The number of gallons of water in the tank at t=10 is
... W(10) = 160,000 -10(8000 -10) = 80100
The number of gallons of water in the tank at t=10.5 is
... W(10.5) = 160,000 -10.5(8000 -10.5) = 76110.25
The rate of change over the interval is
... (W(10.5) - W(10))/(10.5 - 10) = (76110.25 - 80100)/(0.5) = -7979.5
The average rate of change in the number of gallons of water in the tank over the interval is -7979.5 gal/min.
The sign is negative, so the amount of water is decreasing.
Given:
The equation for the area of the first option is:
Where x is the side length of the current square park.
To find:
The side length of the current square park.
Solution:
We have,
It can be written as:
Splitting the middle term, we get
We know that the side length of a park cannot be negative. So, the only possible value of x is 320.
Therefore, the most direct method to solve the given equation is splitting the middle term and the side length of the current square park is 320 meters.