The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the average rate of change in volume (in ft3/ft) when radius increases from 3 feet to 5 feet.     8π     64π     384π     32π     48π

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A: Given, Voltage, V=17 volts Resistance, R=5 ohms The rate of change of resistance with respect to…

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A: Rate at which surface area increases is

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Q: 4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle,…

A: We need to find rate of change.

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A: a). Put x = 15, we get b). Put x = 24, we get

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate (in…

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Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

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Q: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 6 volts is…

A: A voltage V across a resistance R generates a current I = V/R. If a constant voltage of 6 volts is…

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Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar h where r is the radius…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A:

Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: The length l of a rectan-gle is decreasing at the rate of 2 cm/sec while the width w is increasing…

A: (a)Given:

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A: Formula:  Area=length times height A(t)=t(6t+5)

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in…

A: Let the diameter be D cm and radius be r cm  The surface area S of the the sphere in term of…

Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

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Q: If a hemisphere bowl of radius 6 cm contains water to a depth of x cm, the volume of the water is rx…

A: This question is related to application of derivatives.

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

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Q: The radius of a circle increases at a rate of 4 cm/ sec. The rate at which the area of the circle…

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Q: A 25-foot ladder is leaning against a house, as shown in the figure below. If the base of the ladder…

A: Using Phthagorous therome, r2 +x2=252  First we find rate of change in r, then we get Dr/dt in terms…

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A: At the instant when the perimeter of the circle is 20π, then p=2πr20π=2πrr=10 m

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Q: A voltage V across a resistance R generates a current I=V/R. If a constant voltage of 6 volts is put…

A: A voltage V across a resistance R generates a currentI=V/R. V is constant and is 6 volts

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

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Q: The air in a small room 12 ft by 8 ft by 8 ft is 5% carbon monoxide. Starting at t = 0, fresh air…

A: Let v(t) be the volume of CO in the room at time t, and let V be the total volume of the room.The…

Q: The radius of a right circular cylinder is increasing at the rate of 8 in/sec while the height is…

A: Given- drdt=8 in/sec and dhdt=-3 in/sec To Find- The rate of the volume changing when r= 7 in and…

Q: A conical tank full of water is 25 ft high and 15 ft in diameter at the top. If water is flowing out…

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Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

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Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

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Q: 6. Air is being pumped into a spherical ball at a rate of 7 cm³/sec. What is the rate of change of…

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Q: The radius of a sphere decreases at the rate of 5 m/s. when the radius is 10m, then the rate of…

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Q: A spherical balloon has been poked with a needle and air is seeping out at a rate of 2cm³ /hr. Find…

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A: To find the instantaneous rate of change:

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A: expanding at the rate of 16pi in^2/sec of circular loop rate is the radius expanding if radius…

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