Question

The temperature of a substance during an experiment can be modeled by the function f(x)=−7.5cos(πx30)+31.4 , where f(x) is the temperature °c and x is the number of minutes into the experiment. what is the greatest temperature the substance reached during the experiment?

Answer 1

38.9 degrees celsius

Answer 2

Answer :  $f(x)=38.9^0\ C$

Explanation :

It is given that,

The temperature of a substance during an experiment is given by a function as :

$f(x)=-7.5cos(\dfrac{\pi x}{30})+31.4$................(1)

Where,

f(x) is the temperature

and x is the time.

So, for getting a maximum temperature the substance reached during the experiment the value of $cos( \dfrac{\pi x}{30})$ should by minimum.

We know that the value of cos is minimum at $\pi$.

So, $cos( \dfrac{\pi x}{30})=cos\pi$

We get, x = 30

Put the value of x in equation (1)

$f(x) = -7.5cos(\dfrac{\pi \times 30}{30})+31.4$

Since, $cos \pi=-1$

$f(x)=38.9^0\ C$

So, the greatest value of temperature the substance reached during the experiment is $f(x)=38.9^0\ C$.