A ladder 13 ft long leans against a vertical wall. If the top slides down at 3 ft/s, how fast is the angle of elevation of the ladder decreasing when the lower end is 9 ft. from the wall?

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A: Let's find dimension for minimum cost of given rectangular box.

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A: As you have asked multiple questions so I have answered first question as per the guidelines

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A: Given

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A: Topic:- function And it's integration

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Q: solve

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A: LetI=∫212dxWe know that ∫abfxdx=-∫bafxdx, a<bThereforeI=-∫122dxTake constant outI=-2∫12dxWe know…

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A: As per bartleby guidelines we only give first question answers because questions are lengthy.

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A: Given;  Radius=9cm dr/dt=0.4 cm/min

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Q: Convert to a polar coordinates. Show work. 13. (0,-4) |

A: polar coordinate

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A: We have to evaluate the integral.

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A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

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A: We know that L{tn} = n!sn+1        and          L{sin at} = as2+a2        and       L{cos at} =…

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A: Given :y=e2x-1e2x+1

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A: y=(x – 1)(2x – x2)   +sin-1(x – 1) y'(x)=d(x – 1)2x – x2   +sin-1(x – 1)dx        =d(x – 1)2x – x2…

Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral:

Q: 18-19. In xy = 4, let x and y be differentiable functions of t. Evaluate at x = 10 and = 20. dt dy…

A: A detailed solution is given below.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: 17. If you know f(0) = 625 and f (4) = 16 then: %3D %3D (a) Find a formula for f(x) assuming that it…

A: 17.A function satisfies that f0=625 and f4=16

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A: We have to find f"(x) for the given function.

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A: Given

Q: need

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