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n-1-1-n-2-pi-2-6-

Question Number 92555 by arcana last updated on 07/May/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{1}/{n}^{\mathrm{2}} =\pi^{\mathrm{2}} /\mathrm{6} \\ $$ Commented by abdomathmax last updated on 08/May/20 $${this}\:{Q}\:{is}\:{done}\:{see}\:{the}\:{platform}… \\…

two-smooth-spheres-of-masses-2m-and-3m-have-velocites-12i-8j-u-ms-1-and-5i-12j-u-respectively-where-u-is-a-constant-The-spheres-collide-with-thier-line-of-centre-of-parallel-to-j-Give

Question Number 92529 by Rio Michael last updated on 07/May/20 $$\mathrm{two}\:\mathrm{smooth}\:\mathrm{spheres}\:\mathrm{of}\:\mathrm{masses}\:\mathrm{2}{m}\:\mathrm{and}\:\mathrm{3}{m}\:\mathrm{have}\:\mathrm{velocites} \\ $$$$\left(−\mathrm{12}\boldsymbol{\mathrm{i}}\:+\:\mathrm{8}\boldsymbol{\mathrm{j}}\right)\:{u}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{and}\:\left(\mathrm{5}\boldsymbol{\mathrm{i}}\:+\:\mathrm{12}\boldsymbol{\mathrm{j}}\right){u}\:,\:\mathrm{respectively}\:\mathrm{where}\:{u}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{constant}.\:\mathrm{The}\:\mathrm{spheres}\:\mathrm{collide}\:\mathrm{with}\:\mathrm{thier}\:\mathrm{line}\:\mathrm{of}\:\mathrm{centre}\:\mathrm{of} \\ $$$$\mathrm{parallel}\:\mathrm{to}\:\boldsymbol{\mathrm{j}}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{restitution}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{spheres}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{4}},\:\mathrm{find}\:\mathrm{the}\:\mathrm{loss}\:\mathrm{in}\:\mathrm{kinetic}\:\mathrm{energy}\:\mathrm{due}\:\mathrm{to}\:\mathrm{impact}. \\ $$ Terms of Service…

e-x-1-x-2-x-3-2-dx-

Question Number 26909 by sorour87 last updated on 31/Dec/17 $$\int\frac{{e}^{{x}} \left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{2}}{{x}^{\mathrm{3}} }\right)}{−\mathrm{2}}{dx} \\ $$ Answered by prakash jain last updated on 31/Dec/17 $$\int{e}^{{x}} \left(−\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right){dx}…

a-3-b-6-a-b-

Question Number 26839 by Samar khan last updated on 30/Dec/17 $$\mathrm{a}=\mathrm{3}\:\mathrm{b}=\mathrm{6} \\ $$$$\mathrm{a}−\mathrm{b}=? \\ $$ Answered by Rasheed.Sindhi last updated on 30/Dec/17 $$\mathrm{a}−\mathrm{b}=\mathrm{3}−\mathrm{6}=−\mathrm{3} \\ $$…

0-1-dx-1-3x-1-3x-

Question Number 92344 by 675480065 last updated on 06/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{dx}}{\:\sqrt{\mathrm{1}+\mathrm{3x}}−\sqrt{\mathrm{1}−\mathrm{3x}}} \\ $$ Commented by john santu last updated on 06/May/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\sqrt{\mathrm{1}+\mathrm{3}{x}}\:+\:\sqrt{\mathrm{1}−\mathrm{3}{x}}}{\mathrm{6}{x}}\:\:{dx}\:…