F(x) = (1/2)x + 4
Plug y in for f(x).
y = (1/2)x + 4
Swap x and y.
x = (1/2)y + 4
Solve the equation for y =.
Subtract 4 from both sides.
x - 4 = (1/2)y
Multiply each term 2.
2x - 8 = y
Plug f^-1(x) in for y.
f^-1(x) = 2x - 8
f^-1(4) = 2(4) - 8
f^-1(4) = 0
Answer: it will take 9 hours to empty the pool.
Step-by-step explanation:
The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is
30 × 18 × 4 = 2160 ft³
If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + d(n - 1)
Where
a represents the first term of the sequence(initial amount of water in the pool when completely full).
d represents the common difference(rate at which it is being pumped out)
n represents the number of terms(hours) in the sequence.
From the information given,
a = 2160 degrees
d = - 216 ft3
Tn = 0(the final volume would be zero)
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
0 = 2160 - 216 (n - 1)
2160 = 216(n - 1) = 216n + 216
216n = 2160 - 216
216n = 1944
n = 1944/216
n = 9
