The radius r of a sphere is increasing at a rate of 8 inches per minute. (a) Find the rate of change of the volume when r = 12 inches. In. 3/min (b) Find the rate of change of the volume when r = 35 inches. in. 3/min

Q: The radius of a circle is increasing at a rate of 4 centimeters per minute. Find the rate of change…

A: Area of circle having radius r is given by:     A=πr2Given rate of change of radius=drdt=4cm/minRate…

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A:

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change…

A:

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A:

Q: The volume of a sphere is increasing at a rate of 4 cm3/sec. Find the rate of change of its surface…

A: We will use derivative as rate of change

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a)  Find the rate of…

A: Given:The radius r of a sphere is increasing at a rate of 6 inches per minute.

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Q: The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of…

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Q: Assume that the rate of change of air pressure with altitude (distance above the earth) is…

A: Topic:- Differential equation

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A: The surface area S of the body is related to the body's weight W according to S is:

Q: 31. The rate of change of the circumference of a circle when its radius increases at 1 cm/min is Зп…

A: The solution is given in the next step.

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A: Given  At time t  the radius of a sphere is 'r'

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A: Now differentiating with respect to x, we get

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Q: 'ind the average rate of change of h(t) = 3 c on t-3 [1,1+ h]

A: Topic:- calculus

Q: need help

A: Consider the figure below. Let x be the distance between the man and the pole and y be the distance…

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A: We need to find the rate of change of pressure  when temperature is 150K and pressure is 450…

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Q: Find the rate of change of the circumference of a circle with respect to the area when the area is…

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A:

Q: the radius r, of a circle is decreasing at a rate of 2cm per minute. Find the rate of change of  the…

A: givenradius (r)=5 cmdrdt=2 cm/minwe knoww circumference of the circle (C)=2πrdiffrentiatedCdt=2πdrdt

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Q: The volume of a cube decreases at a rate of 0.75 ft3/min. What is the rate of change of the side…

A: Consider a cube with side 'a' The rate at which the volume of cube is decreasing is 0.75 cubic feet…

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Q: The area of a square is increasing at a rate of 16 centimeters squared per second. Find the rate of…

A: Area of square =(side)2

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A: Given: A square with side x. changing with time is given as, xt=4t-2. The objective is to find the…

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A:

Q: The area of a square with sides of length s is given by A = s2 . Find the rate of change of the area…

A: The area of a square with sides of length s is given by , A=s2. To find the rate of change of area…

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Q: A typical male's body surface area S in square meters is often modeled by the formula S = 0 Vwh ,…

A: S=160wh Here, height of a person is  'h' cm and weight of a person is  'w' cm.

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

Q: The radius r of a sphere is increasing at a rate of 8 inches per minute. Find the rate of change of…

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Q: The height of a triangle is increasing at a rate of 2 [cm/min] and its area at a rate of 2 [cm²/…

A: It is given that height of triangle is increasing with a rate 2 cm/min and area with a rate 2…

Q: 4 P = R What is the rate of change of power with respect to resistance? rate of change = Viohm?

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A: The image made from available details in the question

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Q: The quantity (in grams) of a radioactive substance present after t years is Q(t)=100e-0.421t. Find…

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Q: The area of a square with side s is A(s) = s². What is the rate of change of the area of a square…

A: From the given question we find the rate of change at a indicated points.

Q: The area of a square with side s is A(s) = s². What is the rate of change of the area of a square…

A: We are given :  The Area of a square with  side s is A(s) =s2

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Q: The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the…

A: Write the equation of the surface area of sphere solve it as per given in step 2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.