1. When oil was spilled out in the middle of a lake, it spread out on the surface of the water in a circular pattern. The radius of the circular pattern increased at a rate of 3.5 feet per minute. (r(t) = 3.5t ft/min How fast was the area of the circular pattern increasing per minute? Construct the composite function to show how the area was increasing each minute. (A(r) = ar ft2 /min ). Find the radius of the circular pattern of oil 150 seconds after the oil starts to spread. Find the area of the circular pattern of oil 4 minutes after the oil starts to spread.

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A: topic - application of derivatives

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A: We need to find rate of change.

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Q: consider an isosceles triangle of base 16 and edges z, and assume that z is a function of time. if z…

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Q: The legs of an isosceles right triangle increase in length at a rate of 6 m/s a. At what rate is the…

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Q: . Sand is being sifted onto a conical pile at the rate of 0.3 ft /sec. It was also observed thát at…

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Q: 1. of the balloon is increasing when the diameter of the balloon is 20 cm. Air is being pumped into…

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Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: The legs of an isosceles right triangle increase in length at a rate of 5 m/s. a. At what rate is…

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A: NOTE: Refresh your page if you can't see any equations. . here we have y=4 when s=5, s'=300 km/h

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A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: #13 The radius of a sphecical blloon is increasing at the cate of 3inches per second, How fast is…

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Q: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

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Q: Sand is being sifted onto a conical pile at the rate of 0.3 ft/sec. It was also observed thát at any…

A: here we use the volume of the cone  and, use differentiateion dV/dt = 0.3 ft3 / sec

Q: 7. A conical pile is formed by pouring sand at a rate of 30 cm/s. When its base diameter and…

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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.

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Q: 1. Suppose that oil spills from a container and spreads in a circular pattern. If the radius of the…

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Q: a bush fire is burning a circular area whose radius is increasing at a rate of 3ft/min. how fast is…

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Q: ending from the surface. What is the best estimate of its instantaneous change in depth at t = 3 sec

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Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

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A: solution:- draw a right angle triangle:-