The function for the height is

f(0) = 5 cos(0) + 7 = 5 + 7 = 12 (verified)
The period is T = 12 hours.
After 4 hours (t = 4), the height is

A graph of f(t) confirms the answer.
Answer: 4.5 ft
Answer:
200
Step-by-step explanation:
Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
Part 1)
we know that
The equation of the line in slope intercept form is equal to

we have

Isolate the variable y
subtract 2x both sides

Divide by B both sides

Part 2)
we know that
The equation of the line in slope intercept form is equal to

we have

Isolate the variable y
subtract 2x both sides

Divide by 8 both sides

Simplify

Answer:
240 cubic feet
Step-by-step explanation:
l×w×h
12×4=48
48×5=240
Drawing it out, as seen, using the Pythagorean theorem we get that w^2+l^2 (with w=width and l=length)=diagonal^2=24^2+l^2=40^2. Subtracting 24^2 from both sides, we get 40^2-24^2=l^2=1024. Square rooting both sides, we get l=32. Since the perimeter is 2w+2l, we get 32*2+24*2=64+48=112