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Author: Tinku Tara

A-semicircle-contains-a-square-of-possible-largest-area-If-s-is-the-measure-of-the-side-of-the-square-what-is-the-radius-of-the-semicircle-

Question Number 3840 by Rasheed Soomro last updated on 22/Dec/15 $$\mathcal{A}\:\:{semicircle}\:\:{contains}\:{a}\:{square}\:\:{of}\:\: \\ $$$${possible}\:{largest}\:{area}.{If}\:\:{s}\:\:{is}\:{the}\:{measure} \\ $$$${of}\:{the}\:{side}\:{of}\:{the}\:{square},{what}\:{is}\:{the} \\ $$$${radius}\:{of}\:{the}\:{semicircle}? \\ $$ Answered by Yozzii last updated on…

let-f-0-cos-1-x-2-1-x-2-dx-1-determine-a-explicit-form-of-f-2-calculate-0-cos-2-2x-2-x-2-1-dx-

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} \\…

Show-that-the-construction-of-the-rectangle-of-minimum-perimeter-when-its-area-is-ab-where-a-AB-and-b-CD-are-given-is-possible-with-ruler-and-compass-

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…