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Exam 3: Section 6: Differentiation

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In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. At what time will the object reach the ground level? In a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. At what time will the object reach the ground level?

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Question 1
Correct Answer:
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E

Find Find at the point for the equation . at the point Find at the point for the equation . for the equation Find at the point for the equation . .

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Question 2
Correct Answer:
Verified

C

Find the derivative of the function Find the derivative of the function . .

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Question 3
Correct Answer:
Verified

D

Find the derivative of the function Find the derivative of the function . .

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Question 4

Find the derivative of the function Find the derivative of the function . .

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Question 5

Find an equation of the tangent line to the graph of Find an equation of the tangent line to the graph of at the point . at the point Find an equation of the tangent line to the graph of at the point . .

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Question 6

Find the derivative of the function Find the derivative of the function . .

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Question 7

An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places. and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places. when An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places. . Round your answer to three decimal places. An airplane flies at an altitude of 6 miles towards a point directly over an observer. Consider and x as shown in the following figure. The speed of the plane is 400 miles per hour. Find when . Round your answer to three decimal places.

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Question 8

Find Find at the point for the equation . at the point Find at the point for the equation . for the equation Find at the point for the equation . .

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Question 9

A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall. with the perpendicular from the light to the wall. A petrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes an angle of with the perpendicular from the light to the wall.

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Question 10

Find the slope-intercept form of the equation of the line tangent to the graph of Find the slope-intercept form of the equation of the line tangent to the graph of . .

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Question 11

Find the derivative of the function Find the derivative of the function . .

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Question 12

Find the derivative of the function Find the derivative of the function . .

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Question 13

In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the camera when In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places. . Round your answer to four decimal places. In a free-fall experiment, an object is dropped from a height of 144 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t = 0. Find the rate of change of the angle of elevation of the camera when . Round your answer to four decimal places.

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Question 14

A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write as a function of x. as a function of x. A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write as a function of x.

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Question 15

An airplane flies at an altitude of 14 miles toward a point directly over an observer. Consider An airplane flies at an altitude of 14 miles toward a point directly over an observer. Consider and x as shown in the following figure. Write as a function of x. and x as shown in the following figure. Write An airplane flies at an altitude of 14 miles toward a point directly over an observer. Consider and x as shown in the following figure. Write as a function of x. as a function of x. An airplane flies at an altitude of 14 miles toward a point directly over an observer. Consider and x as shown in the following figure. Write as a function of x.

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