Question Number 136505 by rexford last updated on 22/Mar/21 Answered by Dwaipayan Shikari last updated on 22/Mar/21 $${Assuming}\:{soda}\:{was}\:{x}\:{litre}\:{in}\:{quantity} \\ $$$${Your}\:{consumption}=\frac{{x}}{\mathrm{2}}+\frac{{x}}{\mathrm{2}^{\mathrm{3}} }+\frac{{x}}{\mathrm{2}^{\mathrm{5}} }+…={x}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{32}}+…\right) \\ $$$$=\frac{\frac{{x}}{\mathrm{2}}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}}=\frac{\mathrm{2}{x}}{\mathrm{3}} \\…
Question Number 70969 by TawaTawa last updated on 10/Oct/19 Answered by mind is power last updated on 10/Oct/19 $${first}\:{find}\:{how}\:{many}\:{zero}\:{ends}\:\mathrm{80}! \\ $$$${n}=\left[\frac{\mathrm{80}}{\mathrm{5}}\right]+\left[\frac{\mathrm{80}}{\mathrm{25}}\right]=\mathrm{16}+\mathrm{3}=\mathrm{19} \\ $$$${so}\:{we}\:{have} \\ $$$$\mathrm{80}!={d}\ast\mathrm{10}^{\mathrm{19}}…
Question Number 5431 by Rasheed Soomro last updated on 14/May/16 Commented by Yozzii last updated on 14/May/16 $${What}\:{does}\:\boldsymbol{\mathrm{d}}\:{measure}? \\ $$ Commented by Rasheed Soomro last…
Question Number 136500 by rexford last updated on 22/Mar/21 Answered by Dwaipayan Shikari last updated on 22/Mar/21 $${a}−\mathrm{2}{d}+{a}−{d}+{a}+{a}+{d}+{a}+\mathrm{2}{d}+{a}+\mathrm{3}{d}=\mathrm{78} \\ $$$$\Rightarrow\mathrm{6}{a}+\mathrm{3}{d}=\mathrm{78}\Rightarrow\mathrm{2}{a}+{d}=\mathrm{26} \\ $$$${since}\:{a}−\mathrm{2}{d}>\mathrm{1}\Rightarrow{a}>\mathrm{2}{d}+\mathrm{1}\:\:{Greatest}\:{possible}\:{when}\:{a}=\mathrm{2}{d}+\mathrm{1} \\ $$$$\mathrm{2}{a}+{d}=\mathrm{26}\Rightarrow\mathrm{5}{d}+\mathrm{2}=\mathrm{26}\Rightarrow\Rightarrow{d}=\frac{\mathrm{24}}{\mathrm{5}} \\…
Question Number 136497 by mnjuly1970 last updated on 22/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……{nice}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:{prove}::\:\: \\ $$$$\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}}{\mathrm{1}+{ln}^{\mathrm{2}} \left({x}\right)}{dx}=\int_{\mathrm{0}\:} ^{\:\infty} \frac{{sin}\left({x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$ \\ $$ Commented by…
Question Number 5427 by Rasheed Soomro last updated on 14/May/16 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series}\:\mathrm{to}\:\mathrm{infinity}: \\ $$$$\mathrm{1}+\left(\mathrm{1}+\mathrm{k}\right)\mathrm{x}+\left(\mathrm{1}+\mathrm{k}+\mathrm{k}^{\mathrm{2}} \right)\mathrm{x}^{\mathrm{2}} +… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:\:\:\mathrm{and}\:\:\:\:\mathrm{k}\:\:\:\mathrm{being}\:\mathrm{proper}\:\mathrm{fractions}. \\ $$ Commented by Yozzii last updated on…
Question Number 5425 by love math last updated on 14/May/16 $$\int_{\mathrm{1}} ^{\mathrm{3}} {ln}\left(\mathrm{3}{x}−\mathrm{2}\right){dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$\left[{xln}\left(\mathrm{3}{x}−\mathrm{2}\right)\right]_{\mathrm{1}} ^{\mathrm{3}} −\mathrm{3}\int_{\mathrm{1}}…
Question Number 5422 by love math last updated on 14/May/16 $$\int_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} \left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$=\left[\frac{\mathrm{3}}{\mathrm{8}}\left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right]_{\mathrm{0}}…
Question Number 5421 by love math last updated on 14/May/16 $$\int_{\mathrm{0}} ^{\mathrm{2}} \:{xe}^{{x}^{\mathrm{2}} } {dx} \\ $$ Answered by nchejane last updated on 14/May/16 $$=\left[\frac{\mathrm{1}}{\mathrm{2}}{e}^{{x}^{\mathrm{2}}…
Question Number 136494 by liberty last updated on 22/Mar/21 $$\mathrm{5}\left(\sqrt{\mathrm{1}−{x}}\:+\sqrt{\mathrm{1}+{x}}\:\right)=\:\mathrm{6}{x}\:+\:\mathrm{8}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\: \\ $$ Answered by MJS_new last updated on 22/Mar/21 $$\mathrm{I}\:\mathrm{get}\:\mathrm{2}\:\mathrm{solutions} \\ $$$${x}_{\mathrm{1}} =\frac{\mathrm{24}}{\mathrm{25}} \\…