To find the minimum distance between the comet and Earth, we need to find the minimum value of the function g(x) over the interval 0 ≤ x ≤ 30 .
First, note that csc(x) is always greater than or equal to 1, so the minimum value of the function occurs when csc(π/2) = 1 . This happens when x = 15 days.
Plugging x = 15 into the function g(x) , we get:
g(15) = 150,000csc(π/2) = 150,000
Therefore, the minimum distance between the comet and Earth is 150,000 kilometers and it occurs at x = 15 days.
This corresponds to the constant 150,000 in the equation.
A laser rangefinder is locked on a comet approaching Earth. The distance g(x)
, in kilometers, of the comet after x
days, for x
in the interval 0
to 30
days, is given by g(x)=150,000csc(π30x)
What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond?
1 answer