An oil tanker hits a reef and begins to leak oil. The resulting spill is circular in shape and increasing in size. If the radius of the spill is increasing at the rate of 6 m/sec, how fast is the area of the spill increasing when the radius is 100 meters?

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A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

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

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A: Since there are multiple questions present, according to company policy we will be answering only…

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Q: A spherical balloon is being inflated at a rate of 20 cubic centime- ters of air per second. How…

A: We will use chain rule and the information provided.

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A: Let r be the radius of spherical ballon

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A: Using volume  of cone and applications of derivative idea we solve this

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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 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

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Q: A stone dropped into a still pond on a calm day sends out a circular ripple. If the radius increases…

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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 stone is dropped into a quite lake and waves move in a circle at a speed of 3.5 cm/sec.At the…

A: Since, a stone is dropped into a quite lake and waves move in a circle ata speed of 3.5 cm/sec at…

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…

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Q: A Ferris wheel with a radius of 13m is rotating at a rate of one revolution every 2 minutes. How…

A: Given thatRadius of the Ferris wheel is 13 mThe time period of the Ferries wheel is 2 min To find…

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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…

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Q: A spherical balloon is inflated so that its radius increases at a rate of cm/sec. How fast is the…

A: Volume of the sphere is given by:  V = 43πr3

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A: given that plane is flying horizontally at an altitude of 1mi speed=500 mi/h find the rate at which…

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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 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: If a ladder is leaning against a wall and when its base starts to slide away it makes a triangle…

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: A 13 feet ladder is leaning against the wall. The top slips down the wall at a rate of 2 ft/s. The…

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Q: A water tank is in the form of a right circular cone with vertex down, 12 ft. deep and 6 feet across…

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Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3   (r = radius)   Now differentiate with respect to L,…

Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Firstly we will draw the diagram for given information and then find the required as shown below

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: A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A: Given a ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed…

Q: A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in…

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Q: The radius of a sphere, initially zero, increases at the rate of 4 feet per second. Find how fast…

A: Solution :Given  the adius of a sphere, initially zero, increases at the rate of 4 feet per…

Q: Suppose a 10-foot ladder is leaning against a building. The bottom of the ladder slides away from…

A: Solution:-

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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