Question Number 66683 by Tinkutara@ last updated on 18/Aug/19 Commented by mr W last updated on 18/Aug/19 $${each}\:{runner}\:{has}\:{two}\:{possibilities},\:{totally} \\ $$$$\mathrm{2}×\mathrm{2}×\mathrm{2}=\mathrm{8}.\:{such}\:{that}\:{they}\:{don}'{t}\:{collide}, \\ $$$${all}\:{of}\:{them}\:{must}\:{run}\:{in}\:{the}\:{same} \\ $$$${direction},\:{there}\:{are}\:{two}\:{such}\:{possibilities}. \\…
Question Number 66680 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\frac{\mathrm{2}^{{n}} }{\mathrm{3}^{{n}} \left(\mathrm{2}{n}^{\mathrm{3}} \:+{n}^{\mathrm{2}} −\mathrm{5}{n}\:+\mathrm{2}\right)} \\ $$ Commented by Mohamed Amine Bouguezzoul…
Question Number 66681 by Tinkutara@ last updated on 18/Aug/19 Commented by Tinkutara@ last updated on 18/Aug/19 $$?? \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 1139 by 314159 last updated on 30/Jun/15 $${Given}\:{that}\:{f}\:{is}\:{a}\:{polynomial}\:{function}\:{of} \\ $$$${degree}\:\mathrm{8}\:{such}\:{that}\:{f}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}},{f}\left(\mathrm{2}\right)=\frac{\mathrm{1}}{\mathrm{6}},{f}\left(\mathrm{3}\right)=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$${f}\left(\mathrm{4}\right)=\frac{\mathrm{1}}{\mathrm{20}},{f}\left(\mathrm{5}\right)=\frac{\mathrm{1}}{\mathrm{30}},{f}\left(\mathrm{6}\right)=\frac{\mathrm{1}}{\mathrm{42}},{f}\left(\mathrm{7}\right)=\frac{\mathrm{1}}{\mathrm{56}},{f}\left(\mathrm{8}\right)=\frac{\mathrm{1}}{\mathrm{72}} \\ $$$${f}\left(\mathrm{9}\right)=\frac{\mathrm{1}}{\mathrm{90}\:}\:\:.{Find}\:{f}\left(\mathrm{10}\right)\:{and}\:{f}\left(\mathrm{11}\right). \\ $$ Commented by 123456 last updated on 30/Jun/15…
Question Number 132211 by benjo_mathlover last updated on 12/Feb/21 $$ \\ $$$$\mathrm{how}\:\mathrm{fast}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\: \\ $$$$\mathrm{rectangle}\:\mathrm{changing}\:\mathrm{if}\:\mathrm{one}\:\mathrm{side}\:\mathrm{is}\:\mathrm{10} \\ $$$$\:\mathrm{cm}\:\mathrm{long}\:\mathrm{and}\:\mathrm{increasing}\:\mathrm{at}\:\mathrm{a} \\ $$$$\mathrm{rate}\:\mathrm{of}\:\mathrm{2}\:\mathrm{cm}/\mathrm{s}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{side}\:\mathrm{is}\: \\ $$$$\mathrm{8}\:\mathrm{cm}\:\mathrm{long}\:\mathrm{and}\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{at}\: \\ $$$$\mathrm{a}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{3}\:\mathrm{cm}/\mathrm{s} \\ $$ Answered…
Question Number 132205 by Arijit last updated on 12/Feb/21 Commented by Arijit last updated on 12/Feb/21 $$\boldsymbol{\mathrm{Please}}\:\boldsymbol{\mathrm{Help}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}….. \\ $$ Answered by mathmax by abdo last…
Question Number 66670 by naka3546 last updated on 18/Aug/19 Commented by mathmax by abdo last updated on 18/Aug/19 $${let}\:{S}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{3}^{{n}} }{\mathrm{5}^{{n}} \left({n}^{\mathrm{2}} \:+\mathrm{3}{n}+\mathrm{2}\right)}\:\Rightarrow{S}\:=\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 1134 by 314159 last updated on 28/Jun/15 $${Find}\:{the}\:{infinite}\:{product}\:{of}\: \\ $$$$\frac{\mathrm{3}}{\mathrm{2}}×\frac{\mathrm{5}}{\mathrm{4}}×\frac{\mathrm{17}}{\mathrm{16}}×\frac{\mathrm{257}}{\mathrm{256}}×\frac{\mathrm{65537}}{\mathrm{65536}}×… \\ $$ Answered by prakash jain last updated on 29/Jun/15 $$\frac{\mathrm{2}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{2}^{\mathrm{2}} +\mathrm{1}}{\mathrm{2}^{\mathrm{2}}…
Question Number 1133 by 112358 last updated on 29/Jun/15 $${Let}\:{f}\::\:\left[\:\mathrm{0}\:,\:\mathrm{1}\:\right]\:\rightarrow\:\mathbb{R}\:\:{be}\:{a}\: \\ $$$${differentiable}\:{function}.\:{Prove} \\ $$$${that}\:{there}\:{exists}\:{a}\:{c}\:\in\:\left[\mathrm{0},\mathrm{1}\right]\:{such} \\ $$$${that}\: \\ $$$$\frac{\mathrm{4}}{\pi}\left[{f}\left(\mathrm{1}\right)−{f}\left(\mathrm{0}\right)\right]=\left(\mathrm{1}+{c}^{\mathrm{2}} \right){f}^{\:} '\left({c}\right).\: \\ $$ Commented by 123456…
Question Number 132206 by muneer0o0 last updated on 12/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com