Find the unit to the - tangent r = (a cos t, a sin t. h t) − ∞ < t <∞ at any point. Also find the length of one circular helix. where a > 0 and equation of tangent complete turn of helix.

Q: Describe all numbers n EN that satisfy oo(n) = 3. Justify your answer.

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Q: Use the procedures developed in this chapter to find the general solution of the differential…

A: Given a differential equation, y'''-7y''+10y'=3+4sinx. To find the general solution of given…

Q: Graph the appropriate function(s) in each problem, and use the graphing calculator and its features…

A: Given: The cost function is C(x) =0.1x2+35x+15,000 and the Revenue function is R(x) =-0.9x2+385x. To…

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Q: Use the Laplace transform to solve the following ODES: (a) + 3x + 2x = 0 (b) + 2x + 2x = 0 Solve…

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Q: Use the divergence theorem to calculate ff, FdS where F = x²yi - xy² j - xyz k. S is the surface of…

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Q: 9-11. The number of bacteria present in a certain dish after thours is given by B(t)=1000e0.4t 9.…

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Q: Complete the following statements. In general, % of the values in a data set lie at or below the…

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Q: If water is drained from a vertical cylindrical tank by opening a valve at the base, the water will…

A: For a differential equation of the form: y'=f(x, y), Euler's method uses the formula:…

Q: 9. Let T be an operator on an n-dimensional vector space V over a field F. (a) If T has n distinct…

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Q: Let f(t) be a function on [0, ∞o). The Laplace transform of f is the function F defined by the…

A: Solution :-          The given function is                              f(t) = te-2t then , we have…

Q: Given that 1 1 − x =  ∞     n = 0xn, use term-by-term differentiation or integration to find a power…

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Q: Show from the eigenvalues that if A is positive definite, so is A² and so is A-1

A: We have to show from the eigenvalues that if A is positive definite, so is A2 and so is A-1 . We…

Q: Let the matrix of linear transformation L: L: R² →R¹ be defined -{[1] et S= ].[]}be ordered basis…

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Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

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Q: 3. Let X denote the set of all finite subsets of N, including Ø. Define a relation on S₂ if S₁ and…

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Q: Problem 1. Let f(a, y, z) = ln(² 1 y² | 2²). a) What is the direction of maximal increase of f at…

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Q: Prove that 21′(2:) _r′(z)_T'(=+!) r (2) T(²) T (²+1) and thus derive Legendre's duplication formula.…

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Q: You can afford $1,000 per month as a house payment. If you can get a home loan at 5.2% interest for…

A: Given that The monthly payment PMT=$1000Interest rate  r=5.2%=5.2100=0.052Compounded monthly…

Q: QUESTION 2 Find the quotient (x² + 9x + 20) + (x+5) ✓ Write the division as a long division problem.…

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Q: Compute, by hand, the Fourier series representation for the following square wave defined on a €…

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Q: For the following function, find dA in terms of y 7m ○ dA= (10x) dy dA = (10-√√) dy ○ dA = (2y¹) dy…

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Q: The temperature of an exotic liquid in a pipe of length L = 2 can be described by the 1D…

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Q: 1,344,000 ft3 24,000 ft² (Include units in the answer) omm

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Q: Solve the initial value problem below using the method of Laplace transforms. y" - 16y=80t-24e-4,…

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Q: Use​ Newton's method to approximate all the intersection points of the following pair of curves.…

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Q: Find the 3x3 matrix that induces the described action on R3. Rotates the xy plane by 30 degrees,…

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Q: Evaluate the line integral F. dr by evaluating the surface integral in Stokes' Theorem with an…

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Q: Find the average rate of change for the function. f(x)= 1 X-3 between x = -4 and x = 2

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Q: The function e does not have an elementary antiderivative. However, you can find a series…

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Q: 3. by (a) Define a transformation for all A in Mnn. (c) (d) P: Mnn Mnn P(A) = A - AT Identify…

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Q: Suppose that a population develops according to the logistic equation dP dt = 0.02P-0.0002P², where…

A: We will use partial decomposition to solve the differential equation

Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: Problem 3. The quadratic f(x₁,x2) = 3(x₁ +2x₂)² + 4x3 is positive. Find its matrix A, factor it into…

A: Given: fx1, x2=3x1+2x22+4x22 To find: Matrix A.           : Factor A into LDLT. Discuss: Entries of…

Q: Prove whether or not the surface xy - zlogy +eª² zlogy + ez - 1 = 0 can be represented by a function…

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Q: Find the length of the curve 1.2 6² from the point (a, 0, 0) to the point (x, y, z). 1, x = a cos h…

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Q: Derive the 2D Laplacian operator in polar coordinates, using the following relationship between x,…

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Q: Find the value of X₁, X2 and X3 usin Method Gauss-Seidel and Gauss-Jacobi Provide the complete table…

A: Given: x1+2x2-x3=6x1-x2+2x3=-32x1-x2+x3=-1 To find: The values of x1, x2, x3 using Gauss-Seidel and…

Q: -19 -13] Let A = 26 20 Find a matrix P, a diagonal matrix D and P-1 such that A = PDP-¹. P: D || ||…

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Q: 2 Obtain a power series solution of the equation (1 + x²)y” − 3xy' – 5y = 0 - - up to and including…

A: Sol:- 1+x2y'' -3xy' -5y=0A linear homogeneous ODE with constant coefficients has the form of pxy''…

Q: Use Romberg integration to approximate f sin (22) dr up to O(h). As part of your -1 wer, include the…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: 2. Find the inverse Laplace transforms of the following functions. 1 (a) F(s) = (b) F(s) = (c) F(s)…

A: 2. We have to find the inverse Laplace transforms of the following functions:  (a) F(s)=1s3 (b)…

Q: Use the shell method to write and evaluate the de y = 8 - x -1 6- YA 2- x 4

A: We have to find the volume of given region.

Q: This exercise is adapted from a problem from the textbook. Consider the line integral [(x - y) dx +…

A: Given That : Integral ∫Cx-ydx+x+ydy , Where C is the around the triangle with vertices (0,0) , (1…

Q: 5. -X For the function, f(x) = {* a. b. -2<x<0 0<x<2 Graph f(x) for x from (-2,2) Graph the periodic…

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Q: 1. 2y + 184 y". = 6 tan 3x

A: The given problem is to find the general solution for the given differential equation.…

Q: Approximate the root of the equation √√x + x² = 7 using the initial value xo = 7 and using the 4th…

A: To approximate the root of the given equation x+x2=7 with initial value x0=7 using the (1) Newton's…

Q: Using the graph of f (x) shown below, match the functions (i)-(v) with a graph (a)-(e). (i) y =…

A: There are many types of transformations that can be performed in a graph. Some of them are vertical…

Q: n is convergent. Be sure to check n² 2 Use the integral test to determine if n=2 that the conditions…

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