Ralph gets on a ferris wheel at the 6 o'clock position which is located 5 feet off of the ground. once in motion, the ralph's distance feom the ground varies from 5 feet to 25 feet off of the ground every 30 seconds. ( after 30 seconds he is at the 12 o'clock position)
a) sketch a graph of ralph's distance d from the ground over a 1 minute interv as a function of time t. assume t = 0 corresponds to a time wheb ralph was closed to the ground. remember to label your axis.
b) determine what the period, midline, amplitude, and horizontal phase shift.

The distance D from the ground follows a sine law, which begins at D=5 where t=0 and reaches a maximum of D=25 where t=30.

This implies that the sine function has an amplitude of 25-5=20, and a period of 30 seconds.

The resulting function is

In fact, this function:

Has a value of 5 where t=0:

Reaches the maximum at t=30:

Resets after 60 seconds:

So, the period is 60 seconds, the midline is 15 (the middle value between 5 and 25), the amplitude is 20, and there is no horizontal phase shift.

for this case we have the following polynomials:

where,

h (x): is the cost of producing x soccer balls

k (x): is the revenue of x soccer balls.

then the profit is given by:

substituting values we have:

rewriting we have:

answer:

an expression that represents the profit of producing soccer balls is:

a) 14x - 8