Prove that every subset E of R is the union of some family of closed sets. Can every subset E of R be the union of a family of open sets? Prove your answer. 1.94

Q: x' + y = 0 y' – x = 0 x(0) = 1 y(0) = 0.

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Q: 11. to help pay for new costumes for a play, a theater invests $1900 in a 42-month Cd paying 3.6%…

A: Compound interest = total amount of principal and interest in future (or future value) less…

Q: Find the matrix M of the linear transformation T : R² → R² given by 6x1+ 8x2 -7x1+ x2. T М —

A: We have to find the matrix of linear transformation.

Q: Exercise 6. The graph of g consists of two straight lines and a semicircle the following integral.…

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Q: Let 3 21 Г1 —2 A = 3 -6 9 6 Describe all solutions of Aa = ở. +x4 +x3 i = x2

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Q: A 6-foot sub valued at $25 is divided among five players (P1, P2, P3, P4, P5) using the last…

A: Since, fair share = (Price of sub)/number of players Then, fair share = 25/5 = $5 And, P1 cuts the…

Q: 4. Solve the following problem in co,00) x (0,00) for xE(0, 0) for tE [o, oo) U(x,0) = J(X) uc0,t)…

A: We have to solve the following :       ut-∆u=0  in 0, ∞×0, ∞ux, 0=gx for x∈0, ∞u0, t=0 for t∈[0, ∞)…

Q: A school district school board is dividing between five high schools. The school board can hire 300…

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Q: QUESTION 2 Determine the volume of the bushing shown. 52 mm 42 mm 60 mm 20 mm 225 x 103 mm3 235 x…

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Q: Let -2 -6 -1] A = -9 4 -7 -9 -5 a Define the linear transformation T : R³ → R³ by T(#) = A. Find the…

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Q: If -6 9. 7 A 2 -8 then A- ||

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Q: Compute, step-by-step, the first and second derivatives and the maximum valu function on the given…

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Q: бп? + Зп = 3 2n2 – 5 Prove lim 6.

A: Limit of the fractional  value

Q: The regular price of a color TV is $567.22. During a sale, Hill TV is selling the TV for $504.34.…

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Q: EXERCISES 3:Find the directions in which the functions increase and decrease most rapidly at Po,…

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Q: 2. Solve for the linear system 2x + y + z = 2 y + z +w = 2 x + y-z = 0 x + 2z – w = 1

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

A: Note these facts :-

Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

Q: Prove that Σan σ(d) φ (n/d) nτ (n) and ΣIn τ(α)φ(n/d) σ(n). ||

A: As per the question we are given two sum identities including the Dirichlet convolution :…

Q: (6) If u, = x-Pa(x)Pn-1(x) dx, show that nu, + (n – 1)u,-1 = 2, | and hence evaluate u.

A: To get the desired result first we will the recurrence formula for pn(x). Then after simplification…

Q: 2.4 a. Find all the cluster points of the set Q of all rational numbers, and justify your…

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Q: iii. is continuous at a provided g(a) # 0.

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Q: Sumi Kato's savings account has a balance of $1292. After 12 years what will the amount of interest…

A: Compound interest formula

Q: Find the present value of the following deferred annuity due. Periodic Made Payment Period of…

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Q: Find the canonical prime factorization of this using Fermat’s Method and solve for the Number of…

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Q: 1. Find the unique solution first-order boundary value problem 2ru, +4r u, +6u=-2zte u(0, y) =…

A: As per our guidelines we are supposed to solve only one question that is the first one.For the…

Q: 2. Find Inverse Laplace transform for the following functions: s + 7 s2 – 6s + 8 a) F(s)

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Q: -3 -9 If A = 0 1 4 then 1 A-1 =

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Q: 1.1 How many simple graphs are there of four vertices? Draw all of them.

A: As per our guidlines we are supposed to solve only one question that is the first problem. For the…

Q: Let D_8 = . Let S_3 be the symmetric group of degree 3. Let G = D8 x S3. Let H = x and K = x…

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Q: 1 0 0 -2 2r – 4 Consider the matrix A 1 where r is a constant. 1 -r + 2 The values of r for which A…

A: Solution

Q: Consider the function f(T,y)= kr - 2xy + y?. %3D 1. Show that (0, 0) is a critical point of f(T, y).…

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Q: Determine the monthly payment for the installment loan. Annual Amount Financed (P) Rate (r) $1000…

A: To find- Determine the monthly payment for the installment loan. Amount Financed (P) Annual…

Q: Problem 4: Consider the set of polynomials {2+ t, 1 – 5t}. Let p¡(t) = 2 + t and P2(t) = 1 – 5t. Let…

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Q: Complete the following binary arithmetic Divide problem 1100 by 100

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Q: 2.23 Let 1 - x2 f(x): if x € Q, if r ¢ Q. Find all points p at which f is continuous. Prove your…

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Q: Given 15 - A = 2 -5 -4 10 find one nontrivial solution of A = ő by inspection. i = ||

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Q: H.w: Find the LT of the following functions: 1- f(t) = sin³t 2- f(t) = (t² – 5t + 6)e2t 3- f (t) =…

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Q: Iuse series representation to approvimate the integral Hint i Sum the first four terms of the series…

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Q: 7V7

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Q: While on a business trip in February, Bob Barrett charged the following expenses to his company's…

A: Correct option is - D

Q: H.W: find value of matrix A eigen -2 A = 2. 2. 3.

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Q: -11 35 -11 35 1 E) Let b, = and w= b, = Write as a 78 78 1 linear combination of 2 and 1 Solve this…

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Q: x/1 – x dx

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Q: 1- Is the following argument valid or invalid? Why? (x) (~Ux v Hx)                          Ux= x…

A: Given that (x)~Ux∨Hx where Ux=x is unicorn, Hx=x has a horn We can write it as (x)Ux→Hx It means…

Q: In Exercises 6 and 7, the graph of a function f (y) is given. Sketch the phase line for the…

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Q: 5.6.3. Let f(x) 16 interpolation points. Then, plot f(x) along with the resulting (real)…

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Q: sint t

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Q: Inter secting the sphere x*az²4 with the peleme z-L results in two surfaces. Make a roughelon. Let s…

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Q: In June, Carla charged the following expenses to her credit card: winter coat ($231), jeans ($125),…

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