Answer : [tex]f(x)=38.9^0\ C[/tex]
Explanation :
It is given that,
The temperature of a substance during an experiment is given by a function as :
[tex]f(x)=-7.5cos(\dfrac{\pi x}{30})+31.4[/tex]................(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 [tex]cos( \dfrac{\pi x}{30})[/tex] should by minimum.
We know that the value of cos is minimum at [tex]\pi[/tex].
So, [tex]cos( \dfrac{\pi x}{30})=cos\pi[/tex]
We get, x = 30
Put the value of x in equation (1)
[tex]f(x) = -7.5cos(\dfrac{\pi \times 30}{30})+31.4[/tex]
Since, [tex]cos \pi=-1[/tex]
[tex]f(x)=38.9^0\ C[/tex]
So, the greatest value of temperature the substance reached during the experiment is [tex]f(x)=38.9^0\ C[/tex].
