6) The variables x and y satisfy the differential equation X = y(1-2x²), dx and it is given that y = 2 when x = 1. Solve the differential equation and obtain an expression for y in terms of x.

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A: This is a problem related to integration. Based on the general formula we will answer the question.

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A: Solved below

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A: answer is in next step

Q: For items 1-5 A 10-ft ladder is leaning against a house on flat ground. The house is to the left of…

A: A 10‐ft ladder is leaning against a house on flat ground. The house is to the left of the ladder.…

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A: Evaluate improper integral

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Q: Find the sum of the first 125 positive even whole numbers.

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Q: What does the graph of the parametric equations x(t)=3−t and y(t)=(t+1)2, where t is on the interval…

A: t x=3-t y=(t+1)2 (x, y) -3 6 4 (6, 4) -2 5 1 (5, 1) -1 4 0 (4, 0) 0 3 1 (3, 1) 1 2 4…

Q: Solve the given differential equation by undetermined coefficients. y'' − 12y' + 36y = 24x + 2…

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Q: Figure (a) shows a vacant lot with an 80 ft frontage in a development. To estimate its area, we…

A: It is midpoint Riemann sum      here length of interval  △x=20

Q: Evaluate the integral by interpreting it in terms of areas. *18 |x - 9| dx

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Q: Which of the following is a polynomial function?

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Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

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A: Consider a function y = f(x) .Then f '(x) is the rate of change of y with respect to x.

Q: Find the area (in square units) of the region under the graph of the function f on the interval [0,…

A: Given fx=10 ex on the interval 0,3 The formula to calculate the area under the graph y=g(x) on the…

Q: If sint = 4/5 and t is in the first quadrant, find cos(2 t) -7/25 -9/25 7/25 24/25 None of these

A: There is more than 1 question, as per the Q&A guidelines I am answering the 1st question. If you…

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A:

Q: Consider the equation cos(3t) = 0.8. Find the smallest positive solution in radians and round your…

A: We can find the answer the as below.

Q: Question 1: Find the Laplace transform of the given functions by using the table of Laplace…

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Q: Is the function a power function. If it is, write it in the form f(x) = kxP, and state the values of…

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Q: TC=575+2Q

A: ANSWER Is in next step

Q: 5. y = 2 sin x y

A:

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A: We have to solve above question and find length of wire As per bartleby guidelines we have to solve…

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Q: Select the representations that do not change the location of the point a. [-2.-357) D. (-2,-²5) b.…

A: -2, 7π5=-2cos7π5, -2sin7π5π+2π5=7π5=2 cos2π5, 2cos2π5  [FIRST Quadrant]A)-2 cos3π5,…

Q: Determine whether the series converges absolutely, converges conditionally, ges. 4n Σ(-1)", n³+1 n=2

A: Use alternating series test for checking the convergence .

Q: Consider the following. Let u = 4x³ - 1. Find du. du = dx Indicate how the limits of integration…

A: The given definite integral,          ∫01x24x3-14dx

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A: Solving

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A:

Q: Give a formula for the nth positive even integer: Here is a theorem: 1+ 2+3 + ... + n п(n+1) n = Use…

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Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

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Q: [ID # ending in 4 or 7] 2 Əv Determine ( + ду 2²v ах ду if v csch y = ex².

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Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

A: Volume

Q: lim (cos(9x)) (+) x-0+

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Q: Select the conic section represented by the equation. 2x + 5y - 7 = 0 ellipse parabola point…

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Q: Let f(x) = 2x³-7x² + 4x. a. On what interval(s) is f'(x) > 0? b. On what interval(s) is f(x)…

A: Given problem:- Let f(x) = 2x3 - 7x2 + 4x .   a. On what interval(s) is f'(x) > 0?   b. On what…

Q: What two positive real numbers whose product is 22 have the smallest possible sum? The numbers are…

A:

Q: Find the area of the region bounded by the graphs of the equations. y = Vx -1, y = 2, y = 0 , x = 0…

A: We have to find the of the  region bounded by the given equations.