A rectangle has a length of 11 inches and a width of 10 inches whose sides are changing. The length is decreasing by 5 in/sec and the width is shrinking at 4 in/sec. What is the rate of change of the area?

Q: Suppose the radius of a sphere are expanding at a rate of 6 inches per minute. How fast is the…

A: Let us suppose the radius of sphere be R. Given that :   dRdt=6 incheminute.  Radius=Diameter2=122=6…

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Suppose that the radius of circular pattern is “r” and area of the pattern is “A” then, The area of…

Q: There is a water tower with a radius of 5 feet and a height of 30 feet. The water level is 25 feet…

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: What is the rate of change of the area?

A:

Q: A stone dropped into a still pond sends out a circular ripple whose enclosed area increases at a…

A:

Q: The volume of oil in a cylindrical container is increasing at a rate of 150 cubic inches per second.…

A:

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 3…

A: Given that:Rate of increase of radius, drdt=3 ft/s

Q: Suppose the radius of a sphere is increasing at a rate of 5 in/second.  At what rate is the surface…

A: Given that radius of a sphere is increasing at an of 5 in/sec. Let r be the initial radius of the…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: A right triangle has legs of 3 inches and 4 inches whose sides are changing. The short leg is…

A: dhdt=7 in/sec , dbdt = -10 in/sec

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: An equilateral triangle initially has sides of length 20 ft when each vertex moves toward the…

A: We have given an equilateral triangle intially has sides of length 20ft and each vertex moves toward…

Q: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04…

A: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of  0.04…

Q: When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01…

A:

Q: A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The length…

A: Given:A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The…

Q: A triangle has an area that is increasing at a rate of 555 square feet per minute with the height…

A:

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A:

Q: A rectangle has a length of 1 inches and a width of 12 inches whose sides are changing. The length…

A:

Q: A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the ground…

A: Given:A weather balloon is rising vertically at the rate of 10 ft/s. An observer is standing on the…

Q: The length of the rectangle is increasing at a rate of 5cm/s and its width is decreasing at a rate…

A:

Q: Two parallel sides of a rectangle are increasing in length at the rate of 2 in/sec while the other…

A: Given: The two parallel sides of a rectangle are increasing in length at the rate of 2 in/sec. The…

Q: A rectangle has a length of 11 inches and a width of 5 inches whose sides are changing. The length…

A: In the given rectangle  Width b = 5 inches Length l = 11 inches Length increasing rate dl/dt = 9…

Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

A:

Q: When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min.…

A: drdt=0.05cm/minradius, r=52cmArea=πr2Derivative formuladdxxn=n xn-1

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: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

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

A: Solution:-

Q: A fire has started in an open field and is spreading in the form of a circle, with its radius…

A:

Q: When a circular metal plate is heated in an oven, its radius increases at the rate of 0.02 cm/min.…

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: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain…

A:

Q: When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm…

A: Given:When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01…

Q: Suppose the side of a cube is decreasing at a rate of 2 feet per hour. What is the rate of change of…

A: Given: ds/dt=2 side=4ft

Q: A cone with an altitude of 50 cm has its base radius changing at the rate of one millimeter per…

A:

Q: Suppose the radius of a sphere is expanding at a rate of 3 inches per minute. How fast is the volume…

A: Let V & r be the volume and radius of the sphere at any time t respectively. Given that, the…

Q: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

Q: A rectangle has a length of 9 inches and a width of 10 inches whose sides are changing. The length…

A: Length of the rectangle, l =9 inches Width of the rectangle, w = 10 inches The length is increasing…

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: The sides of a square increases in length at a rate of 3 m/sec. At what rate is the area of the…

A:

Q: A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm3 /sec.…

A:

Q: A rectangle has a length of 7 inches and a width of 8 inches whose sides are changing. The length is…

A:

Q: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

A: A right circular cylinder has a radius increasing at the rate of 4 cm per second but its total…

Q: A right triangle has legs of 21 inches and 28 inches whose sides are changing. The short leg is…

A: Length of the legs are 21 inches and 28 inches and the short leg is increasing by 10 in/sec and the…

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: A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into…

A: