Find the rate of change of total profit, in dollars, with respect to time where R(x) = 7x and dx C(x) = 0.03x² +0.9x + 80, when x = 18 and = 15. dt

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A: Topic:- application of derivatives

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A: On solving this we will get

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A: differentiation

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A: We have to find the profit function and average.

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A: Let's solve given diffrential equation by using separation of variables.

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A: Let's find.

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A: see below the calculation

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A: ..

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Q: Find the rate of change of total profit, in dollars, with respect to time where R(x)=80x−0.5x2 and…

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Q: For any real x, what is the maximum value of the expression y = 2(k-x)(x+√x²+k²)?

A: This question can be solved using the concept of maximum and minimum.

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Q: IV.Sketch the ff. curves: Find all its properties. X 1. y= In x

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

A: Solution is given below:

Q: Solutikn is not clear, can it be handwritten please. Thank you.

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Q: Solve the following differential equations: 1 √1-3x (a) -dx + sin y cos 2y + 1 dy = 0 (b) x²y + x³…

A: I am attaching image so that you understand each and every step. Here "c" is integration constant.

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Q: Use the equation to name each of the characteristics listed. Make sure to use proper notation and…

A: Let's find given all characteristics of function.

Q: For a cyclic group of order 420, the number of generators are, (a) 66 (b) 76 (c) 86 (d) 96

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Q: 4.Determine the area bounded above by y: 5 + x² and below by y = 1 + 2x²

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Q: the matrix has two eigen vector one of * this(ulkyl gil) 3 2 0 0 -1 0 1 0 2 12032

A: We want to write the eigen vector.