Question and Answers Forum

Find the least positive integer n for which there exists a set { s_1 ,s_2 ,s_3 ,...,s_n } consisting of n distinct positive integers such that (1−(1/s_1 ))(1−(1/s_2 ))(1−(1/s_3 ))...(1−(1/s_n )) = ((51)/(2010)) .

$${Find}\:{the}\:{least}\:{positive}\:{integer}\:{n}\:{for} \\ $$$${which}\:{there}\:{exists}\:{a}\:{set}\:\left\{\:{s}_{\mathrm{1}} ,{s}_{\mathrm{2}} ,{s}_{\mathrm{3}} ,...,{s}_{{n}} \:\right\} \\ $$$${consisting}\:{of}\:{n}\:{distinct}\:{positive}\:{integers} \\ $$$${such}\:{that}\:\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{\mathrm{1}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{\mathrm{3}} }\right)...\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{{n}} }\right) \\ $$$$=\:\frac{\mathrm{51}}{\mathrm{2010}}\:. \\ $$

Question Number 103903 Answers: 1 Comments: 5

a 100 cm long rod should be divided into 3 parts. the length of each part in cm should be integer. in how many different ways can this be done?

$${a}\:\mathrm{100}\:{cm}\:{long}\:{rod}\:{should}\:{be}\:{divided} \\ $$$${into}\:\mathrm{3}\:{parts}.\:{the}\:{length}\:{of}\:{each}\:{part} \\ $$$${in}\:{cm}\:{should}\:{be}\:{integer}.\:{in}\:{how}\: \\ $$$${many}\:{different}\:{ways}\:{can}\:{this}\:{be} \\ $$$${done}? \\ $$

Question Number 104143 Answers: 1 Comments: 1

A Satellite orbits the esrth in a circle of rsdius 8000km. At that distance from the earth g=6.2m/s2. The velocity of the satelliege is?

$$\mathrm{A}\:\mathrm{Satellite}\:\mathrm{orbits}\:\mathrm{the}\:\mathrm{esrth}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{rsdius}\:\mathrm{8000km}.\:\mathrm{At}\:\mathrm{that}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{g}=\mathrm{6}.\mathrm{2m}/\mathrm{s2}.\:\mathrm{The}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{satelliege}\:\mathrm{is}? \\ $$

Question Number 104176 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (((n/(n+1)))^2 −(2/(n+1))−1)

$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\left(\frac{\mathrm{n}}{\mathrm{n}+\mathrm{1}}\right)^{\mathrm{2}} −\frac{\mathrm{2}}{\mathrm{n}+\mathrm{1}}−\mathrm{1}\right) \\ $$

Question Number 103894 Answers: 3 Comments: 0

(d/(d((d/dx)sinx)))∙sinx=?

$$\frac{{d}}{{d}\left(\frac{{d}}{{dx}}{sinx}\right)}\centerdot{sinx}=? \\ $$

Question Number 103893 Answers: 0 Comments: 0

Question Number 103888 Answers: 2 Comments: 0

find all such numbers: if we make its last digit, say k, as its first digit, the number becomes k times large as before. (□□...□k)→(k□□...□)=k×(□□...□k)

$${find}\:{all}\:{such}\:{numbers}: \\ $$$${if}\:{we}\:{make}\:{its}\:{last}\:{digit},\:{say}\:{k},\:{as}\:{its} \\ $$$${first}\:{digit},\:{the}\:{number}\:{becomes}\:{k} \\ $$$${times}\:{large}\:{as}\:{before}. \\ $$$$\left(\Box\Box...\Box{k}\right)\rightarrow\left({k}\Box\Box...\Box\right)={k}×\left(\Box\Box...\Box{k}\right) \\ $$

Question Number 103881 Answers: 2 Comments: 0

Π_(n=1) ^∞ (((2n−1)(2n+1))/(4n^2 )) ?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\left(\mathrm{2}{n}−\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{4}{n}^{\mathrm{2}} }\:? \\ $$

Question Number 103879 Answers: 2 Comments: 2

Question Number 103874 Answers: 1 Comments: 1

Question Number 103872 Answers: 0 Comments: 3

Question Number 103871 Answers: 1 Comments: 2

∫_0 ^1 ((x^(98) −99x+98)/(logx))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{98}} −\mathrm{99}{x}+\mathrm{98}}{{logx}}{dx} \\ $$

Question Number 103870 Answers: 0 Comments: 0

De^ montrer que la fonction f(x)=x^2 ∙sin((1/x)) admet un DL d′ordre 2.

$$\mathcal{D}\acute {\mathrm{e}montrer}\:\mathrm{que}\:\mathrm{la}\:\mathrm{fonction}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \centerdot\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{admet}\:\mathrm{un}\:\mathrm{DL}\:\mathrm{d}'\mathrm{ordre}\:\mathrm{2}. \\ $$

Question Number 103869 Answers: 0 Comments: 0

by using the Frobinus method solve the deffrentional equation xy^(′′) −2pxy^′ +(p(p+1)+b^2 x^2 )y=0 and give for example for this when p=1,b=2 such that (p,b) be areal number ?

$${by}\:{using}\:{the}\:{Frobinus}\:{method}\:{solve}\:{the}\:{deffrentional}\:{equation} \\ $$$${xy}^{''} −\mathrm{2}{pxy}^{'} +\left({p}\left({p}+\mathrm{1}\right)+{b}^{\mathrm{2}} {x}^{\mathrm{2}} \right){y}=\mathrm{0} \\ $$$$ \\ $$$${and}\:{give}\:{for}\:{example}\:{for}\:{this}\:{when}\:{p}=\mathrm{1},{b}=\mathrm{2}\: \\ $$$${such}\:{that}\:\left({p},{b}\right)\:{be}\:{areal}\:{number}\:? \\ $$

Question Number 103863 Answers: 8 Comments: 0

Pg 1077 Pg 1078 Pg 1079 Pg 1080 Pg 1081 Pg 1082 Pg 1083 Pg 1084 Pg 1085 Pg 1086

Contact: info@tinkutara.com