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Question Number 47043 Answers: 0 Comments: 0

if p is a prime number and (a,p)= then prove that a^(p−1) ≡ 1(mod p)

$${if}\:{p}\:{is}\:{a}\:{prime}\:{number}\:{and}\:\left({a},{p}\right)=\:{then}\:{prove}\:{that}\:{a}^{{p}−\mathrm{1}} \equiv\:\mathrm{1}\left({mod}\:{p}\right) \\ $$

Question Number 47036 Answers: 0 Comments: 0

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

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

Question Number 47035 Answers: 1 Comments: 1

(d^2 +a^2 )y=tan ax by the method of variation of parameters

$$\left({d}^{\mathrm{2}} +{a}^{\mathrm{2}} \right){y}={tan}\:{ax}\:{by}\:{the}\:{method}\:{of}\:{variation}\:{of}\:{parameters} \\ $$

Question Number 47034 Answers: 1 Comments: 0

find angel between spheres x^2 +y^2 +z^2 =29, x^2 +y^2 +z^2 +4x−6y−8z−47=0 (4,−3,2)

$${find}\:{angel}\:{between}\:{spheres}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{29},\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{6}{y}−\mathrm{8}{z}−\mathrm{47}=\mathrm{0}\:\:\left(\mathrm{4},−\mathrm{3},\mathrm{2}\right) \\ $$

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

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

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