Hello,
Let's assume top left corner: A
top right corner : B
Bottom right corner: C
Bottom left corner :D
M= middle of [CD]
ABM is a triangle rectangular isocel:
(3√2)²+(3√2)²=y²
==>y²=2*9*2
==>y²=36
==>y=6
The triangle BCM is rectangular with MB=3√2, MC=y/2=3
x²+3²=(3√2)²
==>x²=9*2-9
==>x²=9
==>x=3
Answer:
Her initial position was:
-29ft
Where we use the minus sign because this is below the ocean's surface.
Now we also know that she keeps descending at a rate of -29ft per minute, then if she keeps descending for t minutes, her position will be:
P(x) = -29ft - 29ft/min*t
Now, we also know that she does not want to descend more than 81ft below the ocean's surface, then we have the inequality:
P(x) ≥ -81ft
-29ft - 29ft/min*t ≥ -81ft
Now let's isolate t in one side:
- 29ft/min*t ≥ -81ft + 29ft = -52 ft
- 29ft/min*t ≥-52 ft
t ≤ -52ft/(- 29ft/min) = 1.79 min
Then the maximum amount of time that she can keep descending is 1.79 minutes.
