A spherical balloon is inflated with gas at a rate of 10 cubic feet per minute. How fast is 4 .3 the radius of the balloon changing at the instant the radius is 2 feet? Hint: V = -r³ 3

Q: A spherical balloon is inflated with air flowing at a rate of 15 cm/s. How fast is the radius of the…

A: The formula to calculate the Volume of the balloon is:              V=43πr3 where r is the radius of…

Q: At a given moment, a plane passes directly above a radar station at an altitude of 6 km. (a) The…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the…

A: Find the length of ladder when bottom of the ladder is increasing at the rate of 0.3m/s when bottom…

Q: SA Spherical ballon is ingiated With goas at the rate af 20 Cm3min. How fast is the fadtus af the…

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Q: The area of a circle increases at a rate of 4 cm? /s. a. How fast is the radius changing when the…

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Q: e skid marks made by an automobile indicated that its brakes were fully applied for a distance of 85…

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Q: The top of a 30-foot ladder is sliding down a wall at a rate of 9 feet per second. How fast is the…

A: In the question it is asked to calculate the speed at which the base of ladder is going away from…

Q: Air is being pumped into a spherical balloon at a rate of 4.5 cubic inches per minute. How fast is…

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Q: 10. A boy is flying a kite at a constant height of 60 ft. If the kite is moving horizontally at the…

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Q: The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is…

A: We have to find

Q: On a certain planet's moon, the acceleration due to gravity is 2.6 m/sec. If a rock is dropped into…

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Q: A kite 50 ft above the ground is moving horizontally at a rate of 4 ft/s. At what rate is the string…

A: Assume  horizontal distance from original position is x diagram according to problem

Q: Air is being pumped out of a spherical balloon at the rate of 25 cm3/s. How fast is the radius…

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Q: baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with…

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Q: Stephanie is standing atop at 13 ft ladder. The ladder is leaning against a vertical wall. The…

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Q: 10. Gas is escaping from a spherical balloon at a rate of 2 cubic feet per minute. How fast is the…

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Q: The base of a 45-foot ladder is being pulled away from wall at a rate of 12 feet per second. How…

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Q: The base of a 40-foot ladder is being pulled away from a wall at a rate of 14 feet per second. How…

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Q: B. Read and answer the problem carefully. 1. A spherical balloon is inflated with gas at the rate of…

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Q: Q1/ Water poured into a conical tank through a faucet, this tank has a base radius of 5 ft and 10 ft…

A: Solution:

Q: The base of a 20-foot ladder is being pulled away from a wall at a rate of 11 feet per second. How…

A: application of derivative

Q: Q-4-A leak in a spherical balloon filled with gas allows the gas to leak at a rate of 3.5 m³ /min .…

A: Given that,       a leak in a spherical balloon filled with gas allows the gas to leak at a rate of…

Q: t is 3 meters above the ground? 6. A spherical balloon is being inflated at the rate of 350 cm /min.…

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Q: A spotlight at a building corridor is fastened to a wall 8 m above the floor . A lady 1.75 m tall…

A: Refer the diagram below. Let x be the distance between the spotlight and the lady and y be the…

Q: the hypotenuse AB of a right triangle ABC is constantly 5 in long. The side AC is increasing…

A: Given that the hypotenuse AB of a right triangle ABC is constantly 5 in long. and the side AC is…

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

A: Area of circle of radius r inA=πr2→dAdr=2πrdrdt→2πrdrdt=6      [∵dAdr=6cm2/sec]    -(1)

Q: A spherical snowball melts at a rate of 2 cubic centimeters per hour. How fast is the radius…

A: We know that the volume of a spherical snowball is v = 43πr3 where v is the volume and r is the…

Q: 0. A plastic container in the shape of a cylinder is being filed with coconut juice at the rate of…

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Q: A lighthouse is located on a small island, 5 km away from the nearest point P on a straight…

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

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Q: A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute. How fast is the…

A: Given, A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute.

Q: A spherical balloon is inflated with air flowing at a rate of 19 cm³/s. How fast is the radius of…

A: Use volume of sphere and differentiate wrt  t and put value

Q: A 13-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: True or False If an object moves at an average speed r, the distance d covered in time t is given by…

A: Consider the given statement. The given statement is true. By the definition of average velocity,…

Q: See attached question

A: Now we will diffrentiate the formula of volume of a sphere  as shown:

Q: t) A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A: solution

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

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Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

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Q: j. A boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a…

A: Given: Height of boat above water level=20 ft……1Length of rope=50 ft……2Rate at which boat is pulled…

Q: Q3: Water is being poured into a hemispherical bowl of radius 3 inches at the rate of 1 in/s. How…

A: Solve

Q: You are inflating a spherical balloon at the rate of 7 cm³/sec. How fast is it radius increasing…

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Q: In calm water, an oil spill spreads out in a circular fashion. Suppose the radius, r, of the spill…

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Q: A spherical balloon is inflated with gas at the rate of 800 cubic centiermeters per minute. How fast…

A: The volume of spherical balloon is given by the formula, V=43πr3 where r is radius of the balloon.…

Q: a girl flies a kite at a height of 300ft. the wind carrying the kite horizontally away from her at a…

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Q: A Ferris wheel with a radius of 15 m is rotating at a rate of one revolution every two minutes.…

A: Follow the procedure given below.

Q: The legnth of a rectangle decreases at 3cm/sec, while its width increases at 2cm/sec. At a certain…

A: Given:     Length of a rectangle decreases at a rate of 3 cm/sec               dldt=-3 cm/sec…

Q: A man 6 ft tall is walking at the rate of 3 ft/s tov streetlight 18 ft high (see the accompanying…

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Q: The base of a 45-foot ladder is being pulled away from a wall at a rate of 6 feet per second. How…

A: Use Pythagoras theorem

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A: As per given by the question, There are given that 25 foot ladders is leaning against a vertical…

Q: A Ferris wheel with a radius of 5 m is rotating at a rate of one revolution every two minutes.…

A: