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Question Number 47026 Answers: 4 Comments: 4

Question Number 47019 Answers: 2 Comments: 2

Question Number 47018 Answers: 1 Comments: 1

find ∫ (√(x+2−(√(x−1))))dx

$${find}\:\int\:\sqrt{{x}+\mathrm{2}−\sqrt{{x}−\mathrm{1}}}{dx} \\ $$

Question Number 47010 Answers: 1 Comments: 1

Question Number 47006 Answers: 1 Comments: 1

Question Number 47005 Answers: 1 Comments: 1

Question Number 47001 Answers: 0 Comments: 0

Question Number 46998 Answers: 1 Comments: 0

In physics how do we find average half-life? please i need help

$${In}\:{physics}\:{how}\:{do}\:{we}\:{find}\: \\ $$$${average}\:{half}-{life}? \\ $$$$ \\ $$$${please}\:{i}\:{need}\:{help} \\ $$

Question Number 46996 Answers: 1 Comments: 0

Question Number 47098 Answers: 1 Comments: 8

prove that:lim_(n→∞) ∫_(−1) ^1 (1+(t/n))^n dt = e−(1/e).

$${prove}\:{that}:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\mathrm{1}+\frac{{t}}{{n}}\right)^{{n}} {dt}\:=\:{e}−\frac{\mathrm{1}}{{e}}. \\ $$

Question Number 46983 Answers: 0 Comments: 0

(u_n ) is a sequence wich verify u_n =n u_(n−1) −λ (λ from R and n≥1) calculate u_n interm of n and λ .

$$\left({u}_{{n}} \right)\:{is}\:{a}\:{sequence}\:{wich}\:{verify}\:{u}_{{n}} ={n}\:{u}_{{n}−\mathrm{1}} \:−\lambda\:\:\left(\lambda\:{from}\:{R}\:{and}\:{n}\geqslant\mathrm{1}\right) \\ $$$${calculate}\:{u}_{{n}} {interm}\:{of}\:{n}\:{and}\:\lambda\:. \\ $$

Question Number 46978 Answers: 2 Comments: 0

Question Number 46977 Answers: 0 Comments: 1

3x+2≡0(mod 7)

$$\mathrm{3}{x}+\mathrm{2}\equiv\mathrm{0}\left({mod}\:\mathrm{7}\right) \\ $$

Question Number 46974 Answers: 2 Comments: 1

Number of integers n for which 3x^3 −25x+n=0 has three real roots is ?

$${Number}\:{of}\:{integers}\:{n}\:{for}\:{which}\: \\ $$$$\mathrm{3}{x}^{\mathrm{3}} −\mathrm{25}{x}+{n}=\mathrm{0}\:{has}\:{three}\:{real}\:{roots}\:{is}\:? \\ $$$$ \\ $$

Question Number 46973 Answers: 1 Comments: 0

Question Number 46972 Answers: 0 Comments: 0

let m,n denote any two possitive relative prime integers,then prove thatφ(mn)=φ(m)∙φ(n)

$$\boldsymbol{{let}}\:{m},{n}\:{denote}\:{any}\:{two}\:{possitive}\:{relative}\:{prime}\:{integers},{then}\:{prove}\:{that}\phi\left({mn}\right)=\phi\left({m}\right)\centerdot\phi\left({n}\right) \\ $$

Question Number 46962 Answers: 0 Comments: 1

Question Number 46959 Answers: 1 Comments: 5

The reminder when polynomial 1+x^2 +x^4 +x^6 +....+x^(22) is divided by 1+x^ +x^2 +x^3 +.....+x^(11) is =?

$${The}\:{reminder}\:{when}\:{polynomial} \\ $$$$\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} +{x}^{\mathrm{6}} +....+{x}^{\mathrm{22}} \:{is}\:{divided}\:{by} \\ $$$$\mathrm{1}+{x}^{} +{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +.....+{x}^{\mathrm{11}} \:{is}\:=? \\ $$

Question Number 46944 Answers: 1 Comments: 3

Question Number 46935 Answers: 1 Comments: 1

Question Number 46925 Answers: 1 Comments: 0

The third term of a GP is 4. The product of first five terms is

$$\mathrm{The}\:\mathrm{third}\:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{GP}\:\mathrm{is}\:\mathrm{4}.\:\mathrm{The}\:\mathrm{product} \\ $$$$\mathrm{of}\:\mathrm{first}\:\mathrm{five}\:\mathrm{terms}\:\mathrm{is} \\ $$

Question Number 46924 Answers: 1 Comments: 0

If ((a−x)/(px)) = ((a−y)/(qy)) = ((a−z)/(rz)) and p, q, r are in AP, then x, y, z will be in

$$\mathrm{If}\:\:\frac{{a}−{x}}{{px}}\:=\:\frac{{a}−{y}}{{qy}}\:=\:\frac{{a}−{z}}{{rz}}\:\mathrm{and}\:{p},\:{q},\:{r}\:\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{AP},\:\mathrm{then}\:{x},\:{y},\:{z}\:\:\mathrm{will}\:\mathrm{be}\:\mathrm{in} \\ $$

Question Number 46923 Answers: 1 Comments: 0

a, b, c are in AP or GP or HP according as ((a−b)/(b−c)) is equal to

$${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}\:\mathrm{or}\:\mathrm{GP}\:\mathrm{or}\:\mathrm{HP}\:\mathrm{according} \\ $$$$\mathrm{as}\:\frac{{a}−{b}}{{b}−{c}}\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 46922 Answers: 1 Comments: 0

Thr 6th term of an AP is equal to 2, the value of the common difference of the AP. Which makes the product a_1 a_4 a_5 least is given by

$$\mathrm{Thr}\:\mathrm{6th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{2},\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{AP}. \\ $$$$\mathrm{Which}\:\mathrm{makes}\:\mathrm{the}\:\mathrm{product}\:{a}_{\mathrm{1}} \:{a}_{\mathrm{4}} \:{a}_{\mathrm{5}} \:\mathrm{least} \\ $$$$\mathrm{is}\:\mathrm{given}\:\:\mathrm{by} \\ $$

Question Number 46921 Answers: 1 Comments: 0

The sum of first two terms of an infinite GP is 1 and every term is twice the sum of the successive terms. Its first term is

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{two}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{infinite} \\ $$$$\mathrm{GP}\:\mathrm{is}\:\mathrm{1}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{successive}\:\mathrm{terms}.\:\mathrm{Its}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is} \\ $$

Question Number 46920 Answers: 0 Comments: 0

If the sides of a triangle are in AP, and the greatest angle of the triangle is double the smallest angle, the ratio of the sides of the triangle is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{double}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{angle},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is} \\ $$

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