Category: Algebra

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

Question Number 163325 by mathlove last updated on 06/Jan/22 $$2a=\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\dots +\frac{1}{\sqrt{2024}+\sqrt{2025}}=?$$ 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) \…

Question Number 32242 by pieroo last updated on 22/Mar/18 $$\mathrm{A}\mathrm{company}\mathrm{manufactures}\mathrm{two}\mathrm{types}\mathrm{of}\mathrm{products};$$$$\mathrm{X}(\mathrm{\$}4.50\mathrm{profit}\mathrm{per}\mathrm{item}\mathrm{x})\mathrm{and}\mathrm{Y}(\mathrm{\$}3.00\mathrm{profit}\mathrm{per}$$$$\mathrm{item}\mathrm{y}).\mathrm{These}\mathrm{items}\mathrm{are}\mathrm{built}\mathrm{using}\mathrm{both}\mathrm{machine}$$$$\mathrm{time}\mathrm{and}\mathrm{manual}\mathrm{labour}.\mathrm{The}\mathrm{X}\mathrm{product}\mathrm{requires}$$$$3\mathrm{hours}\mathrm{of}\mathrm{machine}\mathrm{time}\mathrm{and}\mathrm{two}\mathrm{hours}\mathrm{of}\mathrm{manual}$$$$\mathrm{labour}.\mathrm{The}\mathrm{Y}\mathrm{product}\mathrm{requires}3\mathrm{hours}\mathrm{of}\mathrm{machine}$$$$\mathrm{time}\mathrm{and}\mathrm{no}\mathrm{manual}\mathrm{labour}.\mathrm{If}\mathrm{the}{\mathrm{week}}^{\prime }\mathrm{s}\mathrm{supply}\mathrm{of}$$$$\mathrm{manual}\:\mathrm{labour}\:\mathrm{is}\:\mathrm{limited}\:\mathrm{to}\:\mathrm{8}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{machine} \…

Question Number 163288 by HongKing last updated on 05/Jan/22 Answered by Ar Brandon last updated on 05/Jan/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+{a}^{\mathrm{2}} \mathrm{tan}^{\mathrm{2}} {x}}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sec}^{\mathrm{2}} {x}}{\mathrm{sec}^{\mathrm{2}}…

Question Number 32208 by rahul 19 last updated on 21/Mar/18 Terms of Service Privacy Policy Contact: info@tinkutara.com