The volume cylinder is fixed at a value of V. Find how fast the radius of the cylinder changes with respect ti the height of the cylinder when the radius and height are equal to each other

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: From the Pythagorean theorem, BC2+AB2=AC2

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Q: Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel…

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Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: We have given change in edge with respect to time is 2cm/sec.  We have to find the changes in…

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Q: The length { of a rectangle is decreasing at a rate of 8 cm/ sec while the width w is increasing at…

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Q: The volume of a cylinder is fixed at a value of V. Find how fast the radius of the cylinder changes…

A:

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 25-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 5…

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Q: The length of a rectangle is given by 2t + 3 and its height is √t, where t is time in seconds and…

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Q: A 25ft ladder is sliding down a wall at -6ft/s. How fast is the bottom of the ladder sliding out…

A: Given, Length of ladder= 25 ft  Rate of sliding down = -6 ft/s  We have to find how fast is the…

Q: A truck is 300 kilometers due east of a car and is traveling west at a constant speed of 30km/hr.…

A: (a) Let the initial position of the car be at the origin. Take the x-axis from west to east and the…

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

Q: A rope is attached to a boat at water level, and a man on the dock is pulling on the d) rope at the…

A: Draw a schematic diagram of given figure.

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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Q: pherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At…

A: The radius of the balloon decreases at the rate of =15 cm/min let radius of balloon =r then…

Q: The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and…

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

Q: A weight W is attached to a rope 50 ft long which passes over a pulley at P, 20 ft above the ground.…

A: Given: - A weight W is attached to a rope 50 ft, long which passes over a pulley at P, 20 ftabove…

Q: The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge…

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Q: The side of a cube decreases at a rate of 9 m/sec Find the rate at which the volume changes, when…

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Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Now in triangle ABC, by using Pythagorean theorem, we get

Q: The length l of a rectangle is increasing at a rate of 7 cm divided by sec while the width w is…

A: Given:-             The length l of a rectangle is increasing at a rate of 7 cm/ sec while the width…

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

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Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

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: A ladder 14 ft long rests against a vertical wall. Let 0 be the angle between the top of the ladder…

A: Given:

Q: The volume of a cube is increasing at the rate of 8 cm /sec.How fast is the surface area in creasing…

A: We can find the answer as below

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same…

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Q: Assume that the brakes of an automobile produce a constant deceleration of k ft/sec2. (a) Determine…

A: Given,          Assume that the brakes of an automobile produce a constant deceleration of k ft/sec2

Q: A conical water tank with vertex down has a radius of 13 feet at the top and is 25 feet high. If…

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Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

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Q: A bicyclist accelerates at a constant rate from a standstill to 15 km/hr in 90 sec. a) How fast is…

A: a) Consider the given information: u=0 km/hrv=15 km/hrv=15 ×10003600m/sv=4.17m/st=90sec From…

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Given:

Q: The volume of a cylinder is fixed at a value of V. Find how fast the radius of the cylinder changes…

A: Solve the given problem.

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: A car braked with a constant deceleration of 18 ft/s2, producing skid marks measuring 100 ft before…

A:

Q: against

A:

Q: The volume of a cube is increasing at a rate of 64 in ³/sec. At what rate is the length of each edge…

A:

Q: The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

Q: A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 50 ft before…

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Q: The radius of a circle is increasing at a rate of 2cm/s. How fast is the area of the circle…

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Q: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same…

A: Given: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the…