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Category: Algebra

Solve-the-differential-equation-x-y-1-dx-x-1-dy-0-

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Question Number 161058 by HongKing last updated on 11/Dec/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$$\mathrm{x}\left(\mathrm{y}-\mathrm{1}\right)\mathrm{dx}\:+\:\left(\mathrm{x}+\mathrm{1}\right)\mathrm{dy}\:=\:\mathrm{0} \\ $$$$ \\ $$ Answered by mr W last updated on 11/Dec/21 $$\frac{{dy}}{{dx}}+\frac{{x}}{{x}+\mathrm{1}}\left({y}−\mathrm{1}\right)=\mathrm{0}…

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6-man-8-woman-working-a-job-in-10-days-26-man-48-woman-in-2-days-if-15-man-20-woman-days-

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Question Number 95502 by bobhans last updated on 25/May/20 $$\mathrm{6}\:\mathrm{man}\:+\:\mathrm{8}\:\mathrm{woman}\:\Rightarrow\mathrm{working}\:\mathrm{a}\:\mathrm{job}\:\mathrm{in}\:\mathrm{10}\:\mathrm{days} \\ $$$$\mathrm{26}\:\mathrm{man}\:+\:\mathrm{48}\:\mathrm{woman}\:\Rightarrow\:\mathrm{in}\:\mathrm{2}\:\mathrm{days} \\ $$$$\mathrm{if}\:\mathrm{15}\:\mathrm{man}\:+\:\mathrm{20}\:\mathrm{woman}\:\Rightarrow\:??\:\mathrm{days} \\ $$ Commented by bobhans last updated on 25/May/20 $$\mathrm{my}\:\mathrm{answer}\:\mathrm{4}\:\mathrm{days}.\:\mathrm{it}\:\mathrm{correct}? \\…

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let-the-differential-equation-1-x-y-x-1-x-y-x-1-x-1-x-y-x-y-0-1-y-0-0-then-prove-that-0-y-x-y-x-y-x-e-x-dx-3-2-

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Question Number 161039 by HongKing last updated on 11/Dec/21 $$\mathrm{let}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$$\left(\mathrm{1}\:+\:\mathrm{x}\right)\:\mathrm{y}^{''} \left(\mathrm{x}\right)\:+\:\left(\mathrm{1}\:-\:\mathrm{x}\right)\:\mathrm{y}^{'} \left(\mathrm{x}\right)\:=\:\frac{\mathrm{1}-\mathrm{x}}{\mathrm{1}+\mathrm{x}}\:\mathrm{y}\left(\mathrm{x}\right) \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{1}\:,\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\left(\mathrm{y}^{''} \left(\mathrm{x}\right)\:+\:\mathrm{y}^{'} \left(\mathrm{x}\right)\:+\:\mathrm{y}\left(\mathrm{x}\right)\right)\:\mathrm{e}^{-\boldsymbol{\mathrm{x}}}…

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Solve-for-x-R-3-x-x-3-x-

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Question Number 161035 by cortano last updated on 11/Dec/21 $${Solve}\:{for}\:{x}\:\epsilon\:\mathbb{R}\: \\ $$$$\:\sqrt{\sqrt{\mathrm{3}}−{x}}\:=\:{x}\sqrt{\sqrt{\mathrm{3}}+{x}}\: \\ $$ Answered by Rasheed.Sindhi last updated on 11/Dec/21 $$\:\sqrt{\sqrt{\mathrm{3}}−{x}}\:=\:{x}\sqrt{\sqrt{\mathrm{3}}+{x}}\: \\ $$$$\sqrt{\mathrm{3}}\:−{x}={x}^{\mathrm{2}} \left(\sqrt{\mathrm{3}}\:+{x}\right)…

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1-x-1-x-x-3-0-

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Question Number 161000 by bobhans last updated on 10/Dec/21 $$\:\:\sqrt{\mathrm{1}−\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}}}\:+\:\mid\mathrm{x}−\mathrm{3}\mid\:\geqslant\:\mathrm{0}\: \\ $$ Commented by cortano last updated on 10/Dec/21 $$\:\:\:\mathrm{x}<\mathrm{0} \\ $$ Terms of Service…

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9b-2-25-why-is-this-inside-the-bracket-as-it-is-a-diffetence-of-two-squares-

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Question Number 95469 by 6532 last updated on 25/May/20 $$\left(\mathrm{9b}^{\mathrm{2}} −\mathrm{25}\right) \\ $$$$\mathrm{why}\:\mathrm{is}\:\mathrm{this}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{bracket}\:\mathrm{as}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{diffetence}\:\mathrm{of}\:\mathrm{two}\:\mathrm{squares}? \\ $$ Commented by PRITHWISH SEN 2 last updated on 25/May/20 $$\left(\mathrm{3b}−\mathrm{5}\right)\left(\mathrm{3b}+\mathrm{5}\right)…

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