Use the Table of Integrals to evaluate the integral. (Remember to us S cos(x) sin²(x) - 64 dx

Q: show your work. thanks for your answer

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Q: find the real solutions, if any, of the system.  y=x2  x2+y2=12

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Q: - Find a basis for S for the subspace S. 3 5-0 S=span 1 2

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Q: f(t) = 0.73t3- 2t2+t+0.6 and g(t) =0.17t2-0.5t+1.1    Calculate the area between the graphs of f(t)…

A: Given that f(t) = 0.73t3- 2t2+t+0.6 and g(t) =0.17t2-0.5t+1.1 . For simplicity, we have plotted the…

Q: (5) Let D be a reflection matrix; that is, there is some line W such that for every vector C in D.…

A: Given that D is a reflection matrix. This means that there is some line W such that for every vector…

Q: 5. In this exercise we investigate the sequence {} for any constant b. 10k a. Use the Ratio Test to…

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Q: 4. Show that a bipartite graph with n vertices has at most n²/4 edges.

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Q: 4X--X y = -x + 2y Stability with draw

A: x˙=-xy˙=-x+2y

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Q: 1. What is the center of the given power series? (This is what the book calls “a”.) 2. Determine the…

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Q: Find the best approximation to z by vectors of the form C₁ V₁ + C₂V₂. Z= 3 6 0 -1 V₁² 3 0 -2 V₂ =…

A: Orthogonal projection of z  onto span v1 and v2  is the best approximation to z by vectors…

Q: Solve the given boundary-value y(x) problem. (If an answer does not exist, enter DNE.) y" +9y = 0,…

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Q: Determine if the vector u is in the subspace S¹. (S¹ = {u € R¹|s € S, u · s = 0}) [31 S =span 3 4 2…

A: Introduction: The orthogonal complement is the set of all vectors whose dot product with any vector…

Q: -4 4 3 3 0 4 1 3 0 0 1 1 -4 0 0 0 1 1 0 00-5 4 -4 5 /hen following the standard Gaussian elimination…

A: An elementary row operation and Gaussian Elimination matrix is given.

Q: Consider the following definite integral. 10 0 (10x-x²) dx a. Write the midpoint Riemann sum in…

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Q: (b) u Use the Fourier Transform to find general solution formula for - 4u" +4u = g(x)

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Q: Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. A= 1 3 1 3 4 12 39 4-2…

A: I have explained everything with in the solution. Please go through that.

Q: I do not see a solution

A: Please see the process

Q: A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the…

A: A laser rangefinder is locked on a comet approaching Earth. The distance gx, in kilometers, of the…

Q: 2) Several friends take a fishing trip every year. Each year they have a contest to see who catches…

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Q: 3 Let M₂(R) be the vector space of all 2 × 2 matrices with entries from R. Show that M₂ (R) = W₁ W₂,…

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Q: x=y y = -x-X² Stability with draw

A: x˙=yy˙=-x-x3

Q: 16. Let R* be the multiplicative group of non zero real numbers and let S= the group under the…

A: As per the guidelines I have solved first problem.

Q: 1. Solve the equation between 0 and 2π, 3 sin² (x) + sin(x) = 1 − 3 sin² (x)

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Q: Given that f(x) = x is a solution of (1 − x²)y" − 2xy + 2y = 0_ within −1 < x < 1 find a second…

A: f(x)=x is a solution of DENow1-x2y''-2xy'+2y=0

Q: Evaluate the given integral by making an appropriate change of variables. 4 x - 6y 7x - y dA, R…

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Q: Consider the following proposed variation of Rolle's theorem. Let f: (a, b) → R be a differentiable…

A: We have defined a special real valued differential on (0,1) .

Q: Let f(t) be a C¹ function of t with ƒ'(t) ‡ 0. (a) Put F(x, y) = f(x² + y²). Find the gradient VF at…

A: Let ft be a C1 function of t such that f't≠0 a) Given Fx,y=fx2+y2                      (i) It is…

Q: Let S be a subspace. Prove that S ns¹: = {0}.

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Q: Suppose a velocity field given as V = ti+2t² j, where Cartesian coordinate and t is the time. We…

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Q: Given the 8 letters in the word ABSOLUTE, How many ways can the letters be rearranged?  How many…

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Q: Write the system of linear equations in the form Ax = b and solve this matrix equation for x. 2x₁ -…

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Q: Find the domain and range and describe the level curves for the function f(x,y). f(x, y) = -sin ¹(x²…

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Q: The region D above can be described in two ways. 1. If we visualize the region having "top" and…

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Q: 1. Approximate the sum of the series to 2 decimal places. Σ a. n=1 (-1)" 2"n! (-1)"n b. 100n² +4n+1…

A: 1. a) Given series is ∑n=1∞-1n2n n! Take sum of first five terms, i.e., ∑n=15-1n2n…

Q: (b) 2*1:! k

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Q: 1. N Find the value of the sum: (2i³+ − 3). expression in terms of N. -3). Your answer should be an

A: We determine the value of the sum

Q: 1 (₂) рноле b²-ca étab a-be b-ca c²ab b-ca a^²=bc_b-ca = (a²+ b³ + c²_Babe) ² e-ab 2² bedro

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Q: Which matrices are in reduced echelon form, echelon form and neither? 0120 0001 96 1201 0013 0000 a…

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Q: 2. Solve a²ua²u 8x² ?х მy2 u(0, y) = 1, u(x,0) = 0, = 0, 0<x< un, y) = 1, u(x, n) = 1, , 0<y<n,…

A: Dirichlet boundary conditions are a type of boundary condition that specifies the value of the…

Q: Solve the following equation (1 − x²)y" + 2( (x² − x − 1)y' + - (-x² + 2x + 7-1₁-²2) y = 0

A: Given: The differential equation 1-x2 y''+2 x2-x-1 y'+-x2+2x+7-11-x2 y=0 To find the general…

Q: 3. Given that f(x) = x is a solution of (1 − x²)y" − 2xy + 2y =0 within find a second linearly…

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Q: A rectangular fence enclosing 32 ft² is to be built. The north and south sides are built using…

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Q: i do not think that this is correct

A: The divisors/factors of of 70 greater than 1 are {2,5,7,10,14,35,70}

Q: Consider the two matrices: 2 4 1 -5 (²6) -- (-²3 2²) = Compute A + 3B. The result is equal to: A =…

A: We have been given two matrices A=24-60       and   B=1-5-32   We have to compute the value of…

Q: Approximate the area under the curve graphed below from x=2 to x = 5 using a Left Endpoint…

A: Graph of the function is given, we have to find the area under curve graphed from x=2 to x=5, using…