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…
Question Number 97808 by me2love2math last updated on 09/Jun/20 Commented by me2love2math last updated on 09/Jun/20 $${find}\:{R}\:{E}\:{and}\:{L} \\ $$ Terms of Service Privacy Policy Contact:…
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 $$\:\mathrm{2}{a}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2024}} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{{k}}\:+\sqrt{{k}+\mathrm{1}}}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{2024}} {\sum}}\left(\sqrt{{k}+\mathrm{1}}−\sqrt{{k}}\:\right) \\…
Question Number 163327 by mathlove last updated on 06/Jan/22 $$\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}=? \\ $$$$\left(\frac{\mathrm{6}}{\mathrm{5}}\right)^{{n}} =\left(\frac{\mathrm{6}}{\mathrm{5}}\right)^{\mathrm{3}}…
Question Number 32242 by pieroo last updated on 22/Mar/18 $$\mathrm{A}\:\mathrm{company}\:\mathrm{manufactures}\:\mathrm{two}\:\mathrm{types}\:\mathrm{of}\:\mathrm{products}; \\ $$$$\mathrm{X}\:\left(\$\mathrm{4}.\mathrm{50}\:\mathrm{profit}\:\mathrm{per}\:\mathrm{item}\:\mathrm{x}\right)\:\mathrm{and}\:\mathrm{Y}\:\left(\$\mathrm{3}.\mathrm{00}\:\mathrm{profit}\:\mathrm{per}\right. \\ $$$$\left.\mathrm{item}\:\mathrm{y}\right).\:\mathrm{These}\:\mathrm{items}\:\mathrm{are}\:\mathrm{built}\:\mathrm{using}\:\mathrm{both}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{manual}\:\mathrm{labour}.\:\mathrm{The}\:\mathrm{X}\:\mathrm{product}\:\mathrm{requires} \\ $$$$\mathrm{3}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{machine}\:\mathrm{time}\:\mathrm{and}\:\mathrm{two}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{manual} \\ $$$$\mathrm{labour}.\:\mathrm{The}\:\mathrm{Y}\:\mathrm{product}\:\mathrm{requires}\:\mathrm{3}\:\mathrm{hours}\:\mathrm{of}\:\mathrm{machine} \\ $$$$\mathrm{time}\:\mathrm{and}\:\mathrm{no}\:\mathrm{manual}\:\mathrm{labour}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{week}'\mathrm{s}\:\mathrm{supply}\:\mathrm{of}\: \\ $$$$\mathrm{manual}\:\mathrm{labour}\:\mathrm{is}\:\mathrm{limited}\:\mathrm{to}\:\mathrm{8}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{machine} \\…
Question Number 32239 by rahul 19 last updated on 22/Mar/18 $$\boldsymbol{{F}}{ind}\:{the}\:{sum}\:{of}\:{the}\:{coefficients} \\ $$$${of}\:{all}\:{the}\:{integral}\:{power}\:{of}\:{x}\:{in}\:{the} \\ $$$${expansion}\:{of}\:\left(\mathrm{1}+\mathrm{2}\sqrt{{x}}\right)^{\mathrm{40}} . \\ $$ Answered by MJS last updated on 22/Mar/18…
Question Number 163288 by HongKing last updated on 05/Jan/22 Answered by Ar Brandon last updated on 05/Jan/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{\mathrm{1}+{a}^{\mathrm{2}} \mathrm{tan}^{\mathrm{2}} {x}}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sec}^{\mathrm{2}} {x}}{\mathrm{sec}^{\mathrm{2}}…
Question Number 163285 by mnjuly1970 last updated on 05/Jan/22 $$ \\ $$$$\:\:\:\:#\:\mathrm{Q}{uestion}\:# \\ $$$$\:\:\:\:\:{suppose}\:{that}\:\:{x}_{\mathrm{1}} \:,\:\:{x}_{\:\mathrm{2}} \:\:{are}\:{two}\:{distinct} \\ $$$$\:\:\:\:{roots}\:{for}\:\:\:{ax}^{\:\mathrm{2}} +\:{bx}\:+{c}\:=\:\mathrm{0}\:\:{on}\:\left(\:\mathrm{0},\:\mathrm{1}\:\right). \\ $$$$\:\:\:\:\:{find}\:\:{the}\:{minimum}\:{value}\:{of}\:\:''\:{a}\:''\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}_{\:{min}}…
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Question Number 32203 by rahul 19 last updated on 21/Mar/18 $$\boldsymbol{{N}}{umber}\:{of}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$${z}^{\mathrm{3}} +\frac{\left[\mathrm{3}\left(\overset{−} {{z}}\right)^{\mathrm{2}} \right]}{\mid{z}\mid}=\mathrm{0}\:{where}\:{z}\:{is}\:{a}\:{complex}\:{no}. \\ $$ Commented by rahul 19 last updated on…