Find y as a function of a if y(0) = 12, y(0) = 21, y"(0) = 18. y(x) = y" 16y" +63y = 144e²,

Q: Consider the differential equation = 2xy². Let f(x) be the particular solution with ƒ (1) = 2. a)…

A: As per the question we are given a first order differential equation : dy/dx = 2xy2 And y = f(x) is…

Q: Find the solution of the given initial value problem. 5y""+120y' 800y = 0; y(0) = 11, y'(0) = 26,…

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Q: Find the average value of f(x, y) over the region R. f(x, y) = x² + y² R: square with vertices (0,…

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Q: A bridge is to be constructed to pass over a road, and a surveyor is sent to take some measurements…

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Q: Prove the following statements (a) Vn € N, (2i − 1)² = by mathematical induction: n(2n + 1)(2n − 1)…

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Q: found z already what is w?

A: Definition: A set x1, x2, …, xn of a vector space is linearly independent if there are scalars α1,…

Q: Given surface A₁: x = 2√y + 1 and sphere A₂: x² + y² + z² − 16x + 6y − 4z + 76 = 0 1. Sketch surface…

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Q: a) find the domain and range of the function в Сху) =5 4-x2_ye 4-х

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Q: Find a unit normal vector to the surface x² + 3y +z³ = 147 at the point (5, − 1, 5). O O O 1 √2,636…

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Q: Name the function of the graph below: -T/5 -4- 3- 2 0 --1- --2- --3- -4 f(t) = 3 cos (5πt) f(t) = 5…

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Q: Use a Laurent series to find the indicated residue. f(z) e-z (z-4)² -; Res (f(z), 4)

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Q: 7. The multiplier and the MPC Consider two closed economies that are identical except for their…

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Q: To find the volume of the solid obtained by rotating the region enclosed by the curves y=x²-36 x and…

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Q: (a) y" +9y = 0; y′(0) = 0, y(π/2) = 6 (b) y" +9y=0; y(0) = 0, y(t) = 6 (c) y" +9y = 0; y(0) = 0, y'…

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Q: The matrix below shows when communication exists between people in the group Alex, Beth, Chen and…

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Q: the initial-value problem. y = y = C₁ + C₂ cos(x) + C3 sin(x), (-00, 0); y""+y' = 0, y(n) = 0, y(t)…

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Q: 6. Evaluate the following real integrals by residue theorem 3 211 1 = √² do Cos 0 + 2 sing +3 ans o…

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Q: The symmetric matrix A below has eigenvalues −2 and 1 (multiplicity 2). Find an orthonormal basis B…

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Q: -11-10-9-8 17 -6 -2 4 17 16+ b2t 15 13 11 10- 9 8 6 4 3- 2 b + -2 -3 -4 -6- -7- -10- -13- +-16+ Find…

A: Sol:- As we know the graph of f(x) = tan(x) is similar to above :-

Q: (2) Find the Hessian matrix Hf(x) of the given function and evaluate it at the indicated point. ㅠㅠ…

A: find the hessian matrix and evaluate at the point (a) fx,y=cosx siny , a=π4,π3

Q: 1. -2y (-e) dx + e dy = 0 + ex

A: Equation is homogeneous so substitute y=vx and get a variable separable equation.

Q: Find a basis for the orthognonal complement of U = span 1 -2 1 - 1 -2 1 Number of Vectors: 1 Basis…

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Q: -6 -5 -4 -3 -3 -2 8 HAP 7 6. 5 4 327 -1 -2 -7 1 2 ton 3 4 5 Find an equation for the graph above.…

A: Given is a graph To Find: an equation for the given graph

Q: For each of the following sets of vectors, determine whether it is linearly independent or linearly…

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Q: Determine wo, R, and 8 so as to write the given expression in the form u = Rcos(@ot 8). - u =…

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Q: - The set B = {x² – 2, 4x² − (8 + 3x), 15x² − (28 + 9x)} is a basis for P2. Find the coordinates of…

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Q: Set up a triple integral for the volume of the solid. Do not evaluate the integral. The solid…

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Q: swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at is deepest…

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Q: g(t) = f(2t) d dt

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Q: Use (18) in Section 6.4. x²y" + xy' - (x²x² + ²y = 0 (18) Find the general solution of the given…

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Q: 1. Compute the determinant of the matrix. Show all your work including which row operations and…

A: 1 Given matrix is 811280−72−1−3−7211124. We have to compute the determinant of the matrix. Let…

Q: Question If   X = 2.02 (rounded to 2 decimal places) and Y = 7.482 (rounded to 3 decimal places)…

A: Given that X=2.02 (rounded to 2 decimal places) and Y=7.482 (rounded to 3 decimal places) a We have…

Q: 5. The sum of thrice a number and two equals 6 less than four times the number. Find the number.

A: We have to find a number that satisfy the following condition:     The sum of thrice a number and 2…

Q: Evaluate the integral. 4 1 -t²dt 8 1 Remember that evaluating a definite integral is analogous to…

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Q: 2. Suppose a, b, c, d are integers and that (a, b) = (c,d) = 1. If (g) + (á) show that b = ±d. is an…

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Q: Question In each case determine if x lies in U = span{y, z}. If x is in U, write it as a linear…

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Q: Determine the half-range sine series expansion of the following: f(t) = t² + t, A. B. C. D. y = 4 4…

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Q: Use Res(f(z). Zo) = lim (z-zo)f(z). Res (f(z). Zo) = f(z) = z = = (n = 1)! dz-1 to find the residue…

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Q: If a 20-meter flagpole casts a shadow that is 40 meters long, how long is the shadow cast by a tree…

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Q: Use the method of reduction of order to find a second solution of the differential equation t²y" +…

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Q: Use spherical coordinates to find the mass of the sphere x² + y² + z² = a² with the given density.…

A: We have to using spherical coordinates to find the mass of the sphere x2 + y2 + z2 = a2 with the…

Q: (a) Find the general solution in terms of real functions. (b) From the roots of the characteristic…

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Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

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Q: z = x + y + 1 surface, xy plane, x-axis, y = x plane, x = 1 Draw the graph of the region bounded by…

A: It is asked to sketch the graph of the region formed by z=x+y+1, x-y plane, x-axis, y=x and line x=1…

Q: 8. The order of differentiation in multiple integration of continuous integrand A. has six…

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y" - y'= et cos(t),…

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Q: a) Consider the wave equation π² Un with = UII, -∞<<∞, t≥0 u(z, 0) =sin 7 cOST, u(2,0)=0. Find the…

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Q: 1.8 tbs. = 2.350°F = 3. 12 ounces = quarte cup °C 9 gallon

A: # As per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: 10 *S $0 Pain (8) cze (8) & a

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