Solve by Laplace transform Utt – 9urz = 0, 0 0 %3D u(0, t) = u(r, t) = 0, %| %3D u (x, 0) = 0, u(x,0) = 2 sin x.

Q: Determine whether or not the set s ]日) 2 1. %3D 3. is a basis tor Rš.

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Q: Use the Newton-Raphson formula once to find an improved estimate of a solution to the equation 3x^ 2…

A: Given equation is 3x2 = 7e-x It can be written as 3x2 - 7e-x =0⇒fx =0Here, fx =3x2 - 7e-x First…

Q: Let be yı(x) and y2(x) solutions for a differential equation with constant lineal coefficients y" +…

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Q: Find the Laplace transform of: 1. f(t) = e(-30) sin(2t) cos(3t) cosh(t)

A: Given function can be written as ft=e-3tsin2tcos3tet+e-t2=e-3tet+e-t2sin2tcos3t

Q: Find the Laplace transform of: 1. f(t) = e(3t-7) cos (6t)

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Q: Consider the function R(x) = (3x | 0sxs 1/3 2 - 3x |1/3 < xs 2/3 3x - 2|2/3 sx < 1} (a) Sketch a…

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Q: aw the graph a

A: Given, the curve                  r=63-2cosθ

Q: Find Fourier series [o, 2] an O f cx) %3D SinX

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Q: 1 It is known that y1 (x) 20 =: (2) = are solutions of the differential equation x'y"-by = 0, so…

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Q: 1. Consider the following scenario: Janet, Gail, Susan, and Lisa all walked away from the bus…

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Q: Find the centroid of the region bounded by y? = 16x and y? = 32(x – 8). - NOTE: Enter the exact…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Which of the followings is TRUE for f(x, y) = 3x – y + 6 on the circle a? + y? = 4. Lütfen birini…

A: Given function is fx,y=3x−y+6 and a circle is x2+y2=4. We have to find the maximum and minimum of…

Q: Construct a frequency distribution table with seven classes for the scores below. Determine the…

A: frequency distribution of the given data class interval Tally marks frequency cumulative…

Q: 2. f(t) = v1+ sin t + (7t)14 + t² sin 2t

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Q: Using determinants, find area of each: A. (1,4) (10,2) (8,12) B. (1,-9)(6,-3)(-3,1)(-5,-6) C.…

A: The given problem is related with area of quadrilateral. We have to find the area of the following…

Q: Solve the given ODE using Laplace Transform x"(t) – 4x'(t) + 4x(t) = 4e2t; x(0) = –1,x'(0) = –4 %3D

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Q: 3s² +5s+5 F(s) = (s3+8s²+19s+12)(s³)

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Q: Evaluate the following integral using three different orders of integration. SSS:(r: - y') dV ,…

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Q: Find the line of intersection of the planes z + 2y – z = 1 and z + y + z = 1. Lütfen birini seçin:…

A: Given equation of plane is x+2y−z=1 and x+y+z=1. We have to find the line intersecting of the plane…

Q: f (t) = tcos3 3t dt 0, e-4t

A: Given: f(t)=∫0∞tcos33te-4tdt To find: Value of integral using Laplace transform.

Q: Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. If…

A: We have to find the circulation for the given field using greens theorem where  F(x,y)= (x2+y2)i…

Q: f (t) = v1+ sin t + (8t)15 + t² cos 3t

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Q: Calculate the flow in the field F along the path C. Flow means line integral F = (x - y) i - (x 2 +…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + t²j 0.

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Q: Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. y =…

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Q: [x 1+t 5. Determine the distance between the point (4, 3, 2) and the plane y 2+s z = 3+5+t a. 3.69…

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Q: Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no…

A: Given,    x - 2y = 2  7x - 14y = 14  4x - 8y = 8

Q: 5.2.7 Show that Ae³A™ = eABA' for any orthogonal matrix A.

A: To show: AeBAT=eABAT for any orthogonal matrix A.

Q: The complex number z is defined by z = 3·z + 4.j where z is real. a) Find, in terms of z, the real…

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 351 2

A: Solution :-

Q: B: The temperature at any point in circular metal plate centered at the origin is, T(x, y) = 100…

A: We are given the temperature function T(x,y)=100e-x2+y2we have to find the direction of greatest…

Q: Limit Comparison Test (a). Suppose that E ak and Ebk are series with positive terms. If ak lim = c,…

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Q: d) Prove that the composition of two surjective linear transformations is again a surjective linear…

A: (d) Let T:X→Y be a surjective linear transformation and S:Y→Z also be the surjective linear…

Q: 2. f(t) = V1+ sint + (7t)4 + sin 2t %3D

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. = 13, x, = (1, 2,…

A: Note: Let A be a square matrix and x be an eigen value of A. A non-zero vector V is said to the…

Q: Find the Laplace transform of the following: 2. f(t) = v1+ sin t + (5t)18 + t² cos 2t

A: Here given function as ft=1+sin t+5t18+t2cos 2torft=sin2t2+cos2t2+2sin t2cost2+5t18+t2cos…

Q: During a sneeze, the radius of windpipe decreases. Suppose that the normal radius of the windpipe is…

A: Here we need to find maximum value of V(r) For absolute maximum or minimum  i) verify that the…

Q: Find the work done by F over the curve in the direction of increasing t. F = -8x i + 9x 3y 4 j +…

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Q: The integral TT tan x sec2x dx O none of them is an impróper integral of type I that diverges is an…

A: Solution

Q: Find all the arymptotes of the cubic polynomial ー24y.C2nーツ)+yメーソ)o: aned show thaf Cut the cunne in…

A: Given function is x3-2y3+xy(2x-y)+y(x-y)+1=0 There is no asymptotes parallel to x-axis and y-axis…

Q: Find the Laplace transform of the following: 1. f(t) = e-2t+5) sin³(8t) 3

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Q: Exercise 4.13 –(1) Convexity. Show that the following function is concave: f (x) = 1 – (||Ax+b|l, +…

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: -3)K

A: Here we use vector differentiation

Q: d²y dy + 2b +y = 0 dx dx2

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Q: Consider the box shown below, where 0 <¤< 2,0< y< 1, and 0< z<1. The rectangular prism is subjected…

A: Given E=-2x2yi^-2xy2j^+2xy2zk^ where 0≤x≤2, 0≤y≤1, 0≤z≤1

Q: 16. A playing field measures 120 m by 240 m. Karen wants to mow two-thirds of the field by mowing…

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Q: Find the area of the region outside the cardioid r = 4 – 4 cos 0 and inside the circle r = 12. NOTE:…

A: Area bounded by the region in Polar curves

Q: 3. Write down the name of the conic given by the polar curve r = 6/ (2 - sine). Determine the…

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