} \\ $$$$\frac{\mathrm{5}\pi}{\mathrm{180}},\frac{\mathrm{3}\pi}{\mathrm{180}} \\ $$$${x}\overset{{f}} {\rightarrow}{tg}\left({x}\right),{f}'\left({x}\right)=\mathrm{1}+{tg}^{\mathrm{2}}…
Question Number 144676 by loveineq last updated on 27/Jun/21 $$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{b}\right)\left({b}+{c}\right)\:=\:\mathrm{4}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}+\frac{{b}}{{ca}}\:\geqslant\:\frac{\mathrm{27}}{\mathrm{8}} \\ $$$$\left(\mathrm{Found}\:\mathrm{by}\:\mathrm{WolframAlpha}\right) \\ $$ Answered by ArielVyny last updated on 27/Jun/21 $$ \\…