Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m/s) is the area of the spill increasing when the radius is 39m?

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: A cylindrical tank with radius 6 m is being filled with water at a rate of 3 m³/min. How fast is the…

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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: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius…

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt…

Q: A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm wide…

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Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the surface…

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

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Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…

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Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: It would be best to express length, width, and area as functions of time. I’ll set x = width, y =…

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Given that the diameter= 100 mm So the radius is=r=1002=50 mm Given that the radius of a sphere is…

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

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Q: Suppose the sides of a cube are expanding at a rate of 2 inches per minute, How fast is the volume…

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

A: Let the length be: l Let the width be: w

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

Q: The radius of a sphere is increasing at a rate of 4mm/s. How fast is the volume increasing when the…

A: The rate of change of the radius of the sphere, drdt = 4 mm/s To evaluate : The rate at which the…

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

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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: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Volume of sphere= =43πR3 where R is the Radius of the sphere.

Q: A snowball is melting at a rate of 2.4ft^3 hr^-1 – if the snowball remains a sphere throughout the…

A: given: A snowball is melting at a rate of 2.4ft3/hr. that implies dVdt=-2.4ft3/hr where V is the…

Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: A cylindrical tank with radius 3 m is being filled with water at a rate of 3 m³/min. How fast is the…

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Q: An ice cube that is 3 cm on each side is melting at a rate of 2 cm3 per min. How fast is the length…

A: Given: Length of cube L=3cm Rate of melting =-2cm3

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

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Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

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Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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Q: An isosceles triangular water trough is 5 meters long, 3 meters across the top, and 2 meters deep is…

A: Where we see the application of derivatives to solve the given problem

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

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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: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A:

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

A: Given: A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface…

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

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

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

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: The volume of a cube is increasing at the rate of 6 cm/min. How fast is the surface area increasing…

A: It is given that, the volume of a cube is increasing at the rate of 6 cm3/min.   The objective is to…

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

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Q: A light is hung 7m above straight horizontal path. If a man 2meters tall is walking toward a light…

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Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

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Q: how

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

A: The calculation are as follows

Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

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

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

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Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

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Q: The radius of a sphere is increasing at a rate of 4mm/s.How fast is the volume increasing when the…

A: Given that the radius of a sphere is increasing at a rate of 4mm/s. That is, Now consider the…