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victus00 [196]
3 years ago
7

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 t

emperature °c and x is the number of minutes into the experiment. what is the greatest temperature the substance reached during the experiment?
Physics
2 answers:
vekshin13 years ago
6 0
38.9 degrees celsius
ololo11 [35]3 years ago
6 0

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.

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