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Author: Tinku Tara

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

Question Number 138619 by Dwaipayan Shikari last updated on 15/Apr/21 $$\int_{\mathrm{0}} ^{\infty} \left({e}^{−{x}^{\sqrt{\mathrm{3}}} } −\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{\sqrt{\mathrm{3}}} \right)^{\sqrt{\mathrm{3}}} }\right)\frac{{dx}}{{x}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\psi\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right) \\ $$ Commented by mnjuly1970 last updated on…

Question-7544

Question Number 7544 by Tawakalitu. last updated on 03/Sep/16 Commented by sou1618 last updated on 03/Sep/16 $${x}={OA} \\ $$$${OB}=\sqrt{{x}^{\mathrm{2}} +\mathrm{144}} \\ $$$$\Delta{ABO}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{12}{x} \\ $$$$\Delta{AOB}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{3}\left(\mathrm{12}+{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{144}}\right)…

Question-138613

Question Number 138613 by byaw last updated on 15/Apr/21 Answered by physicstutes last updated on 15/Apr/21 $$\mathrm{This}\:\mathrm{question}\:\mathrm{is}\:\mathrm{real}\:\mathrm{lol}! \\ $$$$\mathrm{2}.\:\left(\mathrm{a}\right)\:\mathrm{Total}\:\mathrm{length}\:=\:\frac{\mathrm{9}}{\mathrm{4}}\:\mathrm{m}\: \\ $$$$\Rightarrow\:\mathrm{lenght}\:\mathrm{used}\:\mathrm{for}\:\mathrm{a}\:\mathrm{job}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{9}}{\mathrm{4}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{m} \\ $$$$\mathrm{length}\:\mathrm{used}\:=\:\frac{\mathrm{9}}{\mathrm{4}}−\frac{\mathrm{3}}{\mathrm{2}}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\mathrm{m} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{lenght}\:\mathrm{used}\:\mathrm{for}\:\mathrm{job}\:=\:\frac{\mathrm{1}}{\mathrm{8}}×\frac{\mathrm{3}}{\mathrm{4}}\:=\:\frac{\mathrm{3}}{\mathrm{32}}…

If-z-1-z-2cos-show-that-z-m-1-z-m-2cosm-

Question Number 138612 by SOMEDAVONG last updated on 15/Apr/21 $$\mathrm{If}\:\mathrm{z}+\:\frac{\mathrm{1}}{\mathrm{z}}\:=\mathrm{2cos}\beta\:.\mathrm{show}\:\mathrm{that}\:\mathrm{z}^{\mathrm{m}} +\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{m}} }\:=\mathrm{2cosm}\beta. \\ $$ Answered by Ar Brandon last updated on 15/Apr/21 $$\mathrm{z}=\mathrm{e}^{\mathrm{i}\beta} \\ $$$$\mathrm{z}^{\mathrm{m}}…

Question-7541

Question Number 7541 by 314159 last updated on 03/Sep/16 Commented by prakash jain last updated on 03/Sep/16 $${a}\left(\mathrm{1}+{r}+{r}^{\mathrm{2}} +{r}^{\mathrm{3}} +{r}^{\mathrm{4}} \right)=\mathrm{211} \\ $$$${a}\:{and}\:{r}\:{integers} \\ $$$$\mathrm{211}=\mathrm{1}×\mathrm{211}\Rightarrow{a}=\mathrm{1}…

Prove-or-disprove-0-a-x-2-e-x-2-dx-1-e-a-2-a-3-1-3-2a-5-1-3-5-2a-7-1-3-5-7-2a-9-1-3-5-7-9-ad-inf-

Question Number 138608 by Dwaipayan Shikari last updated on 15/Apr/21 $${Prove}\:{or}\:{disprove} \\ $$$$\int_{\mathrm{0}} ^{{a}} {x}^{\mathrm{2}} {e}^{−{x}^{\mathrm{2}} } {dx}=\frac{\mathrm{1}}{{e}^{{a}^{\mathrm{2}} } }\left(\frac{{a}^{\mathrm{3}} }{\mathrm{1}.\mathrm{3}}+\frac{\mathrm{2}{a}^{\mathrm{5}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}}+\frac{\mathrm{2}{a}^{\mathrm{7}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}}+\frac{\mathrm{2}{a}^{\mathrm{9}} }{\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}.\mathrm{9}}+{ad}\:{inf}..\right) \\…