Question

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The given function models the number of cars that are put through a quality control test each hour at a car production factory. Some cars are kept overnight at the quality control facility, while some cars arrive at different times of the day.


c(t)= -t^2+8t+20


For how many hours does the quality control facility operate each day?


The best form of the equation for finding the required information is (factored form, standard form, vertex form) . The quality control facility operates for (5,10,8,12) hours each day.

Answer 1

Answer:

The quality control facility operates for 10 hours each day.

Step-by-step explanation:

The given function models the number of cars that are put through a quality control test each hour at a car production factory.

The given function is

$c(t)= -t^2+8t+20$

We need to find the number of hours does the quality control facility operate each day.

Rewrite the given function it factored form.

$c(t)= -t^2+(10t-2t)+20$

$c(t)= (-t^2+10t)+(-2t+20)$

Taking out the common factors from each parenthesis.

$c(t)= -t(t-10)-2(t-10)$

$c(t)= (t-10)(-t-2)$

$c(t)=-(t-10)(t+2)$

The factored form of given function is c(t)=-(t-10)(t+2).

Equate the function equal to 0 to find the x-intercept.

$0=-(t-10)(t+2)$

$t-10=0\Rightarrow t=10$

$t+2=0\Rightarrow t=-2$

Number of hours cannot be negative. So from t=0 to t=10 quality control facility operate the cars.

Therefore the quality control facility operates for 10 hours each day.