Let C be the ellipse given by ² + y² = 1. () Find a polar equation for C. () Find a parametrization for C. ( ) Write down (do not evaluate) a definite integral that gives the perimeter of the ellipse C.

Q: Determine the general/particular solution (whichever applies): y''+ 4y'+ 4y = (3+x)e-2x, when x = 0,…

A: y''+4y'+4y=3+xe-2x

Q: If x² +2y+3z? = x² + 2y² + 3z² = x² + 2y3 +3z3 =2, and x₂x3 +2y₂y3 +3z₂z3 = x3X₁ + 2y3V₁ +3Z3Z1 =…

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Q: Using the fact that A/B = An Be, show that in a metric space, bdy(A) = bdy (Aº)

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Q: 2X1 + 2X2 + X3 >= 1000   2X1 + 2X2 + X3 + X4 = 0   How is draw this graphic?

A: To draw the graphic for this system of linear inequalities, you can follow these steps.Here is a…

Q: Des there exist a geometric progression containing it exists, how many such progressions are possi e…

A: Part A

Q: Let S be a linear transformation from R³ to R² with associated matrix A = - 2 0 -1 2 2 1 2 Let T be…

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Q: Sketch the graph of the following function. Identify the domain and range. f(x)=√x - 2 Domain:…

A: We have to solve given Questions.

Q: If D is the triangle with vertices (0,0), (99,0), (99,21), then 11 D dA=

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Q: The set of polynomials {3t²-3t+5, mt+6t²+10} is a linearly dependent set in P, if 2 m=6 Select one:…

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Q: Which of the following is the even periodic extension of the function f(x)=3x⁹-x²+x³-4, 0<x<L with…

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Q: Obtain the general solution. (EXACT EQUATIONS) 2. y²dx = (xy - x²)dy

A: Given ode is y2dx =(xy-x2 )dy we have to calculate the general solution of the given ode '

Q: So So √√₁-x² √1-x²-y²³ (1 + x² + y²) dzdydx 0

A: The given problem is to evaluate the given triple integral over the given limits of integration.

Q: Find the matrix A of the quadratic form associated with the equation. 6x² - 4xy + 6y² + 16z² - 23 =…

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Q: Let S = {−9t²+2t −7, mt-45t²-35} be a set of 2 polynomials in P, 2° Choose m such that the set S is…

A: The given set S=-9t2+2t-7, mt-45t2-35 of P2. We have to find the value of m such that S is linearly…

Q: A line is measured in sections as follows: AB = 416.24 ± 0.06, BC = 1044.16 ±0.08, and CD = 590.03 ±…

A: A line is measured in sections as follows: AB = 416.24 ± 0.06, BC = 1044.16 ±0.08, and CD = 590.03 ±…

Q: 4. Find the slope of f(x) = hundredth. -3x-1 at (2,-1.65). Use a graphing utility and round to the…

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Q: 2. If an+2 = 6an+1 - 8an + 3 and a0 = 3, a1 = 7, then a6 =

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Q: Prove the following via Mathematical Induction. Show your solutions. Prove 1 + 5 + 9 + … + (4n…

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Q: Solve the following DE: [3sin (y) — 5x ]dx + 2x²cot(y) dy=0 Ox²[sin (y) - 2x]³=C'sin³(y) Oy³[sin(y)…

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Q: Given A = 03-2 00 1 compute et.

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Q: For each of the following, find the form of A and S such that A = SAS 4 -1 -2 3

A: According to the guideline only one question can be answered. Please repost other questions…

Q: If a₁, 92, 93, determinant: ... are in A.P., then find the value of the following ap+ap+m+ap+2m…

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Q: Which example in this section of the textbook shows that estimating limits numerically may not…

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Q: Use cylindrical coordinates to evaluate SG √x²++y² dV, where G is the solid above z = 9 - x² - y²…

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Q: Using mathematical induction, show your solutions to prove that  1 + 5 + 9 + ... + (4n-3) = 2n^2 -…

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Q: Let S₂ be the portion of the paraboloid z = 9-4x² - 4y² on the first octant above the plane z = 1.…

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Q: 7. Find a fundamental matrix for the system *' (t) = A - *(t) for Го a. A = 0 L8 1 0 -14 01 1 7

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Q: √4-x² 1²₂ S +*² S-14-x²-y² x dzdxdy

A: As per the question we are given a triple integral and we will evaluate it by changing it from…

Q: Find the area common to the circles x² + y2 = 4 and x² + y2 = 4x. Answer: 8π/3- 2√3 sq. units

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Q: Evaluate the integral of ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the…

A: The given problem is to evaluate the given path integral of the given scalar function over the given…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Problem 8 Determine the linearization of f(x)=√1 + 3x at a=0.…

A: The Linearization of a function y=f(x) at point x=a is given by…

Q: A berry box, sold to contain a quart of berries is in the form of a frustum of a right pyramid 15…

A: Area of the top of the frustum is 15 in2 Area of the bottom of the frustum is 12.5 in2 The height of…

Q: 9. A biologist has been studying the effects of environmental stressors on a population of frogs.…

A: Let at nth year the population be Pn, then % decrease in nth year is given by                 {(Pn-1…

Q: If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) 1 a +1 b f(b) (x-b) f(c)…

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Q: -). The vectors U = (c²/3, b, 3), V=(√c, 2, 1) are parallel. Find the norm of the vector U.

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Q: A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what…

A: Given, In a raffle, winner will get $200.    We have to find the fair price for a ticket if 1000…

Q: At least one of the series Σn=1_34 and Σn=1 3n³+n converges. 2n4 Select one: O True

A: We show both the series diverges using relevant tests. We recall the test and then give the…

Q: 15. Kitchen's Contracting determines that the marginal cost, in dollars per square foot, of…

A: The given marginal cost: C'(x)=4x13The cost is given by:C(x)=∫C'(x)dx        =∫4x13dx…

Q: Use the second Taylor polynomial for f(x) = cos (x) at x = 3л to estimate cos (1 + 3л). Round your…

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Q: x³ + y³, y³ + z nt) Calculate the flux of the given vector field F = e S where S is the sphere…

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Q: Given the two vectors -9 -5, and = V2 -3 -20 -5 -11 Choose a vector v so that the set {V₁, V2²…

A: The given vectors in ℝ3 are  v1=-9-5-3, and v2=-25-5. We have to find the vector v in ℝ3 such that…

Q: WORK PROBLEMS (6 Question 1 a) i b) c) s): You must provide a clear and detailed solution for each…

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Q: Q2. Obtain the Fourier series for the function given in the diagram below f(x) 2 20 0 2T 3T X -2

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Q: 21.5 Integrate the following function both analytically and using Simpson's rules, with n = 4 and 5.…

A: Given: ∫-354x-33dx We have to evaluate the integral analytically as well as by using Simpson's rule…

Q: Let D be an ellipse rotated counterclockwise radius was 6 and vertical radius was 5. 76-54-3-2…

A: Given: The Horizontal radius of an ellipse=6            The vertical radius of an ellipse=5…

Q: Forever 21 is expected to pay an annual dividend of $2.31 per share in one year, which is then…

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Q: (1 point) Let [] Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of…

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Q: Jse Lagrange multipliers to determine all points on the graph of 3x2 + 2y² -z = 0 nearest the point…

A: To Find: All points on the graph of 3x2+2y2-z=0 that are nearest to (0,0,2) using Lagrange…

Q: To find a particular solution for the differential equation 3y"-24 y' +36 y=e10x with the variation…

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Q: Find the Fourier series of the following function, from the series estimate the value of x= 0175…

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