(8 - 3i)(2 - 7i)=
16 x -56i - 6i + 21i^2
16 x -50i - 21
180^2 + 235^2 = (cliff base to point on bridge)^2
32400 + 55225 = 87625
so cliff base to point on bridge = sqrt of 87625.
Then notice 87625 + d^2 = (x+180)^2
since x^2 +235^2 = d^2,
substitute (x^2 + 235^2) for d^2, like this:
87625 + x^2 + 235^2 = (x+180)^2
87625 + x^2 + 55225 = x^2 + 360x + 32400
87625 + 55225 - 32400 = x^2 - x^2 +360x
360x = 110450
x = about 306.8 feet
h = x+180, so h = 486.8 feet
Remember d^2 = x^2 + 235^2, so
d^2 = 306.8^2 + 235^2
d^2 = 149354.6489
d = about 386.46 feet
Answer: it will take 6 months for both gyms to cost the same.
Step-by-step explanation:
Let m represent the number of months that it will take for the cost of both gyms be the same.
At one gym, there is a $12 start-up fee, and after that each month, m, at the gym costs $20. This means that the total cost for m months is
12 + 20m
At another gym, each month at the gym costs $22. This means that the total cost for m months is 22m
For both costs to be the same, the number of months would be
12 + 20m = 22m
22m - 20m = 12
2m = 12
m = 12/2 = 6