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Class Notes Sec 2'6

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Example 5: An airplane is flying on a flight path that will take ... a rate of 400 miles per hour when s = 10 miles, what is the. speed of the plane? ... – PowerPoint PPT presentation

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Title: Class Notes Sec 2'6


1
Objective Use related rates to solve real life
problems Standards 12.4.3 12.6.5
Class Notes Sec 2.6
r
  • In a conical tank, suppose that the height is
  • changing at a rate of 0.2 foot per minute and
  • that the radius is changing at a rate of 0.1
    foot
  • per minute. What is the rate of change in the
  • volume when the radius is 1 foot and the height
  • is 2 feet?

h
r
h
2
2. Example 2 Suppose x and y are both
differentiable functions of t and are related
by the equation y x2 3. Find dy/dt when x
1, given that dx/dt 2 when x 1.
3
3. Example 3 A pebble is dropped into a calm
pond, causing ripples in the form of
concentric circles. The radius of the outer
ripple is increasing at a constant rate of 1
foot per second. When is the radius 4 feet,
at what rate is the total area A of the
disturbed water changing?
4
  • Example 4 Air is being pumped into a spherical
    balloon at a rate
  • of 4.5 cubic feet per minute. Find the rate of
    change of the
  • radius when the radius is 2 feet.

5
  • Example 5 An airplane is flying on a flight
    path that will take
  • it directly over a radar tracking station. If s
    is decreasing at
  • a rate of 400 miles per hour when s 10 miles,
    what is the
  • speed of the plane?

6
6. Example 6 Find the rate of change in the
angle of elevation of a camera that is 2000 feet
from the lift off of a space shuttle that is
rising vertically according to the position
equation s 50t2 where s is measured in feet and
t is measured in seconds.
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