Find the Laplace transform of f(t) = sin² 5t a. 50/($³+125s) 25/(s³+ 100s) b. C. 25/(s³ + 125s) d. 50/($³+100s) ¡

Q: 8. Evaluate the line integral [x²dx + xe¯dy where C is the closed path along the triangle in the…

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Q: exactly a century by Lettry A batmans seors Fouss. and Sixes on 20 consecutive ball so can be do it…

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Q: Match the differential equation with its direction field. y ′ = 8 − y Give reasons for your answer.…

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Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

Q: 4. Find the surface area of the part of the sphere x² + y² + z² = 1 above the plane z = 1/√2.

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Q: Let f: R\{3} → R\{5} be defined by f(x) = 5x/(x-3). Show that f is bijective and find f-¹.

A: Given f:ℝ\{3}→ ℝ\{5} defined by f(x)=5xx-3. We have to show that function is bijective, and we have…

Q: Eliminate the arbitrary constants. Show complete solution. y=c₁x² + c₂e²x

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Q: 14) Let F(x)=

A: 14. Given,                    F(x)=∫0xsin(8t2)dt.

Q: The set of non-zero real numbers with arithmetic multiplication as an operation is a mono but not a…

A: This statement is false. Because the set of non zero real no is a group.

Q: How will you find the eigenvalues of a square matrix A? By finding the determinant of XI – A. O By…

A: Eigen values and eigen vectors

Q: ( › Given 7 = 178/33 -292553/44682 321593/44682 25405/14894 4 -5 53 ال لیا , 5 2 3 -B-0 and -6 7 -36…

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Q: 2. Let z -1 + i √2 (i) Determine the modulus and the Argument of z. (ii) Locate z, 2², 2³, 24, 25,…

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Q: 6. Write an equation, h(t), modeling the height of your ball as a function of time. h()=4.9t² +9,42t…

A: The height of the ball as a function of t is given by  ht=-4.9t2+9.42t+1.95

Q: Given a hexagon ABCDEF. Find the coordinates of the hexagon if the coordinates of the image after…

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Q: Explain the diagonal-proof method Question 1. Name and explain the proof method that is used to show…

A: We need to explain the proof method that is used to show the uncountability of sets, incompleteness…

Q: Le+ A=22 1 Find on orthogonal matrix Q and a 2-1 diagonal matrix D such that A=QDQT.

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Q: Prove or disprove that 10 is irrational.

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Q: A shipping box or paper carton is to have a square base and figure, you can assume that the top and…

A: To find the dim and smallest surface area for the given box.

Q: initial investm The minimum wage has been rising steadily since 1970. The line y = 0.14x +1.83…

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Q: Evaluate the surface integral fF.ds for the vector field F(x, y, z) = zi + 4xj +10yk S where S is…

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Q: Determine whether the set of solution defined by {ex, x², 3x} is linearly dependent or linearly…

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Q: d) x1 + 2x2 + 2x3 + 5x4 = 11 2x1 + 4х2 + 2x3 + 8x4 = 14 x1 + 3x2 + 4х3 + 8x4 = 19 X1 - X2 + X3 = 2

A: We solve the system of equations.

Q: A car was purchased for $1930 down and payments of $257 at the end of each month for four years.…

A: Given, Down payment for car = $1930 Monthly installment = $257 Time duration (t) = 4 years = 4(12) =…

Q: We are given the following nonhomogeneous differential equation. y"8y' + 20y 200x2 - 78xex To find…

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Q: evalute the mclaurins expanion and evaluate from 3 to 6 6 decimal places

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Q: 5. Give an example to show that g may not be injective when injective. Also give an example to show…

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Q: 3. Determine what t-values is r(t) = (t)i + (t²)j + (t³)k not smooth (if any)? Show work and explain…

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Q: Evaluate the line integral xe' ds, where C' is the line segment from (0,0) to (3,6).

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Q: The Maclaurin series of the function f(x) = 2x² sin(9x) 8 can be written as f(x) = Σ Σ n=0 where a…

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

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Q: Find the conditional probability, in a single roll of two fair 6-sided dice, that the sum is greater…

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Q: Solve the integral in the provided image, where F(x,y) = (sec(x) + x2y2, csc(y) + xyey) and C is the…

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Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: 1. Evaluate the following complex numbers below. a. loge(5 + 3j) b. In (4 + 5j)³j c. log(-15) d.…

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Q: Use the inner product (u, v) = 2u1V₁ + U₂v2 in R² and the Gram-Schmidt orthonormalization process to…

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Q: Let A = 2 1 29 2 36 and let W= COICA). Find on orthonormal basis for W. . Find a basis of W. Set up…

A: (a) Given: A matrix A=2129-1236 and let W=Col(A). To find:  Find orthonormal basis for W. Find a…

Q: True or False? If -1 is an eigenvalue of a 3 × 3 matrix A with associated eigenvector 2 -2 13 X =…

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Q: Approximate the stationary matrix S by computing powers of the transition matrix P shown below.…

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Q: 2. Solve (D²+3D)y = -18x

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Q: Use L'Hôpital's Rule (if possible) to calculate the following limits. If the method doesn't work,…

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Q: Find the Equation for the Graph of a Logarithmic Function Previous (7,-4)

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Q: Inverse Functions beduined Let f: R→ R be defined by f(x) = 3x +2. Show that f is bijective and find…

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Q: (a) Let A, B be n x n matrices. If AB = Onxn show that rank(A) + rank(B) ≤ n . (b) For any n x n…

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Q: Let Ai = [i − 1, i] for all integers i = 1,2,3,4. Find the following. a. A1_________________…

A: Given  Ai = [i-1 , i] ,  We need to find the values A1 , A2 , A3 and A4 , then the union and…

Q: rcentage a) Which table has linear growth? b) For the table with exponential growth, what is the…

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Q: S H R To find the volume of the cone in the picture where S = 5 cm and R = 3 cm:

A: A cone is a three-dimensional structure having height, radius, and slant height where h denotes the…

Q: of Work Problems (1) ( ) (A) Suppose D is the region bounded by the line y=x+3 and the parabola y2 =…

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Q: How does Riemann integral work geometrically, the process of finding the area unde

A: To Explain: Geometrical meaning of Riemann integral.

Q: 13. Which is an example of a veto power voting system? A) |{46 : 47, 4, 4, 6, 6, 7, 7} B) {32:11, 7,…

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Q: log16 2023 = log log

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