Question Number 1682 by Rasheed Soomro last updated on 31/Aug/15 $${Let}\:\mid\:\mathrm{S}\:\mid\:{denotes}\:{number}\:{of}\:{elements}\:{in}\:{a}\:{set}\:\mathrm{S}\:,\: \\ $$$$\mathbb{N}\:{and}\:\mathbb{R}\:{are}\:{sets}\:{of}\:{natural}\:{and}\:{real}\:{numbers}\: \\ $$$${respectively}: \\ $$$$\mid\:\mathbb{N}\:\mid\overset{?} {=}\mid\:\mathbb{R}\:\mid \\ $$ Commented by 112358 last updated…
Question Number 132755 by liberty last updated on 16/Feb/21 Commented by KINTU last updated on 16/Feb/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sinx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{8}}\left(\pi−\mathrm{ln4}\right) \\ $$ Answered by EDWIN88 last…
Question Number 67215 by Learner-123 last updated on 24/Aug/19 Commented by Learner-123 last updated on 24/Aug/19 $$\:\:{help}\:{me}\:{in}\:{Q}.\mathrm{74}. \\ $$ Answered by mr W last updated…
Question Number 1676 by hhhggvghhh last updated on 31/Aug/15 $$\boldsymbol{{hhjghhjjgkggjggigfhpppkknbgjffffg}} \\ $$$$\boldsymbol{{biuggjnggtbnkoyfhjiuhbhuklphh}} \\ $$$$\boldsymbol{{jinbh}}\mathrm{678656}\boldsymbol{{kkiohhuggjngffjkkdooxk}} \\ $$$$\boldsymbol{{ikhhkjhv}}\mathrm{2}\left[\mathrm{65}\sqrt{\sqrt{\mathrm{58}\:\mathrm{889}<\boldsymbol{{lkkjkbmbbnnb}}}}\right. \\ $$$$\boldsymbol{{jkkhjm}}\sqrt{\boldsymbol{{nlm}}\mathrm{6}\boldsymbol{{jikmbh}}\sqrt{\boldsymbol{{jlbj}}}} \\ $$$$\boldsymbol{{jljbnkbbnmnmmnjknbjnrurubv}}\underset{\boldsymbol{{nkjnbmm}}} {\boldsymbol{{m}}} \\ $$$$\boldsymbol{{jjnbbnjnnj}}^{} \\ $$$$\boldsymbol{{nkn}}…
Question Number 1675 by hhhggvghhh last updated on 31/Aug/15 $${scv}\mathrm{2}\left\{{bb}\mathrm{3}{vjhkhbkj}\right\} \\ $$$${nnmvhkvgj}\mathrm{6}{vvfukfjjkhnkgwqqkin} \\ $$$${ckkmnbmbjknn} \\ $$ Answered by 123456 last updated on 31/Aug/15 $${f}_{\omega} \left({z}\right)=\underset{{z}_{\mathrm{0}}…
Question Number 132747 by aurpeyz last updated on 16/Feb/21 Commented by mr W last updated on 16/Feb/21 $$\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{{s}'}=\frac{\mathrm{2}}{{R}} \\ $$$$\frac{\mathrm{1}}{{s}}+\frac{\mathrm{1}}{−\mathrm{2}}=\frac{\mathrm{2}}{−\mathrm{12}} \\ $$$$\frac{\mathrm{1}}{{s}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{s}=\mathrm{3} \\…
Question Number 67208 by mr W last updated on 24/Aug/19 $${Find}\:{the}\:{times}\:{in}\:{a}\:{day}\:{when} \\ $$$${the}\:{hour}'{s},\:{minute}'{s}\:{and}\:{second}'{s} \\ $$$${hand}\:{of}\:{a}\:{clock}\:{occupy}\:{the}\:{same} \\ $$$${angular}\:{position}. \\ $$$$\left[{old}\:{question}\:{reposted}\right] \\ $$ Commented by Kunal12588 last…
Question Number 1673 by 123456 last updated on 31/Aug/15 $$\omega\in\mathbb{R},\omega>\mathrm{0} \\ $$$$\mathrm{0}<\alpha<\beta \\ $$$${f}_{{m}} \left(\alpha,\beta\right)=\frac{\omega}{\beta−\alpha}\underset{\alpha/\omega} {\overset{\beta/\omega} {\int}}\mathrm{sin}\:\left(\omega{t}\right){dt} \\ $$$${f}_{{r}} \left(\alpha,\beta\right)=\sqrt{\frac{\omega}{\beta−\alpha}\underset{\alpha/\omega} {\overset{\beta/\omega} {\int}}\mathrm{sin}^{\mathrm{2}} \left(\omega{t}\right){dt}} \\ $$$${f}_{{m}}…
Question Number 1672 by 123456 last updated on 30/Aug/15 $$\mathrm{lets}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{be}\:\mathrm{two}\:\mathrm{finite}\:\mathrm{sets},\:\mathrm{proof}\:\left(\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\right)\:\mathrm{that} \\ $$$$\mid\mathrm{A}\cup\mathrm{B}\mid\leqslant\mid\mathrm{A}\cap\mathrm{B}\mid\:\Rightarrow\:\mathrm{A}=\mathrm{B} \\ $$ Answered by Rasheed Soomro last updated on 01/Sep/15 $$\boldsymbol{\mathrm{Case}}−\mathrm{1}\:\boldsymbol{\mathrm{W}}\mathrm{hen}\:\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}=\varnothing\:,\:\mid\:\boldsymbol{\mathrm{A}}\cap\boldsymbol{\mathrm{B}}\:\mid=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{SubCase}}\:\:\left(\boldsymbol{\mathrm{a}}\right)\:\boldsymbol{\mathrm{At}}\:\boldsymbol{\mathrm{least}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{B}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{nonempty}}.…
Question Number 132741 by mnjuly1970 last updated on 16/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:\:{calculus}… \\ $$$$\:\:\int_{\mathrm{0}^{\:\:\:\:} \:\:} ^{\:\mathrm{1}} \frac{{dx}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{5}}} }\:=? \\ $$ Commented by MJS_new last updated…