Suppose the side of a cube is decreasing at a rate of 2 feet per hour. What is the rate of change of the surface area of the cube at the moment when the side is 4 feet?

Q: A thin sheet of ice is in the form of a circle. If the ice is melting, at what rate is the radius…

A: Given a thin sheet of ice is in the form of a circle. And the area is 12 square inches.Let the area…

Q: The radius of a right circular cylinder is increasing at a rate of 4 inches per minute, and the…

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A:

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

A: The given data are: Radius of pool= 7 feet Height of pool= 7 feet dVdt=4 cubic feet per minute The…

Q: A hot-air balloon is 150 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Let x be the distance the motorcycle has traveled. Let y be the height of the balloon above the…

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

A: Please refer to the image below.

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

Q: The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square…

A:

Q: An airplane is flying at an altitude of 4 miles and passes directly over a radar antenna. When the…

A: Given that an airplane is flying at an altitude of 4 miles and passes directly over a radar antenna.…

Q: the area of a circle is decreasing at a constant rate of 181 square centimeters per second. at the…

A: Given, dAdt=181cm2sec now we know area of circle is: A=πr2 now derivate both side w.r.t t…

Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

A:

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

A: To solve the following problem of finding the rate of change in height

Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: A 5-foot-tall woman walks at 8 ft>s toward a streetlight that is 20 ft above the ground. What is…

A:

Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

A:

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

A: Rate of change

Q: The volume of a cube decreases at a rate of 0.6 ft° /min. What is the rate of change of the side…

A: Since you have not mentioned I am answering 2nd Question. Given:Volume of a cube decreases at a rate…

Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: A man of 2 mts tall is approaching a lamp post at the rate of 0.5m/sec.if the lamp post is situated…

A:

Q: the top of a 25 foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute.…

A: Given  c=25 ft b= 7ft dbdt=3 ft/minute dcdt=0

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: volume of cube = side3 V= volume  x= side dVdt=24 in3/minutedxdt=? at x=2

Q: A rectangle has a length of 4 inches and a width of 12 inches whose sides are changing. The length…

A: Let x and y be the length and width of the rectangle at any time t respectively. Now according to…

Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

Q: The volume of a cube is increasing at a rate of 9 cubic centimeters per second .How fast is the…

A: Solution:-

Q: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

A:

Q: A 6​-foot-tall woman walks at 9 ft/s toward a street light that is 24 ft above the ground. What is…

A: The height of the woman is 6 ft. and the height of the street light is 24 ft.The woman walks at 9…

Q: Find the rate of change of the surface area of the cube when the volume is 8 cm". A block of ice in…

A:

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: A right triangle has legs of 18 inches and 24 inches. The short leg is decreasing by 3 in/sec. The…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: to find:- dH/dt.

Q: Suppose the length of the diagonal of a square is increasing at the rate of 2 inches per second. At…

A:

Q: A right triangle has legs of 27 inches and 36 inches whose sides are changing. The short leg is…

A: Given that  Right triangle has  AB = 27 inches  BC = 36 inches Rate of change of short leg i.e. 27…

Q: If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is the…

A: Given dr/dt = 3

Q: An ice cube that is 3 cm on each side is melting at the rate of 2 cubic cm per min. How fast is the…

A:

Q: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing…

A:

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A:

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

A:

Q: A cone shaped icicle has an initial radius of 10 inches and a height of 15 inches. Once the height…

A:

Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg…

Q: Each side of a square is increasing at a constant rate of 4 centimeters per second. At what rate is…

A:

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 33 inches and 44 inches . The short leg is decreasing by 4…

Q: The side of a square sheet is increasing at rate of 4 cm per minute ,At what rate is the area…

A:

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

A:

Q: A rectangle has a length that is increasing at a rate of 16 mm per second with the width being held…

A:

Q: Mohamad Salah poured orange juices into a cylindrical red tank whose height = of its radius. If the…

A: We have to find rate of change of Radius.