Find the general solution to the non-homogeneous differential equation. y" + 4y' - 5y = 15x² + 7ex y(x) =

Q: Solve the system of equations. 4x-7y+z=16 x+y=5 Select the correct choice below and, if necessary,…

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Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: xy-3y=-24×70 ×(1)=1,y(1):4,ゾ(1)=-52; 1/10=4x221,×,×53 y(x)=

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Q: 4. If xo E E, xo is not an accumulation point of E, and f: E→ R, prove that, for every sequence…

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Q: Let fa(z) = 29 0 if x 20, if x < 0. (a) For which values of a is f continuous at zero? (b) For which…

A: Given: Here is the given function, fa(x) = xa if x &gt;00 if x≤0 To determine: The values of a is f…

Q: Let X = {a, e, h, l, r, t, w}, Y = {1, 2, 5, 7, 17, 18, 21, 27, 30}, and ƒ : X → Y with ƒ = {(a,…

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Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

Q: we now wish to show that an infinite complete orthonormal set is never a basis in a Hilbert space.…

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Q: actice15: Problem 8 nt) X = {−3,−2, 4, 5, 6, 7, 18}. Let f: XZ by f(x) = 10x + 5. range of the…

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Q: Example (continued): -1 1 1 If P = 0 0 1 1 2 0 then D = 1 -1 1 If P = 0 0 1 1 0 Incorrect answer.…

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Q: 3.

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Q: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: Calculate the median of the following data: X f 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 3 7 12 16 22 20…

A: As per the guidelines I have solved first problem.

Q: Given the following bases for P2, find P, the change of coordinates matrix from B to C. C-B B =…

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Q: a) Differentiate the function below with respect to x. 3+7x –3–52 f(x) = 33

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Q: Find the volume of the solid which lies below the surface f(x,y) = 5x² and above the planar region…

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Q: This is an example of an Undamped Forced Oscillation where the phenomenon of Beats Occurs. Find the…

A: We have to find the solution of the initial value problem x" + 14.44x = 3cos(4t) with initial…

Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: 6. Given F= 28 at (1, 0, 0) in Cylindrical coordinate represent vector in Cartesian coordinates,…

A: Vector field F=2ρ⏞ Cylindrical coordinates to cartesian coordinates ρ2=x2+y2 2ρ^=2x^+2y^ at point…

Q: f α and p are constructible, then a ± p, ap and a/p when ß # 0, are also constructible.

A: (i) Since ? and ? are constructible so that (?,?) is constructible. The circle (x-?)2 +y2 =?2 is…

Q: Find the absolute maximum and minimum of the function f(x) = x³ +1.5x² - 6x + 3.5 on the interval…

A: The given function is f(x)=x3+1.5x2-6x+3.5 The objective of finding the absolute maximum and minimum…

Q: Find the point of the way from (1, 3, 2) to (-9, -8, 10). 0 P=0 0

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Q: Evaluate the integral [[F.n dA for the data F= [y³, a³, 2³], S S: x² + 4y² = 4, x ≥ 0, y ≥ 0,0 ≤ z ≤…

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Q: If T: R² → R³ is a linear transformation such that then the standard matrix of Tis A = T([1]) T([^])…

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Q: Set up the system for the linear least squares approximation for the data (-2,0), (2,3) and (3,1)

A: Given: Data points are -2 ,0 ,2 ,3 ,3,1. To Find: Set up a system for linear least square…

Q: In Exercises 21-26, evaluate det(A) by a cofactor expansion along a row or column of your choice.…

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Q: 3. Use logarithmic differentiation to compute the derivative of x²(x − 3) arctan (2x) √1+x² f(x): No…

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Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: 9.) Find the function whose 2nd derivative is given by f"(x) = 1 - 4x where f'(-1) = 1, and f(-1) =…

A: Given that, f''(x)=1-4x ........equation-(1)now integrating both sides of equation-(1) we…

Q: For a certain loan, the interest I due at the end of a loan period is given by  I = Prt,  where P…

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Q: Let L : R 2 → R 2 be the linear map given by L(x1, x2) = (x1, 2x1 − x2). Write down the matrix AL of…

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Q: 3. dy R dt = y 1+t +1²

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Q: Yes No No Yes No Which of the following matrices are orthogonal? -1 0 01 0 0 0 1. 0 1 2. 3. 4. 1 21…

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Q: '/][** f(x, y, z) = Z, E = {(x, y, z) | x² + y² ≤ 25, x ≥ 0, y ≥ 0,0 ≤ z ≤ 1} Evaluate the triple…

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Q: B: Find Inverse Laplace Transformer for the following function:- 3s³-s²-3s + 2 3 S² (S-1)² F(s) =

A: I have explained everything with in the solution. Please go through that.

Q: 3. Show that there exist 100 consecutive positive integers that are not perfect squares.

A: Here we have to show that there exists 100 consecutive positive integer that are not perfect square.…

Q: Let S be the parallelogram determined by the vectors b - - - - - and 2 = ( ² ) - - - - and let A 11…

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Q: B: Represent the area of the regions A, as a double integral in polar from, then evaluate it. A₁…

A: The give figure is: We have to express area of the region A1 as double integrals in polar form and…

Q: Consider the Secant Method applied to minimising f(x) = x² + x³ in |x| < 1. We know the minimiser is…

A: Introduction: The Secant Method is a numerical root-finding algorithm that is used to find the roots…

Q: 20. Let ƒ(x, y) := (x² + y²) sin(√√² (x, y) = (0,0) with f(0,0) = 0. Show that f is differentiable…

A: The given function is fx,y=x2+y2sin1x2+y2for x,y≠0,00for x,y≠0,0. with f0,0=0 . To show the function…

Q: Evaluate the triple integral fff(x² + y² + z²), dV, where E is the region inside the cylinder x² +…

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Q: Show that if {fn} converges uniformly on {fn} converges uniformly on [a, b]. (a,b) and {fn(a)},…

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Q: This is the wrong answer. Please give me the correct answer.

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Q: Estimate the volume of the solid that lies below the surface z = xy and above the following…

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Q: or items 13-14, Let the mapping F: N→A be defined as F (z) = ¹ (13) Evaluate 100-F (5) - 20. (14) Is…

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Q: How can numerical methods find solutions to systems of equations? Provide your own explanation of…

A: From intermediate value theorem we know a function fx is real valued and continuous  in a closed…

Q: dy dx dy dx + + 318 2y X = y = sin(x) 1 x² " given that y = 2 when x = 1 dy dx + 2y tan(x) = sin(x),…

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Q: Find the extreme values of f(x,y,z) = xyz +5 on the intersection of the plane z=1 with the sphere x²…

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Q: For each of the graphs below, use the level curves of the function z = f(x, y) to decide the sign…

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