Question Number 202591 by Calculusboy last updated on 30/Dec/23 Answered by mr W last updated on 30/Dec/23 $$\frac{{dy}}{{dx}}+\mathrm{1}+\frac{{y}}{{x}}=\mathrm{0} \\ $$$${let}\:{y}={xt} \\ $$$$\frac{{dy}}{{dx}}={t}+{x}\frac{{dt}}{{dx}} \\ $$$${t}+{x}\frac{{dt}}{{dx}}+\mathrm{1}+{t}=\mathrm{0} \\…
Question Number 202616 by hardmath last updated on 30/Dec/23 $$\mathrm{If}\:\:\:\:\:\frac{\mathrm{a}}{\mathrm{a}\:+\:\mathrm{b}}\:−\:\frac{\mathrm{1}\:−\:\mathrm{a}}{\mathrm{a}\:−\:\mathrm{b}}\:=\:\mathrm{x} \\ $$$$\mathrm{Find}\:\:\:\:\:\frac{\mathrm{1}\:−\:\mathrm{b}}{\mathrm{a}\:−\:\mathrm{b}}\:+\:\frac{\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 30/Dec/23 $$\frac{{a}}{{a}\:+\:{b}}\:−\:\frac{\mathrm{1}\:−\:{a}}{{a}\:−\:{b}}\:=\:{x} \\ $$$$\Rightarrow\:\frac{{a}}{{a}\:+\:{b}}\:−\:\mathrm{1}\:−\:\frac{\mathrm{1}\:−\:{a}}{{a}\:−\:\:{b}}\:−\:\mathrm{1}\:=\:{x}\:−\:\mathrm{2} \\…
Question Number 202584 by cortano12 last updated on 30/Dec/23 $$\:\:\: \\ $$ Answered by dimentri last updated on 30/Dec/23 $$\mathrm{2}\:\begin{pmatrix}{\mathrm{m}}\\{\mathrm{2}}\end{pmatrix}\:−\:\mathrm{4m}\:=\:\mathrm{84} \\ $$$$\:\mathrm{m}^{\mathrm{2}} −\mathrm{5m}−\mathrm{84}\:=\:\mathrm{0} \\ $$$$\:\mathrm{m}\:=\:\mathrm{12}\:…
Question Number 202581 by Frix last updated on 30/Dec/23 Commented by Frix last updated on 30/Dec/23 $$\mathrm{An}\:\mathrm{easy}\:\mathrm{one}:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}. \\ $$ Answered by mr W last updated…
Question Number 202614 by a.lgnaoui last updated on 30/Dec/23 $$\mathrm{find}\:\mathrm{x} \\ $$$$ \\ $$ Commented by a.lgnaoui last updated on 30/Dec/23 Commented by a.lgnaoui last…
Question Number 202636 by ibroclex_adex last updated on 30/Dec/23 $$\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\:^{\mathrm{3}} \sqrt{\mathrm{4}^{\mathrm{5}−\mathrm{x}} }}{\int_{\mathrm{4}} ^{\mathrm{6}} \left(\mathrm{x}−\mathrm{1}\right){dx}}\:=\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2x}−\mathrm{1}} }\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\mathrm{Solution}}…
Question Number 202604 by MATHEMATICSAM last updated on 30/Dec/23 $$\mathrm{If}\:{x}\:=\:\frac{\sqrt{{a}\:+\:\mathrm{1}}\:+\:\sqrt{{a}\:−\:\mathrm{1}}}{\:\sqrt{{a}\:+\:\mathrm{1}}\:−\:\sqrt{{a}\:−\:\mathrm{1}}}\:\mathrm{and}\: \\ $$$${y}\:=\:\frac{\sqrt{{a}\:+\:\mathrm{1}}\:−\:\sqrt{{a}\:−\:\mathrm{1}}}{\:\sqrt{{a}\:+\:\mathrm{1}}\:+\:\sqrt{{a}\:−\:\mathrm{1}}}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{{x}^{\mathrm{2}} \:−\:{xy}\:+\:{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} \:+\:{xy}\:+\:{y}^{\mathrm{2}} }\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} \:−\:\mathrm{3}}{\mathrm{4}{a}^{\mathrm{2}} \:−\:\mathrm{1}}\:. \\ $$ Answered by Rasheed.Sindhi…
Question Number 202605 by hardmath last updated on 30/Dec/23 Commented by mr W last updated on 30/Dec/23 $${what}\:{do}\:{you}\:{mean}\:{when}\:{you}\:{write} \\ $$$$\underset{={b}} {{max}}\:\underset{={a}} {{min}}\:\left(…\right)\:? \\ $$ Commented…
Question Number 202633 by hardmath last updated on 30/Dec/23 Answered by cortano12 last updated on 31/Dec/23 $$\:\mathrm{5}\clubsuit\mathrm{6}\:=\:\mathrm{5}−\mathrm{6}=−\mathrm{1} \\ $$$$\:\left(\mathrm{5}\clubsuit\mathrm{6}\right)\clubsuit\mathrm{9}\:=\:−\mathrm{1}\clubsuit\mathrm{9}\:=\:−\mathrm{1}−\mathrm{9}=−\mathrm{10} \\ $$ Commented by hardmath last…
Question Number 202630 by ajfour last updated on 30/Dec/23 Commented by Frix last updated on 31/Dec/23 $$\left[\mathrm{I}\:\mathrm{forgot}\:\mathrm{to}\:\mathrm{check}\:\Rightarrow\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{positive}\:\mathrm{root}\right. \\ $$$$\left.\mathrm{is}\:\mathrm{false}\right] \\ $$ Commented by Frix…