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((\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( (\pi x)/(30))` should by minimum.

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

So,
`cos( (\pi x)/(30))=cos\pi`

We get, x = 30

Put the value of x in equation (1)

`f(x) = -7.5cos((\pi * 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`.