The temperature at a point in a ball with conductivity K is inversely proportional to the distance from the center of the ball. Find the rate of heat flow across a sphere S of radius a with center at the center of the ball.

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A: 1 day = 24 hrs = 24* 60 minutes = 24*60*60 seconds=86400 seconds 7.5 gallons = 1 cubic feet So 9…

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A: Given:

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A: We will use derivative as rate of change

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Q: Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

A: Rate of change of volume of cube

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Q: The volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a…

A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…

Q: A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a…

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the…

Q: If the rate of change of the side length of an equilateral triangle is 2br / sec, what is the rate…

A: Please rate and feel free to ask any query about any part of the question.  I have used applications…

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Q: What is the average rate of 5. If f (t) = -3t + 7t, describes the movement of a whale in meters.…

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Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. Find the…

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Q: The surface area of a sphere increases at a rate of 55 m²/sec. Then the rate at which the radius…

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Q: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change…

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Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

A:

Q: What is the rate of change of the volume of a ball (V = (4/3)pai r3 ) with respect to the radius…

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Q: The radius of a spherical balloon is decreasing at a rate of 2 - in/sec. Which of the following is…

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A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

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A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: What is the rate of change of the volumeof a ball (V = (4>3)pr3) with respect to the radius…

A: The volume of a ball with radius r is given by V=43πr3 Recall that the rate of change is given by…

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

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Q: 2. Find the rate of change of a volume V of a cube with respect to (a) the length w of a diagonal of…

A: Consider a cube of a side a , and diagonals z and w  We know that Pythagorean theorem , Hypotenuse 2…

Q: The radius of a sphere is increasing at the rate of 2 meters per se of change of the volume with…

A: Given: The radius of a sphere is increasing at the rate of 2 meters per second.

Q: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

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Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: The height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

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Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles, as shown.…

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Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Given that radius =7 ft dVdt=9 cubic ft per minutefind dhdt Also V=πr2h

Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

A:

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: The area A(t) of a circular shape is growing at a constant rate. If the area increases from 97 to…

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Q: For many species of fish, the allometric relationship between the weight W and the length L is…

A: Here the given that, the allometric relationship between the weight W and the length L is…

Q: Find the rate of change. Volume V of a cylinder with respect to radius if the height is equal to the…

A:

Q: Let A be the area of a circle with radius r that is increasing in size with respect to time. If the…

A: We have to find rate of change of the radius when radius is 6 cm and rate of change of area is given…

Q: The volume V of a right circular cone of radius r and height h is given by V = Tr²h. Find a formula…

A: To find the instantaneous rate of change:

Q: A spherical balloon is inflated at a rate of 21 cm's1. Find the rate of change of the surface when…

A: Volume (V) of the sphere = (4/3) pi r3 Surface area (S) of the sphere = 4 pi r2 where r is the…

Q: The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

A: