Question

2 fill in the blank 3 points
the table below shows the height of water in a tank, in inches, measured every three hours over a 24-hour period while the tank is being drained and then refilled.
t(hours) h(inches)
0 120
3 93
6 72
9 57
12 48
15 45
18 48
21 57
24 72

1. is there any symmetry, if so where? type your answer... x= type your answer...
2. is there a relative maximum, if so where? type your answer... x= type your answer... y= type your answer...
3. is there a relative minimum, if so where? type your answer... x= type your answer... y= type your answer...

Explanation:

Step1: Check for symmetry

Compare h(t) and h(24-t):
$h(0)=120, h(24)=72$; $h(3)=93, h(21)=57$; $h(6)=72, h(18)=48$; $h(9)=57, h(15)=45$; $h(12)=48$.
Mirror values across x=12: $\frac{0+24}{2}=12$, $\frac{3+21}{2}=12$, etc.

Step2: Identify relative maximum

Find highest h(t):
Max value is 120 at t=0.

Step3: Identify relative minimum

Find lowest h(t):
Min value is 48 at t=12.

Answer:

1. Yes, symmetry about x=12; x=12
2. Yes, at x=0; x=0, y=120
3. Yes, at x=12; x=12, y=48