Question

A reservoir for an automatic sprinkler begins with 12 gallons of water. Some of this water evaporates before the reservoir is filled up. After the reservoir is filled, the sprinkler then turns on to water the plants. The amount of water, y, in gallons, in the reservoir can

be modeled by the equation y = -x3 + 6x2 - 2x + 12 where x is the amount of time in minutes.

a. Solve -x3 + 6x2 - 2x + 12 = 0.

b. Determine which zeros, if any, make sense for the context. Justify your decision.

Answer 1

Explanation:

a. Solving -x³+ 6x² - 2x + 12 = 0 can be complex without specific numerical methods, but I can help you with an approximate solution. One root of this equation is around

x≈2.14 (rounded to two decimal places).

b. In the context of time (minutes), we discard negative solutions. Therefore, the only relevant solution for this problem is

x≈2.14 minutes.