1. At a certain instant, the length of a rectangle is 3 inches and is increasing...

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1. At a certain instant, the length of a rectangle is 3 inches and is increasing at the rate of 1 inch per minute. At the same instant, the width is 2 inches and is decreasing at the rate of .5 inches per minute. Is the area increasing or decreasing? 2. A boat is pulled into a dock by a rope with one end attached to the front of the boat and the other end passing through a ring attached to the dock at a point 5 feet higher than the front of the boat. The rope is being pulled through the ring at the rate of 0.6 feet per second. How fast is the boat approaching the dock when 13 feet of rope are out? 3. Suppose you take a car trip, traveling east along a very long highway, starting at time t = 0. Let x t be the number of gallons of gasoline used during the first hours, and let s(t be the distance traveled in that time. Because you're using very cheap gasoline that's not good for the engine, your fuel efficiency (measured in miles/gallon) decreases as fuel is consumed. The graph of fuel efficiency as a function of gasoline used is shown in the graph below. ds dx 301 25 201 15 101 51 0 5 10 X 15 x (gallons) 20 1. At a certain instant, the length of a rectangle is 3 inches and is increasing at the rate of 1 inch per minute. At the same instant, the width is 2 inches and is decreasing at the rate of .5 inches per minute. Is the area increasing or decreasing? 2. A boat is pulled into a dock by a rope with one end attached to the front of the boat and the other end passing through a ring attached to the dock at a point 5 feet higher than the front of the boat. The rope is being pulled through the ring at the rate of 0.6 feet per second. How fast is the boat approaching the dock when 13 feet of rope are out? 3. Suppose you take a car trip, traveling east along a very long highway, starting at time t = 0. Let x t be the number of gallons of gasoline used during the first hours, and let s(t be the distance traveled in that time. Because you're using very cheap gasoline that's not good for the engine, your fuel efficiency (measured in miles/gallon) decreases as fuel is consumed. The graph of fuel efficiency as a function of gasoline used is shown in the graph below. ds dx 301 25 201 15 101 51 0 5 10 X 15 x (gallons) 20

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1 To determine whether the area is increasing or decreasing we need to calculate the rate of change of the area of the rectangle The area of a rectang... View the full answer