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Author: Tinku Tara

0-1-1-6x-15x-2-20x-3-15x-4-6x-5-x-6-1-6-dx-pi-3-Or-0-1-1-kx-k-k-1-2-x-2-k-k-1-k-2-6-x-3-1-k-dx-pi-ksin-pi-k-

Question Number 135366 by Dwaipayan Shikari last updated on 12/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{\mathrm{6}}]{\mathrm{6}{x}−\mathrm{15}{x}^{\mathrm{2}} +\mathrm{20}{x}^{\mathrm{3}} −\mathrm{15}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{5}} −{x}^{\mathrm{6}} }}{dx}=\frac{\pi}{\mathrm{3}} \\ $$$${Or} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{{k}}]{{kx}−\frac{{k}\left({k}−\mathrm{1}\right)}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{{k}\left({k}−\mathrm{1}\right)\left({k}−\mathrm{2}\right)}{\mathrm{6}}{x}^{\mathrm{3}}…

Question-69829

Question Number 69829 by TawaTawa last updated on 28/Sep/19 Commented by TawaTawa last updated on 28/Sep/19 $$\mathrm{The}\:\mathrm{question}\:\mathrm{says}\:\mathrm{do}\:\mathrm{not}\:\mathrm{use}\:\mathrm{Newton}'\mathrm{s}\:\mathrm{law}\:\mathrm{and}\:\mathrm{kinematic} \\ $$ Commented by TawaTawa last updated on…

The-acceleration-of-a-particle-moving-in-a-straight-line-is-defined-as-a-6t-20-m-s-2-where-t-is-in-seconds-Knowing-that-s-0m-when-t-3s-and-that-t-5sec-when-v-2m-s-Determine-the-total-distance-trav

Question Number 69827 by Learner-123 last updated on 28/Sep/19 $${The}\:{acceleration}\:{of}\:{a}\:{particle}\:{moving} \\ $$$${in}\:{a}\:{straight}\:{line}\:{is}\:{defined}\:{as}\:{a}=\mathrm{6}{t}−\mathrm{20} \\ $$$${m}/{s}^{\mathrm{2}} ,\:{where}\:{t}\:{is}\:{in}\:{seconds}.\:{Knowing} \\ $$$${that}\:{s}=\mathrm{0}{m}\:{when}\:{t}=\mathrm{3}{s}\:{and}\:{that}\:{t}=\mathrm{5}{sec} \\ $$$${when}\:{v}=\mathrm{2}{m}/{s}.\:{Determine}\:{the}\:{total} \\ $$$${distance}\:{travelled}\:{when}\:{t}=\mathrm{11}{s}. \\ $$ Answered by…

S-1-2-3-4-S-

Question Number 4285 by Filup last updated on 07/Jan/16 $${S}=\mathrm{1}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+…}}} \\ $$$${S}=??? \\ $$ Commented by RasheedSindhi last updated on 07/Jan/16 $$\mathrm{S}=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}+\sqrt{\mathrm{4}+…}}} \\ $$$${S}\left({n}\right)=\sqrt{\left({n}+\mathrm{1}\right)+{S}\left({n}+\mathrm{1}\right)} \\…

Probability-Urn-I-contains-5-red-and-3-green-balls-Urn-II-contains-2-red-and-7-green-balls-One-balls-is-transferred-at-random-from-urn-I-to-urn-II-After-stirring-1-ball-is-chosen-from-urn-II-

Question Number 135352 by EDWIN88 last updated on 12/Mar/21 $$\underline{\mathrm{Probability}} \\ $$$$\mathrm{Urn}\:\mathrm{I}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{red}\:\mathrm{and}\:\mathrm{3}\:\mathrm{green}\:\mathrm{balls}.\:\mathrm{Urn}\:\mathrm{II} \\ $$$$\mathrm{contains}\:\mathrm{2}\:\mathrm{red}\:\mathrm{and}\:\mathrm{7}\:\mathrm{green}\:\mathrm{balls}.\:\mathrm{One}\:\mathrm{balls} \\ $$$$\mathrm{is}\:\mathrm{transferred}\:\left(\mathrm{at}\:\mathrm{random}\right)\:\mathrm{from}\:\mathrm{urn}\:\mathrm{I}\:\mathrm{to}\:\mathrm{urn}\:\mathrm{II} \\ $$$$.\:\mathrm{After}\:\mathrm{stirring}\:,\:\mathrm{1}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{from}\:\mathrm{urn}\:\mathrm{II}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\left(\mathrm{final}\right)\:\mathrm{ball}\:\mathrm{is} \\ $$$$\mathrm{green}?\: \\ $$ Answered…

The-following-image-shows-the-functiond-f-x-xe-1-1-x-and-g-x-x-1-Can-you-explain-as-to-why-as-f-x-that-f-x-g-x-

Question Number 4281 by Filup last updated on 07/Jan/16 $$\mathrm{The}\:\mathrm{following}\:\mathrm{image}\:\mathrm{shows}\:\mathrm{the}\:\mathrm{functiond} \\ $$$${f}\left({x}\right)={xe}^{\frac{\mathrm{1}}{\mathrm{1}−{x}}} \:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:{g}\left({x}\right)={x}−\mathrm{1} \\ $$$$ \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{as}\:\mathrm{to}\:\mathrm{why}\:\mathrm{as}\:\mid{f}\left({x}\right)\mid\rightarrow\infty, \\ $$$$\mathrm{that}\:{f}\left({x}\right)\rightarrow{g}\left({x}\right). \\ $$ Commented by Filup last…