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 24 days, is given by g(x)=250,000csc(π/24x). b. Evaluate g(4). Enter the exact answer.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 24 days, is given by g(x)=250,000csc(π/24x).
b. Evaluate g(4).
Enter the exact answer.
g(4)=
c. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond?
The minimum distance between the comet and Earth is____________ km which is the stretching factor. It occurs at ____________ days.
d. Find and discuss the meaning of any vertical asymptotes on the interval [0,28].
x=
Step1
(b) g(x)= 250,000cosec(π/24x)
g(4)= 250,000cosec(π/24*4)
= 250,000cosec(π/96)
= 250,000cosec(1.875)
250000*30.56
= 764000
Note:
If g(x)= = 250,000cosec(π/24x)
= 250,000cosec(π/24*6)
= 250,000cosec(π/4)
= 250,000 cosec(2)
500000
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