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Chapter 4 | Applications of Derivatives
previous equation, we arrive at the equation
600=5000 ⎛
⎞ ⎠ dθ
⎝ 26 25
dt .
Therefore, dθ
dt = 3 26
rad/sec.
4.3 What rate of change is necessary for the elevation angle of the camera if the camera is placed on the ground at a distance of 4000ft from the launch pad and the velocity of the rocket is 500 ft/sec when the rocket is 2000ft off the ground?
In the next example, we consider water draining from a cone-shaped funnel. We compare the rate at which the level of water in the cone is decreasing with the rate at which the volume of water is decreasing. Example 4.4 Water Draining from a Funnel Water is draining from the bottom of a cone-shaped funnel at the rate of 0.03ft 3 /sec. The height of the funnel is 2 ft and the radius at the top of the funnel is 1ft. At what rate is the height of the water in the funnel changing when the height of the water is 1 2 ft?
Solution Step 1: Draw a picture introducing the variables.
Figure 4.6 Water is draining from a funnel of height 2 ft and radius 1 ft. The height of the water and the radius of water are changing over time. We denote these quantities with the variables h and r , respectively.
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