Question Number 134255 by shaker last updated on 01/Mar/21 Commented by Dwaipayan Shikari last updated on 01/Mar/21 $${C}_{{m}} ^{{n}} \:\:\:\:\:\left({n}<{m}\right)\:{is}\:{not}\:{defined} \\ $$ Commented by mr…
Question Number 134249 by abdurehime last updated on 01/Mar/21 Answered by mr W last updated on 01/Mar/21 Commented by mr W last updated on 01/Mar/21…
Question Number 68714 by Learner-123 last updated on 15/Sep/19 Answered by mr W last updated on 15/Sep/19 $${acceleration}\:{of}\:{object}\:{C}=\frac{\mathrm{1}.\mathrm{2}}{\mathrm{2}}=\mathrm{0}.\mathrm{6}{m}/{s}^{\mathrm{2}} \\ $$$${force}\:{in}\:{cable}=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{375}×\frac{\mathrm{10}+\mathrm{0}.\mathrm{6}}{\mathrm{10}}=\mathrm{198}.\mathrm{75}\:{N} \\ $$$${power}\:{input}=\frac{\mathrm{198}.\mathrm{75}×\mathrm{0}.\mathrm{6}}{\mathrm{0}.\mathrm{85}}=\mathrm{140}.\mathrm{3}\:{watt} \\ $$ Commented…
Question Number 134251 by Dwaipayan Shikari last updated on 01/Mar/21 $$\underset{{n}=\mathrm{1}} {\overset{{n}} {\sum}}{nsin}\left({n}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 01/Mar/21 $$\underset{{n}=\mathrm{1}} {\overset{{n}}…
Question Number 68712 by Rio Michael last updated on 15/Sep/19 $${given}\:{that}\:{x}\:{and}\:{y}\:{are}\:{two}\:{numbers}\:{other}\:{one}.\: \\ $$$${given}\:{that}\:\:{a}>\mathrm{0}\:{and}\:{b}>\mathrm{0} \\ $$$${and}\:\:{a}^{{x}} \:=\:{b}^{{y}} \:=\:\left({ab}\right)^{{xy}} \:\:{show}\:{that}\:\:{x}\:+\:{y}\:=\mathrm{0} \\ $$ Commented by Prithwish sen last…
Question Number 68710 by peter frank last updated on 15/Sep/19 Commented by Prithwish sen last updated on 15/Sep/19 $$\mathrm{x}+\mathrm{y}=\mathrm{0}…….\left(\mathrm{i}\right) \\ $$$$\mathrm{x}−\mathrm{y}=−\mathrm{4}……\left(\mathrm{ii}\right) \\ $$$$\mathrm{solving}\:\mathrm{x}=−\mathrm{2},\mathrm{y}=\mathrm{2} \\ $$$$\therefore\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{center}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{circle}}\:\boldsymbol{\mathrm{is}}\:\left(−\mathrm{2},\mathrm{2}\right)…
Question Number 3172 by Rasheed Soomro last updated on 07/Dec/15 $$\mathcal{H}{ow}\:{many}\:{different}\:\:{clock}−{type}\:{dials}\:{can}\:{be}\:{made}\: \\ $$$${containing}\:{first}\:{n}\:{natual}\:{numbers}\:{with}\:{the}\:{property} \\ $$$${that}\:{sum}\:{of}\:\:{any}\:{two}\:{numbers}\:{of}\:{consecutive}\:{positions}\:{be} \\ $$$${a}\:{prime}\:{number}. \\ $$$$\mathbb{N}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},…\right\} \\ $$ Commented by Rasheed Soomro…
Question Number 134237 by mathlove last updated on 01/Mar/21 $${f}\left({x}\right)=\frac{\mathrm{2}{x}^{\mathrm{100}!} }{\left(\mathrm{100}!\right)!}+{x}^{\mathrm{100}} +\mathrm{1} \\ $$$${faind}\:\:\:\:\:\frac{{d}^{\mathrm{100}!} {f}\left({x}\right)}{{dx}^{\mathrm{100}!} }=? \\ $$ Answered by malwan last updated on 01/Mar/21…
Question Number 68703 by Maclaurin Stickker last updated on 15/Sep/19 $$\frac{{d}}{{dx}}\left({ln}\left(\sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}}\right)\right)=? \\ $$ Commented by MJS last updated on 15/Sep/19 $$\frac{{d}}{{dx}}\left[\mathrm{ln}\:\sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}}\right]=\frac{\mathrm{1}}{\mathrm{2}}×\frac{{d}}{{dx}}\left[\mathrm{ln}\:\frac{{x}^{\mathrm{2}}…
Question Number 134239 by ruwedkabeh last updated on 01/Mar/21 $${can}\:{i}\:{ask}\:{for}\:{some}\:{help}? \\ $$$${how}\:{to}\:{prove}\:{this}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}<\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{3}} }}<\frac{\pi}{\mathrm{6}} \\ $$ Commented by Dwaipayan Shikari last updated…