Respuesta :
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:
42 objects are required to keep the computer busy for exactly 9 seconds
Solution:
Given function is:
Computer can sort x objects in t seconds, as modeled by the function below:
[tex]t = 0.005x^2+0.002x[/tex]
We have to find number of objects required to keep the computer busy for exactly 9 seconds
Therefore t = 9
Substitute t = 9 in given function
[tex]9 = 0.005x^2+0.002x\\\\0.005x^2+0.002x - 9 = 0[/tex]
Let us solve the above equation by quadratic formula,
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text{ for } 0.005x^2+0.002x - 9 = 0 , \text{ we have } a = 0.005 ; b = 0.002 ; c = -9[/tex]
Substituting the values of a = 0.005 ; b = 0.002 ; c = -9 in above quadratic formula we get,
[tex]\begin{aligned}&x=\frac{-0.002 \pm \sqrt{0.180004}}{0.01}\\\\&x=\frac{-0.002 \pm 0.4242}{0.01}\\\\&x=\frac{-0.002+0.4242}{0.01} \text { or } x=\frac{-0.002-0.4242}{0.01}\\\\&x=42.22 \text { or } x=-42.62\end{aligned}[/tex]
Ignoring negative value,
x = 42.22 ≈ 42
Thus 42 objects are required to keep the computer busy for exactly 9 seconds
