Question

A computer can sort x objects in t seconds, as modeled by the function below:

t=0.005x^2+0.002x

How many objects are required to keep the computer busy for exactly 9 seconds?

Round to the nearest whole object.

Answer 1

t = 9 = 0.005x^2 + 0.002x

0.005x^2 + 0.002x - 9 = 0

To solve this quadratic equation divide by 0.005

x^2 + 0.4x - 1800 = 0

x = {-b +/- √[b^2 -4ac] } / 2a = {-0.4 +/-√[0.16 + 7200]} / 2 = { - 0.4 +/- 84.85}/2 =

Use only the positive result: x = 42.2 = 42

Answer: 42