Evaluate the following integral using trigonometric substitution. S dt 1²√36-1² OC. t-6 tan 0 Rewrite the given integral using this substitution. dt 1²√36-1² (Simplify your answers. Type exact answers.) Evaluate the integral. S = de dt 1² √36-1² (Type an exact answer.)

Q: Find three positive numbers whose product is 86 such that the sum of their squares is as small as…

A: Let the three numbers be x, y and z. x + y + z = 86 -----(1) ⇒ z = 86 - x - y ------(2) Product, P =…

Q: Problem 2 Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x²y³ - ky)dy = 0…

A: Concept: Take into account the equation P(x, y)dx + Q(x, y)dy = 0 . If v(x, y) = c, the differential…

Q: Concept Check: Evaluate the following integrals: e³x dx 1-2e³x 2. ·S₁ TENTIA

A: To evaluate the given integral.

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Q: 3. Use the variation of parameters method to find the general solution of the following Des 2ex ex +…

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Q: Question 6 Determine the derivative of - sec z cosz-sin r sec" tan z sec² z 1-sin z sec² z O cos²x -…

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A: Given,Demand Function D(q) = -2q + 250(A) Revenue from selling 105 itemsRevenue function = q ×…

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A: The given function fx=x2-5x+15 We have to find the interval on which fx is differentiable.

Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral £{f(t)} =…

A: Given function is ft=9,    0≤t<30,    t≥3 We need to find laplace tranform of the given function.

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A: See this solution in below.

Q: Find the Maximum value of the function f(x,y)=x^2−y^2−2y on the curve x^2+y^2=4.

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Q: 0 = XP(^vx-2)^x + ^p (Tvx-tv^) differential equations.

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Q: 1. Find the double integral over the region R bounded by the functions. Choose the more convenient…

A: To find:- ∬Rx3y2dA ; y=x,y=0,x=1 ∬xeydA ; y=x,y=0,x=1 ∬RxydA ; y=x2+1,y=3-x2

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Q: 3. fxe (4-x²) dx

A: ∫ xe4-x2dx

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Q: d csc 0 if tan 0 = 0 = and terminates in QII. Answer exactly. 15 Preview TIP Enter your answer as a…

A: Topic:- trigonometry ratios

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A: See the details solution in below

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Q: Number 1: Given a first-order differential equation: /1 + x² dy − ydx = 0 A) Solve for the general…

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Q: Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x² y³ - ky)dy = 0 a) Solve…

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Q: the

A: We have to find the following conditions from the given information

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Q: Problem 2 Given the following differential equation: (y³+kxy4 - 2x)dx + (3xy2 + 20x² y³-ky)dy = 0 a)…

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A: see below the answer and explanation

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A: Let x m be  length and y m be  width of rectangle  Perimeter of rectangle=2x+y m Area of…

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