Find the centroid of the region bounded by y? = 14x and y² = 28(x – 7). NOTE: Enter the exact answers. (7, 9) = (?,?)

Q: Find T, N, B, K and t for r(t) = ti +÷e2tj whent = In 2. %3D

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Q: -2 1 -1 1 -1 1 3 (a) does the inverse of the matrix exist? Your answer is (input Yes or No): Are the…

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Q: Q1 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane. b) Find the…

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Q: Write out the subsets A, B,C defined below by listing their elements between braces. A = {x € S : x²…

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Q: Consider the equation z13 = (-1+ i). Find the value of z which satisfies this equation and which has…

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Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: (a) Use mathematical induction to prove the following inequalities: (i) 2n +1<n² for n 2 3 (ii) n² +…

A: We are going to prove the following inequalities by using mathematical induction .…

Q: 3. Use the Laplace transform method to solve the initial value problem r = 6x1 + 11r2, r = -4x1 –…

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Q: 8. Suppose that a market research firm is hired to estimate the percent of adults living in a large…

A: Note: As per our guidelines, we are supposed to answer only one question (first question), and the…

Q: The matrix A = -3 -2 -7| has an eigenvalue ) = -4. 1 3 ind an eigenvector for this eigenvalue. ry to…

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Q: +9 =zxe %3D

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Q: 04: Find the distance between the parllel lines L, and L2 where L1: x = 2 - t, y = 2t, z = 1+t L2: x…

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Q: Find the Fourier Series expansion of the graph and its characteristics given below. sin t, 0<t <a f…

A: Hint: Fourier series expansion of the function ft in the interval 0&lt;t&lt;2π is given by…

Q: 4. Construct a slope field for the differential equation dy (t + 1)(y – 1) dt %3D for -2 <t < 2 and…

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Q: 8 k 8 -9 2 O -6 -5 7 9 Let A 0 0 k 6 7 1 2 0 0 0 3 choose When is det(A) > 0? choose Always Only…

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Q: If the determinant is equal to zero solve for x. * 3 1 1 1 ol (i) 3 4 -30 1

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Q: Find the solutions of the system of inequalities by graphing: x + y 2

A: The region shaded by both inequalities is the solution of the system of inequalities.

Q: (f) Find the average value of f(z) = 1 - z| on the interval [–1, 1). f(3x +2) + f(2 – 5z) (g)…

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Q: Question 2: Find the inverse Laplace transform of 10 a) F(s)= s(s+2)(s+3)? b) F(s)=- s? +4s+5 1 -2s…

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, D[x] and D[y]…

A: We have to solve the given system of differential equation using Laplace transform.

Q: Julie's quilt measures 72 inches by 80 inches. There are 9 squares across the width and 10 squares…

A: If the length and width of a quadrilateral are equal, then it is called a square.

Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

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Q: Find the values that make the equation true. a -6 9 -4 b -3 -1 -9 f d 5 2 4 7 c -1 e -6 Enter you…

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Q: 5. Which of the following conditions is sufficient to conclude that a subset F of a metric space is…

A: We want to find sufficient condition to conclude that F is closed.

Q: Solve the equation. dy dx dx -- dy %3D

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Q: Your answer is correct. Suppose that vi - (2.4, 0, 7), v2 - (6,-3. 8. 3) and va - (-4,0,4, 5). Is…

A: The solution is given as

Q: Louis Lane can’t decide whether she wants to buy a car or lease a car. She is looking at a $28,000…

A: From given data we can see here Total Principal amount = P = $28,000 Time = t = 48 months and…

Q: 1. Encode LOVE (Use capital letters. No space) 2. Find the decoding formula. Select the letter only…

A: To encode and decode the given message .

Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: Q2/apply Gauss Elimination method to solve the equation? x+ 4y - z = -5 x + y- 6z = -12 3x - y -z =…

A: Given equations are x + 4y - z = -5 → (1)x + y - 6z = -12 → (2)3x - y - z = 4 → (3)

Q: Compute the following limit. 1-cos(x) as a approaches 0 495 500 O 490 O 505

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Q: 4) 11 yd. 3 yd Volume:

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: E real matrix with an eigenvalue A = 5 + 3i and corresponding eigenvector -1+ v = i nental set…

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Q: Match the solution curve with one of the differential equations. 元 O y"- 5y'- 6y = 0 O y" + 4y = 0 O…

A: The solution of the graph is y''+y=0

Q: Solve the differential equation dy y(0) = –1. %3D da x³ +1 There is no need to isolate y.

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Q: In the differential equation (6x – 3y +2)dx-(2x – y-1)dy=0, we let the substitution dx =

A: Given differential equations is non homogeneous differential equation.. We have to find the…

Q: A. Polynomial: Basic Concept, Long Division and Synthetic Division (Week 1) 1. Find (i) the constant…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: II. Solve the following differential equations using the substitution suggested by the equation. 1.…

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Q: has associated unit eigenvector ūı

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Q: 11. 3北 x(t) = e to

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Q: Evaluate: > Si(0.5)-1

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Q: Let r = (2,-i, 1), and y = (-i, 3,1 + i) be vectors in C3. Compute (x, y), ||x||, |ly|l, and…

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Q: Problem: 3 a. Find the domain of (fo g)(x) if f(x) = and g(x) 3x-1 %3D x+4 %3D 5x-2 ズー1

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question…

Q: g statements are helpful- prem 3.59

A: Yes

Q: fCt) = 3e 4t C1- 3t + 2t?)

A: The Laplace transformation formulas are Lekt=1s-k, Ltnft=-1nFns, where Lft=Fs. Simplify the given…

Q: Let f(x) = VT – 2 + k, where k is a constant. Suppose we want to evaluate | f(x) dz. Vā da – 2/ da +…

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Q: Find the eigenvalues A1 < A, and associated orthonormal eigenvectors of the symmetric matrix -5 -5 3…

A: We have to find eigenvalue and orthonormal eign vector.

Q: nd r'(t), r"(t), and r'(t) · r"(t). r(t) = 4 cos(t)i + 3 sin(t)j a) r'(t) b) r"(t)

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Q: Find the solution of the following heat conduction problem using the variable separation method. ôT_…

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