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Answer:
- equation: d(h) = 0.25|h -1600| -400
- depth is 250 ft at 1000 ft and 2200 ft from the west edge
Step-by-step explanation:
The crater shape can be modeled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.
d(h) = 0.25×|h -1600| -400
We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.
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At a depth of 250 ft, the distance from the west edge can be found from ...
-250 = 0.25|h -1600| -400
150 = 0.25|h -1600| . . . . . . . . add 400
600 = |h -1600| . . . . . . . . . . . multiply by 4
This resolves to two equations:
- -600 = h -1600 ⇒ h = 1000
- 600 = h -1600 ⇒ h = 2200
The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.
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<em>Comment on the equation</em>
We have chosen to make depths be negative numbers. If you want the equation to give positive numbers for depth, multiply it by -1:
d = 400 -0.25×|h -1600|
