Brett is joining a new gym. he can join power plus or heavy hulk. at power plus, it will cost $34.65 per month, plus a sign-up fee of $23.00. at heavy hulk, it will cost $34.90 per month, plus a sign-up fee of $38.00. right now, heavy hulk is cutting their sign-up fee in half for new members. if brett signs up at a gym today, after how many months will the cost of the memberships be the same?

Let n be the number of months that the cost of the memberships fee be the same. Such that for Power plus, the cost would be
                                      23 + 34.65n
For Heavy Hulk, after cooking the new members fee will have a total cost of,
                                   19 + 34.90n
Equating the two,
                                23 + 34.65n = 19 + 34.90n
The value of n from the equation above is 16. Thus, after 16 months the membership costs will be the same. 

435 ft

Step-by-step explanation:

Reference angle = <P = 49° (angle of elevation)

Opposite side = 500 ft

Adjacent side = d = ?

Apply trigonometric function, TOA.

This:

Tan P = opp/adj

Tan 49 = 500/d

d × Tan 49 = 500

d = 500/Tan 49

d = 434.643369 ≈ 435 ft (to the nearest foot)