The 2nd, 31st and last term of A.P. are 7, 4 2 and – 6, respectively. Find the first term and the number of terms.

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A: Given function  f(x,y) = x2 + 3y3 + 9y2 - 3x  Then fx(x,y) = 2x - 3  fy(x,y) = 9y2 + 18 y  fxx(x,y) ...

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Q: 9. Find the particular integral of differential equation (D² +a² ]y =bcosax.

A: Particular integral of the second order differential equation.

Q: Discrete Math Let k be a positive integer. Use induction to prove that (k −1)^(n+1) +k^(2n−1) is di...

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Q: Q/ Solve the following linear system: (Group E) x + y + z = 5 2x + 3y + 5z = 8 4x + 5z = 2 a. Using ...

A: Given system of linear equations is  x + y + z = 5  2x + 3y + 5z = 8  4x + 5z = 2

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A: Newton Raphsons method

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A: Given V = -aa0, -b0b | a, b ∈ℝ 

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Q: Q1/ Solve the following system using Inverse matrix 0.5 x+3.1 y- 0.2 z 5.9 1.2 x- 2.5 y+0.7 z 2.2 0....

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Q: Solve the problem. Let a1 = 5, a = , and b = Ematrix (( -2 )( 3 )( 1 )) Ematrix (( -23 )(-3 )( 22 ))...

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Q: A open interval is homeomorphic to either a closed interval or a half open interval. O True O False

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...

Q: (-3x - 5 if x > 7 ep 1 of 3: Evaluate this function at x = 9. Express your answer as an integer or s...

A: Given f(x) = -3x - 5  if  x > 7

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Q: Determine if following integrals are Lebesgue integrable

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Q: (c) Solve the difference equation Yt+2 – 4Yt+1+4Y; = 2(2') + t² - Given initial values Y, = 2 and Y,...

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Q: int of (cos2x - sin2x cos2x / cosx - sinx) dx = 1/3 F(x) + C. What is F(x)   Please include explan...

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Q: (1) What number must replace the question mark? 4 4 7 6. ? 9 1 2

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Q: Determine it this new def ot O wald make Va Vector Space

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Q: Attached below is a description and the differential equations problem/question: What is the soluti...

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A: This is a problem of a linear transformation, vector space.

Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)   ...

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Q: 4. Solve the homogeneous differential equation x’dy+(y² +xydx=0.

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Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

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Q: Solve for the Laplace transform f(t) = 2(t-4)^4 x(t) = (t+2)sin(t-4) x(t) = 3(t/4)e^(-t/5)

A: Some of the formula of Laplace transform Leat=1s-aLtnf(t)=(-1)n-1ddtF(s)Lsinat=as2+a2L[cosat]=ss2+a2...

Q: 10. If a triangle is equilateral, then it is equiangular. If it is an equilateral triangle, then it ...

A: This is a problem of logic.

Q: f(n)={1 if n is odd; n if n is even  Prove or disprove. f(n) is O(n).

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Q: 9(x+ k)- 2g(z) + g(#- k) g"(2)- use the Taylor series 9(x +k)-9(a) + kg'(1) + 1 9" () ++ n! g(m) () ...

A: This is a problem of Taylor's theorem and application.

Q: 1.T.1 Let U be the set of all twice-differentiable functions f : R → R satisfying f"(x) + 2f'(x) – 3...

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Q: (2, 2) (0, 2) C1 C3 C2 (2, 0) 3 (0, 0) -1 1.The equation of C3 can be expressed as z= p+ qi + ce®yhe...

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Q: 42 Ex: Ginen te fallasing daka : Xo ーL5 」1.5 X -2 fex)ら Fined he quadruic spline inkerpolahing fun. ...

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Q: gtx) 6x - 7; h(x) 1.7* Find the derivative of f(x) g(x) h(x).

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