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A map is drawn with a scale of 1/2 inch to 5 actual. miles. If the map distance is 8 inches, whats the actual. distance
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Answer:
Step-by-step explanation:
Given
Population changes exponentially
------1
-----2
divide 1 & 2 we get
Substitute in 1 we get
Thus
See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
