4. Complete this problem as a write-up. Manipulate ||u – v||2 to show that it can be written as ||u||2 + ||v||2 – 2u•v.

Q: Find the general solution of the following ODE's: y' + 3x²y = x²

A: The given differential equation is y'+3x2y=x2 It is of the form of linear differential equation…

Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

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Q: Evaluate h(2), where h = (gon. s (2) = –ig(2) =?+1 1 f (z) . h(2)

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Q: Compute A?x and A3x the correct way: ´1 0 () 0 1 A = 3 0 2 0 1 1 1

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Q: To the recipient, the following commendation is given in its standard form max z = Ax1 +B x2 A=6…

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Q: 10- Solve the problem: Utt-4uxx = xt, 00 u(x,0) = x, 4(x,0) = 0, u(0, t) = 0, Ux(1,t) = 1+t, t20 %3D

A: Given, utt-4uxx=xt;   0<x<1, t>0 ⋯⋯⋯⋯1ux,0=x,   utx,0=0,   0≤x≤1,⋯⋯2u0,t=0,   ux1,t=1+t,…

Q: Answer the following question accordingly: a) Let A=|2 3 -1 3 a and B-l= where %3D 2 5 a ato and a $…

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Q: 1. If u" (x) u'(x) 1 x + b' solve u.

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Q: (3) Let X n(µ,4) and Var(2x)= E(5-8x) find u.

A: Given that X follows normal distribution with mean mu and Variance 4 E(X)= mu Var(X)= 4 Given that,…

Q: s(2) f(z) is analytic in C

A: Ans : false

Q: .3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

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Q: Solve this problem About Faktorial with the full step, thank u Prove that :…

A: Note: There seems to be a typo in the question k!(k−2)!(k−1)!(k−3)! and the actual question should…

Q: Find all values of n such that y = xn satisfies x2y" - 12y = 0

A: To solve the equation x2y''-12y=0, we first need to find y''. y'' can be obtained by differentiating…

Q: Suppose that X~ B(21, 0.25). Find: a. u : b. o (round to two decimals):

A: Mean of binomial distribution, mu= np Her sample size n= 21  Probability, p= 0.25 Mu= 21*0.25 = 5.25…

Q: В. a = lass)-(21-1) given that w= In(6x + 2y³ – 3z).

A:

Q: II. Let U = R, 1 = { x eR | x5 – 26x3 + 25x = 0 }, J = { x € R | |4x + 2| > 10 } and K = { x €R | x?…

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Q: [ u#(u – 1)"-1 đu (1+x!/n dx = n

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Q: The solution set for X satisfying both |x – 1| 1 is O a) None of these O b) (-o, 3] O c) (1, 3] O…

A: Given: x-1≤2 & x>1 We know that; if x≤a , a>0 then -a≤x≤a And If x>a , a>0 then…

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

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Q: 4 16 Define T: R? - R° by T(x) = Ax, where A = 1 3 -

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Q: 1. Rewrite c(x) x² +5x+2 in the form y = p(x) + r(x) where r has degree less than b. x-3 6(x) 2.…

A: The objective of the question is rewrite the given equation and end behavior.

Q: 1. Show that (a) exp(2±3лi) = -e²; (c) exp(z+лi) = - expz. πί p ( ² + 7² ) = √ = (1 + i); 4 (b) exp

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Q: -10 If AXT = B, then X= Let A = %3D 0 2

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Q: Solve the following P.D.E. , with the following conditions: u(0,y) = 0, u(L,y) = 0, u(x,0) = 0 and…

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Q: Calculate the convolution: x * 2 * e2* . x2 e2a O a. 4 4 8 e2a Ob. 4 4 8 - 4 2 4 O d. 1 x2 e2æ 4 2 4…

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Q: Let X = n(u,4) and Var(2x) = E(4–7x) find u.

A: As per our guidelines we are suppose to answer first question .

Q: Which of the following is a possible y" + k'y = 0

A: Given that: y''+k2y=0

Q: the following DE are Bernouli type and solve: 1. y’ – x = y 2. y’ + 5y/x = x 7 y 4

A:

Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: In (y*) y' = 3 x²y

A:

Q: Let S be the set of integer solutions to the equation x1 +x2+x3+x4 = 30, where x; > 0 for i = 1,2,…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Which of the following is nota possible rvalue? A. 1.6 О В. -0.6 С. 0.3 ) D. -0.3

A: In this case, we need to identify the correct option.

Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0.

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Q: (9) Let X z b(n,) and E(3x) = E(3– 5x) find n.

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Q: 3 Reverse the order of whyndien of ? X (6x-2) dyds x- 4

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Q: Which one of the following alternatives provides a statement that is FALSE? Select one: O a. vx € Z,…

A: Set of integers is , Z ={...,-3,-2,-1,0,1,2,3,...} ∀x  ∈ Z  means for any x in Z that property holds…

Q: Prove that the value of the expression (а — 1)(а — 3)(а — 4)(а — 6) + 10 is positive for every a E…

A: The critical points for the function are the set of values where the function attains its maximum…

Q: (a) Compute /(2) dr, given that f(b) 3 and that | af'(a) dr b(1 + f(-b)). (b) Computei (2) dz. given…

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Q: (34 If ā = 27 +j- 3k, 5 = T-2J +k; č = -i+J-4K, d = i +J +k then compute (āxb)x (7 xd

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Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

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Q: Ex. Save the following sef of Lincar equations using with R=11 over relaxation 10X, +X2 +X3 12 X, +…

A: In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the…

Q: (33) Let X = b(20, p) and E-x) = E(3–10x) find p. р.

A: Let X follows binomial distribution with parameters ( n =20, p) The mean of X is, Use the…

Q: I find B such that AB = C. If 5 0 3 A = 2 01 9. C = 3 5 c- (* :)

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Q: Consider the systenm o o-21 x + %3D 0 3 Frnel the ennit s tep esponse of the system.

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Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

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Q: Suppose that X ~ B(18, 0.51). Find: a. u: b. o (round to two decimals):

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Q: Solve the following linear independent and Wronskian. 2. Are the functions y, = e* and y2 = x…

A: Here we have to determine whether the given functions are linearly independent.  We have,  y1=ex…