7(20) Prove the Fundamental Theorem of Algebra: Every polynomial of degree k≥1 has precisely k roots counting multiplicity.

Q: 3. Solve the following equation algebraically. Explain your process. [A6], [C3] 0=18x4+87x3+3x²-108x…

A: First, we need to solve the equation 0 = 18x^4 + 87x^3 + 3x^2 - 108x. This is a polynomial equation…

Q: (1) A pulling force 7=32 lb is applied to the cord, which is wound securely around the inner hub of…

A: Step 1: Step 2: Step 3:

Q: Prove: f(x) = 1+x² is Lipschitz continuous in R.

A: Step 1: Step 2: Step 3: Step 4:

Q: What is the inverse Laplace Transform of this function if one term is 1/s and the other is 1/s+a?

A: The inverse Laplace transform of F(s) is f(t) = 3 + 4e^-2t - 7e^-5t

Q: Suppose lim f(x) = L, where L = R and lim g(x) = +∞. 8+←8 1. Prove: if L > 0, then lim f(x)g(x) 8+←…

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Q: Please solve this question it has sub parts to it. Appreciate your time. Also consider what the…

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Q: Q1/ What is the relationship between Laplace transform 00 L[u(t)] = F(s) = e-stu(t)dt 0. and the…

A: Q1: Relationship Between Laplace Transform and the Given TransformAnalysis: The given transform,…

Q: Solve the IVP: dy dx = -12x + 3y where y(1) = 10 -3x+2y Solve your solution equation explicitly for…

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A: (a) Identify which of the points in the table are critical points.A critical point occurs when the…

Q: Given the letters A, B, C, D, E, F, G, H, I, J: (a) How many length-5 lists can be made from these…

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A: 11. If y = 3x, then x = log⁡3 y:This is true because the logarithmic form x = log⁡3y is equivalent…

Q: 6. Evaluate Jezdz, where C is the circle |z = 4 taken with counter-clockwise (i.e. anti- clockwise)…

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Q: 3. Let's explore the role of the resistance R in an LCR circuit by setting R 0 in (1.6.1) and then…

A: Step 1Setting ( R = 0 ) in the differential equation changes it to:  Q′′+LC1​Q=LV0​​The homogeneous…

Q: Write by hand on a piece of paper.

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the Fourier Series of f over the specified interval. f(x) = cos3(x) on −π ≤ x ≤ π (HINT: There…

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Q: Find the value of a so that the work done by the force ♬ = (y² + 1)² + (z+y) in moving from (0,0) to…

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Q: ②Find the solution of the BUP: x²4"-24+x=0 4(2)=0, 4(3) = 0 + 2<x<3 -using the shooting method- use…

A: import numpy as npfrom scipy.optimize import root_scalardef f(x, y1, y2):   return y2def g(x, y1,…

Q: Don't use chat gpt It

A: Step 1:Step 2: Step 3: Step 4:

Q: 2. Given the periodic square function shown as x(t) -6 2 (a) Declare the function as a Scilab…

A: a)// Define the square wave function x(t) function y = square_wave(t) y = 0 * t; // Initialize…

Q: 22.5 Problem. Repeat the work above for the transport IVP U₁ + Ux = 0, −∞ <x, t< ∞ Ut u(x, 0) =…

A: 1. Apply the Fourier transform to u in x:Let û(k,t) be the Fourier transform of u(x,t) with respect…

Q: For the differential equation y"-4y+20y=-180x² + 232z-170-186e + 136ze* Find the solution of the…

A: Complementary Solution :​​    Particular Solution :​​

Q: Calculate the mean of the following values:  125.474 125.468 125.481 125.476 125.472 125.473 125.483…

A: Step 1:Given data set :…

Q: In the system shown, m = 4 kg, 0 = 40°, µ¸ = 0.5 and µk = 0.3 and the wheels are frictionless. (a)…

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Q: Consider the matrices A = 4 - 2 -2 8 and B = B 1 2 <-2 4 Check the correct answer. O Both A and B…

A: To solve this problem, we need to check whether the given matrices A and B are diagonalizable. A…

Q: Evaluate √c 42²+42-3dz = Sc (2z-1)(2z+3)dz for the following contours: (a) The circle || = 1 with…

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Q: L[u(t)] = F(s) = Q1/ What is the relationship between Laplace transform u(t)dt -st e and the…

A: The transforms you have mentioned are related in their structural form but differ in the details of…

Q: Please write it out and explain thank you :D

A: ;Correction: The unit of maximum velocity is cm/s.

Q: Find the general solution of this ODE: fy dy +4 dt2 +13y = 12e 5t dt om The solution will be of the…

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Q: Pls help ASAP, and pls show all work and steps and circle the final answer.

A: Step 1: To find the minimum value of 3cos2x - 8.We know that the value of the cosine function lies…

Q: (7) Determine the required horizontal force P that the worker must exert on the rope to position the…

A: Mass of crate, m = 50 kg. Thus, weight, W = mg = 50 × 9.81 = 490.5 N. g -acceleration due to gravity…

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Q: (a) Use the Laplace transform to solve the initial value problem. Here you must use unit step…

A: (a) Solving the initial value problem using the Laplace transform: 1. The Laplace transform of the…

Q: The Inverse Laplace Transform of the function F(s) = (1/s^3) * e^(-s) is * O (1/6) (t-1)^3 * u(t-1)…

A: let's apply these steps to our function F(s)=s31​e−sFirst, the inverse Laplace transform of s31​​…

Q: 2. (a) Using contours, sketch by hand (not by computer or IT tools) the scalar field f(r) x + y² in…

A: (a) Sketching the scalar field.The scalar function is given by,f(r​)=x+y2Represents a family of…

Q: @ Find the nth term of the series. 1 + 4 × ² + 1 8 X² + 3/16 x + 11 960 X+ prove that the Series 4 -…

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Q: E R w switch L In the circuit shown in the figure above a generator supplies a voltage of E(t) = 50…

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Q: Geography Lesson Lesson 39 Assignment Player Write the word sentence as × | The quotient of a number…

A: The word sentence 'The quotient of a number g and -4 is at most 5' can be translated into the…

Q: Pls help ASAP. pls show all work and steps. Pls circle the final answer

A: If you have any problem let me know in comment box thank you.

Q: Note for the student: For the SVD, eigenvalue decompositions, and matrix approximations, you may use…

A: Step 1: Step 2: Step 3: Step 4:

Q: Q.1) (a) Given y = f(x) = (x²+6) for a > 0, determine the inverse function f-1(x). (b) Evaluate the…

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Q: Ex 49: Show that if u is a subspace of V then u= Span (W)

A: Step 1    Step 2

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Q: Pls help ASAP, pls show all work and steps. Pls circle the final answer.

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Q: Linear Algebra Show calculations

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Q: Pls help ASAP, and show all work and steps and please circle the final answer.

A: Given Function:The original function is y=log⁡2(x), which represents the logarithm base 2 of x. Step…

Q: explain and give example of CAUCHY-RIEMANS EQUATION

A: Step 1:Cauchy-Riemann equations: The Cauchy-Riemann equations are a set of two partial differential…

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Q: Earthworks

A: To compute the area of the shape in the diagram, the figure looks like a trapezoid based on the two…

Q: what is this

A: Step 1: I suppose you want to find the missing number.  Step 2: Here the RHS is  85​ Step 3: The…