Assume x and y are functions of t. Evaluate dt y³ = 2x² +6: dx dt -=4, x= 1, y = 2 for the following. (Round to two decimal places as needed.)

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A: A.

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A: Topic = Functions

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Q: 1. Show that u(x,t)= etsin kx satisfies the partial differential equation_u₁ = α² uxx

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Q: 49. Your new puppy needs a rectangular dog run outside. You have 50 feet of fencing and plan use the…

A: Answer to the question number 49 is given below.     We want to find the maximum area.

Q: ion 2. Find the domain of the vector function r(t) = (√5 – t², 1⁄2, et). t-

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Q: If A is a symmetric matrix, then AT OA O AI O diagonal matrix none of the above

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Q: frequent problem in surveying city lots and rural lands adjacent to curves of highways and railways…

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Q: Problem 4: Find the derivative (f'(x)) of a) f(x) = (x² − 3x)(7x+15), b) f(x) = = x-5 x²-x+7

A: Given f(x)=(x2-3x)(7x+15)DIfferentiate…

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A: area between curve

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A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

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Q: 5. The sequence of partial sums of the equation Σ (a)3/2 (b) 3/4 n=1 3n-1 (c) 1/3 (d) -1/3

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Q: x = −1+5t y = 3-s-2t z= −2+s

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Q: DIFFERENTIAL

A: Please refer to the image below

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A: I have explained the solution.

Q: By using partial method solve [ 2x² cos x dx

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Q: B: Solve the following integrations: a- [x³e-2x¹ dx b-fdx +10 c-f3sec³x. tanx dx arks

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Q: D Operator: Solve the DE y" - 7y" +14y - 8y = 0 y = c₁e¹ + c₂e²x + c3e4x Oy=c₁e²x + c₂e4x + c3e6x y…

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Q: 10.) L So exte-x dx È

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A: slope of tangent = slope of given curve  step 1  we have to find slope of curve  slope = dy/dx  so…

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A: Find out the domain of the function.

Q: let fx= 2x^3-x^2-12x+1 find the critical numbers of fx, determine the location of the relative…

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Q: How many solutions are there between the plane P₁: (x, y, z)=(4,-3,-1) + s(1, -3,1)+t(2,4, -3) and…

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Q: If a = (-1, 1, 2) and b = (1,3,1), then which of the following gives |a - b|? Select one: O√9 O -√9…

A: This question is related to vectors, we will solve it using given information.

Q: (t) below, find f'(x). f(x) = (3x³ + 3x²-4).x²

A: Given a function f(x)=(3x3+3x2-4)x2 Formula used : d(xn)=nxn-1

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Q: 2.1 2.3 2.4 2.5 1. 2. 2.1 QUESTION 3 2.2 2.3 Sketch the graphs of fand g on the same set of axes for…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

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A: The objective of the question is find the general solution of the given differential equation.

Q: dh dth-19 1.4324 Incorrect Incorrect m/min m/min

A: Follow the procedure given below.

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Q: I can't seem to understand the solution. Can someone write it down?

A: An inner city revitalization zone is a rectangle that is twice as long as it is wide. A diagonal…