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Category: Algebra

if-a-and-b-are-positive-numbers-then-an-b-p-converges-if-p-gt-1-and-diverges-if-p-1-

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Question Number 163396 by HongKing last updated on 06/Jan/22 $$\mathrm{if}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers} \\ $$$$\mathrm{then}\:\:\Sigma\:\left(\mathrm{an}\:+\:\mathrm{b}\right)^{-\boldsymbol{\mathrm{p}}} \:\:\mathrm{converges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}>\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{diverges}\:\mathrm{if}\:\:\boldsymbol{\mathrm{p}}\leqslant\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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Question-163385

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Question Number 163385 by HongKing last updated on 06/Jan/22 Answered by mahdipoor last updated on 06/Jan/22 $$\mathrm{5}+{e}^{{x}} {sin}\left({x}+\frac{\pi}{\mathrm{4}}\right)+{e}^{−{x}} {cos}\left({x}+\frac{\pi}{\mathrm{4}}\right)= \\ $$$$\mathrm{5}+\sqrt{\mathrm{2}}\left(\left(\frac{{e}^{{x}} +{e}^{−{x}} }{\mathrm{2}}\right){cosx}+\left(\frac{{e}^{{x}} −{e}^{−{x}} }{\mathrm{2}}\right){sinx}\right)=…

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if-y-2-ax-2-bx-c-Show-that-y-d-3-y-dx-3-3-dy-dx-d-2-y-dx-2-0-

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Question Number 97818 by I want to learn more last updated on 09/Jun/20 $$\boldsymbol{\mathrm{if}}\:\:\:\:\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:\:=\:\:\boldsymbol{\mathrm{ax}}^{\mathrm{2}} \:+\:\boldsymbol{\mathrm{bx}}\:+\:\:\boldsymbol{\mathrm{c}} \\ $$$$\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}:\:\:\:\:\:\:\boldsymbol{\mathrm{y}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{3}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{3}} }\:\:+\:\:\mathrm{3}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:\:\:=\:\:\:\mathrm{0} \\ $$ Answered…

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2a-1-1-2-1-2-3-1-2024-2025-

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Question Number 163325 by mathlove last updated on 06/Jan/22 $$\mathrm{2}{a}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}}+\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+…+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2024}}+\sqrt{\mathrm{2025}}}=? \\ $$ Commented by cortano1 last updated on 06/Jan/22 $$\:\mathrm{2}{a}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2024}} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{{k}}\:+\sqrt{{k}+\mathrm{1}}}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2024}} {\sum}}\left(\sqrt{{k}+\mathrm{1}}−\sqrt{{k}}\:\right) \\…

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1-20-100-n-216-125-n-

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Question Number 163327 by mathlove last updated on 06/Jan/22 $$\left(\mathrm{1}+\frac{\mathrm{20}}{\mathrm{100}}\right)^{{n}} =\frac{\mathrm{216}}{\mathrm{125}}\:\:\:\:\:\:{n}=? \\ $$ Answered by Rasheed.Sindhi last updated on 06/Jan/22 $$\left(\mathrm{1}+\frac{\mathrm{20}}{\mathrm{100}}\right)^{{n}} =\frac{\mathrm{216}}{\mathrm{125}}\:\:\:\:\:\:{n}=? \\ $$$$\left(\frac{\mathrm{6}}{\mathrm{5}}\right)^{{n}} =\left(\frac{\mathrm{6}}{\mathrm{5}}\right)^{\mathrm{3}}…

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A-company-manufactures-two-types-of-products-X-4-50-profit-per-item-x-and-Y-3-00-profit-per-item-y-These-items-are-built-using-both-machine-time-and-manual-labour-The-X-product-requires-3-hou

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Question Number 32242 by pieroo last updated on 22/Mar/18 $$\mathrm{A}\:\mathrm{company}\:\mathrm{manufactures}\:\mathrm{two}\:\mathrm{types}\:\mathrm{of}\:\mathrm{products}; \\ $$$$\mathrm{X}\:\left(\$\mathrm{4}.\mathrm{50}\:\mathrm{profit}\:\mathrm{per}\:\mathrm{item}\:\mathrm{x}\right)\:\mathrm{and}\:\mathrm{Y}\:\left(\$\mathrm{3}.\mathrm{00}\:\mathrm{profit}\:\mathrm{per}\right. \\ $$$$\left.\mathrm{item}\:\mathrm{y}\right).\:\mathrm{These}\:\mathrm{items}\:\mathrm{are}\:\mathrm{built}\:\mathrm{using}\:\mathrm{both}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{manual}\:\mathrm{labour}.\:\mathrm{The}\:\mathrm{X}\:\mathrm{product}\:\mathrm{requires} \\ $$$$\mathrm{3}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{machine}\:\mathrm{time}\:\mathrm{and}\:\mathrm{two}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{manual} \\ $$$$\mathrm{labour}.\:\mathrm{The}\:\mathrm{Y}\:\mathrm{product}\:\mathrm{requires}\:\mathrm{3}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{no}\:\mathrm{manual}\:\mathrm{labour}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{week}'\mathrm{s}\:\mathrm{supply}\:\mathrm{of}\: \\ $$$$\mathrm{manual}\:\mathrm{labour}\:\mathrm{is}\:\mathrm{limited}\:\mathrm{to}\:\mathrm{8}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{machine} \\…

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