Question Number 69375 by mathmax by abdo last updated on 22/Sep/19 $${let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\alpha\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\alpha\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\mathrm{2}+\mathrm{2}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\…
Question Number 3838 by Rasheed Soomro last updated on 22/Dec/15 $${Show}\:{that}\:{the}\:{construction}\:{of} \\ $$$$\:\:\:\:\:\:\mathrm{the}\:\mathrm{rectangle}\:\mathrm{of}\:\mathrm{minimum}\: \\ $$$$\:\:\:\:\:\:\mathrm{perimeter}\:\mathrm{when}\:\mathrm{its}\:\mathrm{area}\:\:\mathrm{is}\:\boldsymbol{\mathrm{ab}}\: \\ $$$$\:\:\:\:\:\:\mathrm{where}\:\boldsymbol{\mathrm{a}}=\boldsymbol{\mathrm{AB}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}=\boldsymbol{\mathrm{CD}}\:\mathrm{are}\:\:\mathrm{given} \\ $$$${is}\:{possible}\:{with}\:{ruler}\:{and}\:{compass}.\:\:\:\:\: \\ $$$$ \\ $$ Commented by…
Question Number 69373 by nadia1111 last updated on 22/Sep/19 $${x}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{3} \\ $$ Commented by mathmax by abdo last updated on 22/Sep/19 $${what}\:{is}\:{the}\:{question}? \\ $$…
Question Number 3836 by Rasheed Soomro last updated on 22/Dec/15 $${A}\:{square},{whose}\:{area}\:{is}\:{s}^{\mathrm{2}} ,{contains}\: \\ $$$${a}\:{semicircle}\:{of}\:{possible}\:{largest}\:{area}. \\ $$$${Determine}\:{radius}\:{of}\:{the}\:{semicircle}. \\ $$ Commented by Yozzii last updated on 24/Dec/15…
Question Number 134905 by bramlexs22 last updated on 08/Mar/21 $$\mathrm{Combinatorics} \\ $$What is the number of ways of distributing 9 different objects among 5 persons…
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Question Number 3832 by Yozzii last updated on 21/Dec/15 $${Show}\:{that},\:\forall{a},{b}\in\mathbb{R}^{+} , \\ $$$$\:\left(\frac{{a}}{{b}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{{b}}{{a}}\right)^{\mathrm{1}/\mathrm{3}} \leqslant\left\{\mathrm{2}\left({a}+{b}\right)\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\right\}^{\mathrm{1}/\mathrm{3}} . \\ $$$$ \\ $$ Commented by RasheedSindhi last updated…
Question Number 3830 by Rasheed Soomro last updated on 21/Dec/15 $$\mathcal{D}{raw}\:{a}\:{rectangle}\:{of}\:{maximum}\:{perimeter}, \\ $$$${by}\:{ruler}\:{and}\:{compass},{when}\:{area}\:{is}\:\boldsymbol{\mathrm{ab}}.\: \\ $$$$\left(\boldsymbol{\mathrm{AB}}\:=\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{CD}}=\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{given}}.\right) \\ $$ Commented by prakash jain last updated on 22/Dec/15…
Question Number 134902 by faysal last updated on 08/Mar/21 Commented by bobhans last updated on 08/Mar/21 $$\mathrm{use}\:\mathrm{that}\:\left(\mathrm{1}+\mathrm{sec}\:\mathrm{2x}\right)\mathrm{cot}\:\mathrm{2x}\:=\:\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2x}}{\mathrm{sin}\:\mathrm{2x}}\:=\mathrm{cot}\:\mathrm{x} \\ $$ Answered by bobhans last updated on…
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