66. Find a basis for the vector space of all 3 × 3 symmetric matrices. What is the dimension of this vector space?

Q: 19. Evaluate fln(x)dx A) ln(x) + x + C B) x ln(x) − x + C C) e* -x + C ex D) In²(x) + C 2 E) None of…

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Q: Find the inverses of the matrices in Exercises 29-32, if they exist. Use the algorithm introduced in…

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Q: Vectors A and B are shown. What is the magnitude of a vector Cif C = A - B? 40 60 50 O a. 10 O b. 78…

A: Squaring on both sides, Given, And, angle between  is

Q: 10. When creating a right-endpoint Riemann sum on the interval [5, 10] using 10 rectangles, the 6th…

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Q: 1. Prove that 35121 (mod 1024).

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Q: 1. Jane is trying to find the area of the shaded region in terms x and in terms of y. She needs your…

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Q: 2. Determine whether the following games have saddle points. For games without a saddle point, using…

A: Note: Since you have posted multiple questions ( questions that are not related to each other) we…

Q: 1. Show that 25 is a strong pseudoprime base 7, i.e., passes Miller's test base 7.

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Q: Over what interval does the graph of the rational function have positive, decreasing slope? 4 2 0 2…

A: If the slope of the tangent to the graph of a function  at point is positive then we say that the a…

Q: Let X be the set {1, 2, 3, 4, 5, 6}, Y the set {a, B, 7, 8}, and ƒ the map f(1) = a f(2)= a ƒ(3) = d…

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Q: The particles of a fluid move symmetrically in space with regard to a fixed centre, prove that the…

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Q: Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a

A: We show that the question doesnt hold for a=1 and k=1

Q: At the National Baseball Batting Contest, the organizers have set up game booths for the…

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Q: Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 311 1 3…

A: The given matrix is .Also the eigen values are

Q: 6. Let r, denote the least nonnegative residue of 10 (mod 7). Compute ri for i= 1,..., 6. Compute…

A: To compute the least nonnegative residue of 10^i (mod 7) for i = 1 to 6, you can start by…

Q: How do you know the region in polar coordinates? How to find the polar coordinates?

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Q: 1. Find all solutions of the system of congruences x = 4 (mod 5), x = 5 (mod 6).

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Q: Proving that a certain linear operator  T on a Hilbert space H is compact, and calculate the norm of…

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Q: The relation R on Z defined by aRb if a2 ≡ b2 (mod 4) is known to be an equivalence relation.…

A: R is an equivalence relation  if   is known to be an equivalence relation.To prove this, we need to…

Q: 18. 8x So (42.8210) dx A) undefined B) In(6) – In(10) C) In(10) - In(6) D) ln(6) – In(10) + C E)…

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Q: Find the remainder when 2108 is divided by 31.

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Q: Clarissa is tearing her test (1 sheet of paper) into small pieces. She picks up a piece of paper and…

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Q: Let 2x² + 9xy + 4y² + 4x − 12y - 16 = 0. dy Use partial derivatives to calculate at the point…

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Q: Use the small increments formula to estimate the change in z = 2x3 y when x increases from 0.1 to…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given function f(x) = 4 + excos(5x)Now we can see that f(x) generated by  1, excos(5x)

Q: For a prime p suppose that n = 2º − 1 is not a prime. that n is a pseudoprime base 2. how every…

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Q: w is the orthogonal projection of the vector v upon the vector u where v:=vector([1,-1,1]);…

A: The orthogonal complement If w is the orthogonal projection of the vector v upon the vector u is .

Q: 4. Let B be a collection of all arithmetic progression of positive integers. Show that B is a basis…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 14. Over which intervals if f(t) equal to zero? A) [2,3] B) [4,5] C) [2,5] D) [0, 1.5, 3.5, 6] 15.…

A: We have to find Over which intervals if f(t) equal to zero? And What is the maximum value of f(t)?

Q: Let z(x, y) Calculate Әх ду дх ду & ar ar' 20 20 > Note: To produce the 0 symbol, type the word…

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Q: Find the area of a triangle having vertices A(3, 2), B(1, 8), and C(8, 12).

A: We have to find the area of triangle having vertices (3,2) , (11,8) and (8,12).

Q: For the plane that passes through (−4,1,5), (−7,−3,1), and (−2,3,9), the implicit equation is:

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Q: 2.16 Find the time t needed to empty an inverted conical tank with the base radius 3 ft and height 6…

A: According to the given data, find the time(t):

Q: Consider the vector field F shown in the figure below together with the paths C₁, C₂, and C3. 1 ? 1…

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Q: Use the method of Lagrange multipliers to solve optimization problems with two constraints. Find the…

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Q: Exercise 4. [Separ able space] Let X be a set of all real sequences (zn)neN converging to 0. Prove…

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Q: 8. Does the sequence of functions fn(x) = sin” ïx I[0,n](x), n ≥ 1, converge in Lebesgue measure on…

A: The sequence of functions in question is given by:fn(x)=sinn⁡πx⋅I[0,n](x),where n≥1,Here, sinn⁡πx…

Q: Determine the range of O a) ) ) {\v=yER} O b) | * SER} Oc) | * 3. ER} d) | y +1.yER} f(x) = 3r-1 r-5

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Q: 3. Compute R6 if f(x) = x(x-1) on [2,5]? A) 2.11 B) 0.0372 C) 0.372 D) 3.72 E) None of the above.

A: We have to find the value of R_6

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Q: Find the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: Step 1. Find the domain of the function. Step 2. Find the x, y intercepts. Step 3. Determine if the…

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Q: Find linearly independent functions that are annihilated by the given differential operator. (Give…

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Q: Let w(x, y, z) = √x2 + y² + 2² where x = -8ret, y = 2ter & z = ert. дw дw Oz Әх ду дz Әх ду…

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Q: Match f(x) with its graph without using a calculator. X-4 f(x) = O A. G O B. 10 Q G O C. 10 O D. Q P

A: The given function .The aim is to sketch the graph of the function.

Q: 1. Solve the linear recursion an = 2an-1 + 15an-2 with ao = 0 and a₁ = 2

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Q: Define f: [0, 1] → R by Let f(x) = 0 " 9 XER\Q x € Q and x = p/q Show that ƒ € R[0, 1] and find f…

A: Given that    by  Claim:  is  discontinuous on Justification: Let   be  arbitrary and  suppose  that…

Q: 2. Prove that a) A(BC) = (AB)C b) (AB)¹ = BT AT

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Q: 3. 1 χα (tr + 92 dx (x – ga-1 πα sin(πα)’ –1 < a < 1, a # 0

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Q: Suppose S is a set with conditions c₁, ₂,... The following questions involve the quantities, S., E,…

A: S(t), E(t), and L(t) are related as,S(t)-   S(t) is the set of elements in S that satisfy exactly t…