Question Number 179449 by Shrinava last updated on 29/Oct/22 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{3sinx}\:+\:\mathrm{4}\left(\mathrm{y}\:+\:\mathrm{cosx}\right)\:=\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{9} \\ $$ Answered by mr W last updated on 29/Oct/22 $$\mathrm{3}\:\mathrm{sin}\:{x}+\mathrm{4}\:\mathrm{cos}\:{x}−\mathrm{5}={y}^{\mathrm{2}} −\mathrm{4}{y}+\mathrm{4}…
Question Number 48368 by behi83417@gmail.com last updated on 22/Nov/18 Answered by MJS last updated on 22/Nov/18 $${a}^{\frac{\mathrm{1}}{\mathrm{3}}} −{b}^{\frac{\mathrm{1}}{\mathrm{3}}} ={c} \\ $$$${a}−\mathrm{3}{a}^{\frac{\mathrm{2}}{\mathrm{3}}} {b}^{\frac{\mathrm{1}}{\mathrm{3}}} +\mathrm{3}{a}^{\frac{\mathrm{1}}{\mathrm{3}}} {b}^{\frac{\mathrm{2}}{\mathrm{3}}} −{b}={c}^{\mathrm{3}}…
Question Number 48367 by behi83417@gmail.com last updated on 22/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 23/Nov/18 $${xy}−\mathrm{1}=\sqrt{\mathrm{3}}\:\left({x}+{y}\right) \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}=\frac{{x}+{y}}{{xy}−\mathrm{1}} \\ $$$$\frac{{x}+{y}}{\mathrm{1}−{xy}}=−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$${tana}={x}\:\:\:{tanb}={y}\:\:\:\:{tanc}={z} \\ $$$${tan}\left({a}+{b}\right)=−\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}…
Question Number 179436 by Shrinava last updated on 29/Oct/22 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}}\:\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{x}\:+\:\mathrm{2}}{\mathrm{2x}\:+\:\mathrm{1}} \\ $$$$\mathrm{Find}:\:\:\:\:\:\mathrm{g}^{−\mathrm{1}} \left(\mathrm{f}\left(\mathrm{3}\right)\right)\:=\:? \\ $$ Commented by cherokeesay last updated on 29/Oct/22 $${y}=\frac{{x}+\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}}\Leftrightarrow\mathrm{2}{xy}+{y}={x}+\mathrm{2}\Rightarrow \\ $$$${x}\left(\mathrm{2}{y}−\mathrm{1}\right)=\mathrm{2}−{y}\Leftrightarrow{x}=\frac{\mathrm{2}−{y}}{\mathrm{2}{y}−\mathrm{1}}…
Question Number 179435 by Tawa11 last updated on 29/Oct/22 Commented by a.lgnaoui last updated on 29/Oct/22 $$\mathrm{V}? \\ $$ Answered by Peace last updated on…
Question Number 113894 by Aina Samuel Temidayo last updated on 16/Sep/20 Commented by MJS_new last updated on 16/Sep/20 $$\mathrm{let}\:{x}=\mathrm{2}\wedge{y}=\mathrm{4} \\ $$$$\mathrm{2}^{\mathrm{4}} =\mathrm{4}^{\mathrm{2}} =\mathrm{16} \\ $$$$\left({x}/{y}\right)^{\left({x}/{y}\right)}…
Question Number 113886 by Aina Samuel Temidayo last updated on 16/Sep/20 Answered by MJS_new last updated on 16/Sep/20 $$\left({a}\right) \\ $$ Commented by Aina Samuel…
Question Number 113876 by Aina Samuel Temidayo last updated on 16/Sep/20 $$\mathrm{If}\:\mathrm{2}^{\mathrm{x}} =\mathrm{4}^{\mathrm{y}} =\mathrm{8}^{\mathrm{z}} \:\mathrm{and}\:\mathrm{xyz}=\mathrm{288},\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{4y}}+\frac{\mathrm{1}}{\mathrm{8z}} \\ $$ Answered by Olaf last updated on…
Question Number 113885 by Aina Samuel Temidayo last updated on 16/Sep/20 Answered by MJS_new last updated on 16/Sep/20 $${x}=\frac{\mathrm{ln}\:{bc}}{\mathrm{ln}\:{a}}\:\:\:\:\:{y}=\frac{\mathrm{ln}\:{ac}}{\mathrm{ln}\:{b}}\:\:\:\:\:{z}=\frac{\mathrm{ln}\:{ab}}{\mathrm{ln}\:{c}} \\ $$$$\mathrm{ln}\:{a}\:={o};\:\mathrm{ln}\:{b}\:={p}\:;\:\mathrm{ln}\:{c}\:={q} \\ $$$${xyz}=\frac{{o}}{{p}}+\frac{{o}}{{q}}+\frac{{p}}{{o}}+\frac{{p}}{{q}}+\frac{{q}}{{o}}+\frac{{q}}{{p}}+\mathrm{2}={x}+{y}+{z}+\mathrm{2} \\ $$…
Question Number 113857 by ayenisamuel last updated on 15/Sep/20 $${find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which}\:{the} \\ $$$${line}\:{y}={kx}−\mathrm{3}\:{does}\:{not}\:{meet}\:{the}\:{curve} \\ $$$${y}=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+{k}. \\ $$ Answered by MJS_new last updated on 15/Sep/20 $$\mathrm{first},\:\mathrm{intersect}\:\mathrm{them}…