Prove that "C, . (n-r) COS r=0 2ræ n = -n.2n-1.cos n T - n

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Q: Let r(t) (t¹ + 4, t² + 2t¹, − 4t³). Find the line (L) tangent to r(t) at the point (20, 36, 32) = L:…

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Q: Integrate. Show all u-substitutions. 3x - 15 a) ſ √³x-15 dx 2 -

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Q: X Question 7 Find the matrix for T(w) = projí where v = [−1 −4 −8]ª. DNE X

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Q: QUESTION 7 To test the effectiveness of a new treatment for patients with skin cancer, a randomised…

A: Randomization is necessary for these types of tests. So option one is wrong.

Q: Find the Inverse Lapiace Transform of F(s) = 3! (S-2)4

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Q: Find the sum of the series: Check Answer ∞ n=0 (-1)^36¹+3 2n + 1

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Q: Suppose the Caesar cipher is used to encrypt the message "QUICK." Which of the following cipher text…

A: Given that, Caesar cipher is used to encrypt the message "QUICK". The cipher text which corresponds…

Q: K How much more would you earn in the first investment than in the second investment? $51,000…

A: This is the final answer.

Q: Use Laplace transform to solve the given initial value linear systems 2 dx +4¹ +x−y = 3e' dy dt dt…

A: Given equations are      2x't+4y't+x(t)-y(t)=3et -------(1)           and…

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

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Q: A company produces foam mattresses in two sizes: regular and king size. It takes 5 minutes to cut…

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Q: The Maclaurin series of the function f(x) = 3x² sin(10x) 8 can be written as f(x) = Σ nx" n=0 where…

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Q: 10. A student has an illness that typically lasts about 24 hours. The temperature, FF in degrees…

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Q: tersection of the three given  planes.

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Q: Let there be set of a, b, c. Prove A×(B∩C) = (A∩B)×(B∩C)

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Q: Given z¹-z-12 2z+10 . apply your understanding of rational functions to sketch the graph of √f(x).…

A: The given function fx=x2-x-122x+10. We have to sketch the graph of the function fx.

Q: Determine the solution of the differential equation dy I +y=x²+x dr

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Q: Knowing that eigenvalues of A are ₁ = 3 and ₂ = 5 diagonalize this matrix; diagonal matrix D and an…

A: A=184-21142-8-1 Eigen values of A are λ1=3, λ2=5

Q: Solve the system. C1 12 x3 _X4. -10 0 -10 7 Submit Question +8 1 1 I I -10 0 4 6x2 612 3 + C4 2x4 -…

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Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve it.…

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Q: n different toys have to be distributed among children. Find the number of w which these toys can be…

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Q: 15. Find the general solution to the system of differential equations x' = Ax, where [3 1 0 0] 0310…

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Q: Find an orthogonal basis of R4, containing vector [1, 1, 1, 1].

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Q: 1. Show that Led edx + (xe" + sinz)dy + ycoszdz is independent of the path and evaluate the integral…

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Q: 2 1 4 b 3 d 1 2 5 2 4 3 f bo g 3 3 Longest Path: Shortest Path: *write your answer in this forma *no…

A: In that figure we find longest path and shortest path.

Q: chapp prove AX (BNC) = (A ne) x (Anc) nur ANG ISA-B

A: Let, A = {1}        B = {2, 3}        C = {3, 4}     Then, B ∩ C = {3}    Then, A × (B ∩ C) = {1} ×…

Q: An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). A= L = 0 U=0 4 2 -3-4

A: Given That : A matrix A=42-3-4 To Find : LU factorization of the given matrix .

Q: What is the graph's vertex set V? V = {EX: W, X What is the graph's edge set E? E = {Ex: {w, x}, {x,…

A: The set of all vertices of a graph is called vertex set of that graph.

Q: Consider the following matrix: A = -4 00 2 10 1 0 4 -10 0 1 4 -15 0 0 7 a) Find the distinct…

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Q: Question 2 [ a) [ 1 Let f(x, y) = 1-y³ - 2yx² + 3x² + 3y² and h(x, y) = x² + 2y². Find all the local…

A: Since there are many questions, therefore find the solution of the first question.

Q: American general offers a 9 years annuity with a guaranteed rate9.76 compounded annually. How much…

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Q: Dean) Define F4 to be the set of all 2 x 2 matrices F₁ = {[8 a+b] : ab € P₂} . F4= Prove that F4 is…

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Q: TMA manufactures 37-in. high definition LCD televisions in two separate locations, Locations I and…

A: here we will form a linear programming problem from given data and then solve it graphically by…

Q: A weighted Gauss quadrature formula for the weight function x is 6+√6 6-√6 [*xf(x) dx = (1 - 30) · ƒ…

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Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)^ 00 n + 3 n =…

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Q: (a) How many triples (x, y, z) of nonnegative integers satisfy x+y+z=100? ww many triples (x, y, z)…

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Q: - cx - y) + az = 0 bx + ay - 3 = 0 rough the a straight line, then find th

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Q: 3. Find JJs F ndS, where S is the part of the paraboloid z = = x² + 3y2 that lies inside the…

A: The given problem is to set up and integral with evaluates the given surface integral of vector…

Q: a. How many different teams can be chosen if there must be exactly three male palyers on the team?…

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Q: Given r = 2 cos 20 a) Find all tangent lines at the pole. b) Find the area of one petal of r. Show…

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Q: <11 } 2c1

A: We have to find  ℒ-113s+1 We know ℒ-11s-a=e3t

Q: Approximate -0.2 0.1 cotxdx using N = 8 of the Trapezoidal Rule and calculate the error. Round off…

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Q: Jause the series ER=1(41)k1 *) = In (1+x), for-1 < x≤ 1 to determine the Maclaurin series and the…

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Q: Determine if the graphs below contain Hamiltonian cycle, Eulerian cycle, both cycles, or none at…

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Q: There are three factories located at AR, IN, and TX respectively. From these locations, a certain…

A: Let xij be the number of units shipped from factory i to warehouse j.   Demand 50 35 Supply…

Q: -8 X (x²+4)³/² -dx (use proper notation)

A: Given: ∫-∞∞xx2+432dx We have to evaluate the given integral.

Q: 2-6 Use Stokes' Theorem to evaluate ff, curl F. ds. 2. F(x, y, z) = x² sin zi + y2j + xy k, S is the…

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