Solve the following integral equation using Laplace transformation y(t) = 1+ cos(t – u)y(u)du

Q: Compute the following limits using L'Hospital's rule if appropriate. Use INF to denote oo and MINF…

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Q: () Consider matrix A = and vectors x = and y = Calculate matrix B = (A – A")² and vector w = Bx.…

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Q: Find the surface area of a cylinder with a base diameter of 12 in and a height of 9 in. Write your…

A: To find the surface area of cylinder.

Q: Find the Galois group of the splitting field of x + 2 over Q and identify the automorphism and the…

A: Solution :-

Q: Problem 1: Given: -2,3,8, 13, ... Find the following: (a) 6th term of the sequence; (b) an formula…

A: Here we use arithmetic progression.

Q: The measure of arc BC is 97 degrees. What is the measure of angle BCE to the nearest 100th? C D Type…

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Q: Let R = {(x, y) € R² | In y <r <1n1< y< e} and let S be the surface defined by the vector function…

A: First we find the region of (u,v) such that the projection of surface on xy-plane is R.

Q: Let FCK be a field extension, wl

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Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2…

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Q: f(t) = t? cos 6t 2s(108-s?) А. (s2 -36)3 2s(s? -108) C. (s2-36)3 2s(108-s2) В. (s2+36)3 2s(s?-108)…

A: Given function f(t)=t2cos6t. We have to find the Laplace Transform. Formula will use 1.…

Q: Express the griven below in rectangulat form Co (cos le0° + i sin 180°) a. le + oI b.-et Di -1 + oi

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Q: Problem 6. Find all positive primes p such that n = 1001p satisfies that a" = a mod n for all a.

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Q: Using the theorem on determinants, show that 1 a a2 A = 1 b b2 = (b – a)(c – a)(c - b) 11 - с с2

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Q: 3s - 2 Find the Inverse Laplace Transform of G (s) = 2s² – 6s – 2 A 8(1) = 3e 2 sinh cosh 13 B 8 (1)…

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Q: Let {xn} be a bounded sequence of real numbers. Prove that {xn} converges if and only if lim inf xn…

A: Proof

Q: Find the volume of the solid within the cylinder r2 + y? = 4 that is bounded below by the xy-plane…

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Q: Use Fermat's Little Theorem to find each value. Remember, x-1) =1 (mod p). Write your answer in…

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Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.

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Q: Draw a colored ball from the bag. There are five balls of different colors ( red, blue, pink, green…

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Q: 5 2 ; B = -2 -2B

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Q: Find all proper nontrivial subgroups of Z; x Z, × Z;. Find all subgroups of Z; x Z4 of order 4.

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Q: Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initially…

A: Given: Tank1: The volume of tank 1=50 gals x1(t)= amount of salt at time tx1(0)=50 gals× 1…

Q: Box Plots Use the following Box Plot about the height of boys and girls to answer these questions.…

A: The box plot is given about the height of boys and girls.

Q: urvilinear integral: Find de x dx + yay is the perimeter of the where (0.0), (4,0) ,(0,1), (4, d)…

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Q: 12. The graph of f is shown below on the xy-plane. Explain why y = 0.8(x – 1) + 0.4(x – 1)² + 0.1(x…

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Q: Let F(x) = f(x) + g(x)e* + h(x)e2x+ C be the antiderivative of G(x) = (x + e*)“, Determine the value…

A: The given problem is to determine the value of f(x)+g(x)+h(x) for x=1.69 where F(x) =…

Q: Match graphs A-D in the following figure with the functions below. Assume a, b, c and d are positive…

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Q: Prove: If S is compact, and f is continuous on S, then f takes a minimum value some- where in S.

A: Since S is compact and f is continuous, f[S] is a compact subset of R and therefore closed and…

Q: find the coordinates of the centroid of the plane area bounded by the parabola y=4-x^2 and the…

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Q: Using Gamma function evaluate xe-3x dx.

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Q: a bc a Jalue of b ac is: 1 c ab (a) 0 (b) 1 (c) -1 (d) none of these Select the correct response: d…

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Q: Question B1 a. Calculate the line integral [F•dr. where F = 3x²y²i + 2x°yj for the curve C. Here C…

A: We need to find line integral of vector field  line integral of vector field F→ along a curve C…

Q: Show that in the factor ring Z[i] / , the element x + is a unit.

A: Given a factor ring Zx2x+1=a0+a1x,+⋯+2x+1 |a1∈Z  As 2x+1+2x+1=0+2x+1 Since,  2x+1∈2x+1   as aH=H iff…

Q: Let (G, ) denote the set of all 2 x 2 real matrices A with det{A} 0 Question 5. and det { A} E Q…

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Q: How many iterations is needed in order to solve for one real root of f (2) = 2 + 2 - lusing…

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Q: Use the method of undetermined coefficients to solve the initial value problem. y"+ 4y = 2 + 8ed,…

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Q: |a,6,d e а a, b, d E R}. S2x2 b d Do three matrices 1 A1 = 0 1 1 0 A2 = A3 1 0 - 1 | form a basis of…

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Q: Problem: A loan of Php 1500 at 12 % annual interest rate. The loan was made on June 22 and due on…

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Q: A standard dorm bedroom at most collegue 10ft wide by 15ft long. A LEGO 2by4(2*4) brick is 0.90cm…

A: The formula to calculate the volume of a cuboid is V=lbh, where l, band h are the length, breadth…

Q: ミ xy

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Q: Consider the triangle shown in the figure below. a. Find the equation of the straight edge OA. b.…

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Q: Consider the following two matrices: -2 1 - C = 7 -1 D = 2 3 3 -2 Which of the following four…

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Q: Let R be the ring of continuous functions from R to R. Prove that M = {f e R : f(0) = 0} is a…

A: To show that the given subset M of R is a maximal ideal, we first show that M is a ideal of R and…

Q: Prove 1 +,+ i++ = 2 – for all positive integers n. |

A: We want to prove 1 + 12 + 14 + ... + 12n = 2 - 12n

Q: (n + 1)(2n + 1)/6 for the positive integer r )What is the statement P(1)? -) Show that P(1) is true,…

A: Given, P(n) be the statement that                 12+22+ . . .+n2=n(n+1)(2n+1)6  for the positive…

Q: Find a primitive root (i.e. a primitive (p? – 1)st root of unity) in F3[i], and write down the…

A: F3i : It is the unique field of three elements. It can be defined as the ring of integers of modulo…

Q: f(t) = 2t² + 4t – 3 4+2s-3s? А. c 4+4s-3s? С. s3 2+2s-3s2 В. 2+4s-3s2 D. s3

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Q: 6° Szx dx t yay where L cs parabol y=-x(x-) arc

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Q: Approximate the root of 2 - 11.722 + 17.72-5 0 using three iterations of Newton-Raphson Method. Use…

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Q: 5. In previous problems dealing with two species, one of the animals was the predator and the other…

A: (b) we have given the system A dxdt =-5x+2xydydt =-4y+3xy we have to determine all the equilibrium…