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Question-110614

Question Number 110614 by mathdave last updated on 29/Aug/20 Answered by Dwaipayan Shikari last updated on 29/Aug/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\left({cosx}\right)^{\pi} }{\left({cosx}\right)^{\pi} +\left({sinx}\right)^{\pi} }{dx}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\left({sinx}\right)^{\pi}…

Prove-that-4n-lt-2-n-for-all-n-5-

Question Number 176102 by MathsFan last updated on 12/Sep/22 $$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\:\:\:\:\mathrm{4}\boldsymbol{\mathrm{n}}<\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{n}}\geqslant\mathrm{5} \\ $$ Answered by a.lgnaoui last updated on 12/Sep/22 $${n}=\mathrm{5}\:\:\:\mathrm{2}^{\mathrm{5}} =\mathrm{32}\:\:\:\:\:\:\:\:\:\mathrm{4}×\mathrm{5}=\mathrm{20}<\mathrm{32} \\…

it-seems-too-hard-for-many-here-to-post-their-questions-as-questions-answers-as-answers-and-comments-as-comments-hereby-I-introduce-the-next-step-I-ll-post-answers-and-the-task-is-find-questions

Question Number 110539 by Her_Majesty last updated on 29/Aug/20 $${it}\:{seems}\:{too}\:{hard}\:{for}\:{many}\:{here}\:{to}\:{post} \\ $$$${their}\:{questions}\:{as}\:{questions},\:{answers}\:{as} \\ $$$${answers}\:{and}\:{comments}\:{as}\:{comments}… \\ $$$${hereby}\:{I}\:{introduce}\:{the}\:{next}\:{step}:\:{I}'{ll}\:{post} \\ $$$${answers}\:{and}\:{the}\:{task}\:{is},\:{find}\:{questions} \\ $$$${to}\:{these}\:{answers} \\ $$$$\left(\mathrm{1}\right)\:\zeta\left(\mathrm{3}\right)+\pi{ln}\mathrm{2} \\ $$$$\left(\mathrm{2}\right)\:\pi{H}_{\mathrm{0}} \left(\mathrm{7}\right)…

Question-110528

Question Number 110528 by mathdave last updated on 29/Aug/20 Answered by nimnim last updated on 29/Aug/20 $$\int\left[\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\frac{\mathrm{7}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}+\frac{\mathrm{6}}{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}\right]\mathrm{dx} \\ $$$$…… \\ $$$$……. \\…

Three-bags-labelled-R-B-and-W-cotains-Red-Blue-and-White-balls-respectively-of-equal-sizes-the-ratio-of-the-balls-in-the-bag-are-R-B-2-3-and-B-W-4-5-All-the-balls-are-removed-into-a-big

Question Number 176056 by otchereabdullai@gmail.com last updated on 11/Sep/22 $$\:\mathrm{Three}\:\mathrm{bags}\:\mathrm{labelled}\:\mathrm{R},\:\mathrm{B}\:\mathrm{and}\:\mathrm{W}\: \\ $$$$\:\mathrm{cotains}\:\mathrm{Red},\:\mathrm{Blue}\:\mathrm{and}\:\mathrm{White}\:\mathrm{balls}\: \\ $$$$\:\mathrm{respectively}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{sizes},\:\mathrm{the}\:\mathrm{ratio}\: \\ $$$$\:\mathrm{of}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\:\mathrm{R}:\mathrm{B}=\mathrm{2}:\mathrm{3}\: \\ $$$$\mathrm{and}\:\mathrm{B}:\mathrm{W}=\:\mathrm{4}:\mathrm{5}.\:\mathrm{All}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{are}\: \\ $$$$\mathrm{removed}\:\mathrm{into}\:\mathrm{a}\:\mathrm{big}\:\mathrm{bag}\:\mathrm{and}\:\mathrm{properly}\: \\ $$$$\mathrm{mixed}\:\mathrm{together}.\:\mathrm{If}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{one}\:\mathrm{after}\:\mathrm{the}\:\mathrm{other}\:\mathrm{with}\: \\…