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Category: Arithmetic

Question-180498

Question Number 180498 by Spillover last updated on 12/Nov/22 Commented by Frix last updated on 13/Nov/22 $$\mathrm{more}\:\mathrm{challenging}\:\mathrm{extra}\:\mathrm{work}: \\ $$$$\omega=\frac{\left(\frac{\mathrm{log}_{{a}^{\mathrm{3}} +{b}^{\mathrm{4}} } ^{\mathrm{2}} \:{z}}{\mathrm{25}}−{R}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \pm\left(\left(\left(\frac{\mathrm{log}_{{a}^{\mathrm{3}}…

Question-49357

Question Number 49357 by peter frank last updated on 06/Dec/18 Commented by maxmathsup by imad last updated on 01/Jan/19 $$\left.\mathrm{2}\right)\:{let}\:{prove}\:{that}\:{y}^{\left({n}\right)} \left({x}\right)=\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \left({n}−\mathrm{1}\right)!}{\left(\mathrm{1}+{x}\right)^{{n}} }\:\:{with}\:{y}\left({x}\right)={ln}\left(\mathrm{1}+{x}\right) \\ $$$${by}\:{recurrence}\:{on}\:{n}\:\:{for}\:{n}=\mathrm{1}\:\:\:{y}^{\left(\mathrm{1}\right)}…

Question-49299

Question Number 49299 by peter frank last updated on 05/Dec/18 Commented by maxmathsup by imad last updated on 05/Dec/18 $$\left.{a}\right)\:{let}\:{I}\:=\int\:\:\frac{{x}\:{e}^{\mathrm{2}{x}} }{\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} }{dx}\:\:{changement}\:\mathrm{2}{x}\:={t}\:{give} \\ $$$${I}\:=\int\:\frac{{te}^{{t}} }{\mathrm{2}\left(\mathrm{1}+{t}\right)^{\mathrm{2}}…

Question-180364

Question Number 180364 by peter frank last updated on 11/Nov/22 Answered by Acem last updated on 11/Nov/22 $${S}_{\mathrm{1}} =\:\mathrm{150}\:\mathrm{log}_{\mathrm{5}} \:\frac{{m}}{\mathrm{3}}=\:\mathrm{150}\:\mathrm{log}_{\mathrm{5}} \:\mathrm{5}^{\mathrm{2}} =\:\mathrm{300}\:=\:{S}_{\mathrm{2}} \\ $$ Terms…

Question-180363

Question Number 180363 by peter frank last updated on 11/Nov/22 Answered by mr W last updated on 11/Nov/22 $${t}={y}^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$${y}={t}^{\mathrm{2}} \\ $$$$\left(\frac{\mathrm{2}\:\mathrm{log}\:{t}}{\mathrm{log}\:\mathrm{3}}\right)^{\mathrm{2}} −\mathrm{log}\:{t}−\frac{\mathrm{3}}{\mathrm{2}}=\mathrm{0} \\…

Let-K-be-a-field-and-a-b-K-Show-that-x-a-x-b-if-and-only-if-a-b-

Question Number 49236 by cesar.marval.larez@gmail.com last updated on 04/Dec/18 $${Let}\:{K}\:{be}\:{a}\:{field}\:{and}\:{a},{b}\in{K}.\:{Show}\: \\ $$$${that}\:\left({x}−{a}\right)\left({x}−{b}\right)\:{if}\:{and}\:{only}\:{if}\:{a}={b} \\ $$ Commented by kaivan.ahmadi last updated on 05/Dec/18 $$\left(\mathrm{x}−\mathrm{a}\right)\left(\mathrm{x}−\mathrm{b}\right)=? \\ $$ Commented…