A sports trainer has monthly costs of $80 for phone service and $40 for his website and advertising. In addition he pays a $15 fee to the gym for each session in which he works with a client. Required:
a. Write a function representing the average cost
b. Find the number of sessions the trainer needs if he wants the average cost to drop below $16 per session.

Step-by-step explanation:

The average cost for the training session provided he is a sports trainer can be computed as follows:

Let's assume that;

average cost = C(x)

the no. of session = x

Then:

Now, suppose the trainer wants the average cost C(x) to drop below $16;

Then, we have the following function:

By cross multiply:

120 + 15x ≤ 16x

120 ≤ 16x - 15x

120 ≤ x

Therefore, the required no. of session, if the average cost should drop below $16, is 120.

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2