A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft/sec. (a) How fast is the top of the ladder sliding down the wall then? (b) At what rate is the angle θ between the ladder and the ground changing then?

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A:

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A:

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) S sin x+cos x sin³ x cos³ x…

A:

Q: a) Find the area of the triangle determined by the given point P₁(1, 2, 4), P2(1,-1, 3), P(-1,-1,2)

A: As per Bartleby guideline, only the first question has been answered. Please repost mentioning the…

Q: (B): If A = 2i + 3j - 4k; B = 3i - 4j + 5k and C = i + j - k, find: (ii)B.C (iii)A. (B+C)and (A+B).C…

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Q: Discuss the topic from algebra you used in completing this exercise. Give an example of a business…

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Q: defined on the interval [-5, 7]. a.) f(x) is concave down on the open b.) f(x) is concave up on the…

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A: Using substitution and differentiation,

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A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

A:

Q: (c) State the Fundamental Theorem of Calculus Part II.

A: In this question we have to state the Fundamental Theorem of Calculus Part II.

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Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y² ;

A: Find the derivative

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A: We will use ratio test.

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

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Q: C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

A:

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A: We can solve this as follows:

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A:

Q: Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The…

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