The function f(t) = 33 sin (pi over 2t) − 20 models the temperature of a periodic chemical reaction where t represents time in hours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take?

Maximum: 53°; minimum: −13°; period: 4 hours

Maximum: 33°; minimum: 20°; period: pi over 2 hours

Maximum: 13°; minimum: −53°; period: 4 hours

Maximum: 35°; minimum: 35°; period: 8 hours

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Аноним Аноним · Answer 1 · 2017-08-07T16:06:58+02:00

Maximum is when pi / 2t = 1 so that's 33-20 = 13 degrees
minimum when pi/2t = -1 - that gives -33-20 = -53 degrees

Its C

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wagonbelleville wagonbelleville · Answer 2 · 2019-03-20T05:59:54+01:00

Answer:

C. Maximum: 13°; minimum: −53°; period: 4 hours

Step-by-step explanation:

The function modelling the temperature with respect to time is,

[tex]f(t)=33\sin (\frac{\pi}{2}t)-20[/tex]

It is required to find the maximum and minimum value of the temperature.

Since, we know,

[tex]-1\leq \sin x\leq 1[/tex] for all values of x.

Then, [tex]-1\leq \sin (\frac{\pi}{2}t)\leq 1[/tex] for all values of t.

Thus, we get,

Maximum value is obtained when [tex]\sin (\frac{\pi}{2}t)=1[/tex]

That is, [tex]\sin (\frac{\pi}{2}t)=1[/tex], [tex]f(t)=33-20=13[/tex].

So, maximum temperature is 13°

Minimum value is obtained when [tex]\sin (\frac{\pi}{2}t)=-1[/tex]

That is, [tex]\sin (\frac{\pi}{2}t)=1[/tex], [tex]f(t)=-33-20=-53[/tex].

So, minimum temperature is -53°

Also, we have,

If the function f(x) has period P, then the function f(bx) will have period [tex]\frac{P}{|b|}[/tex].

Since, [tex]\sin x[/tex] has period [tex]2\pi[/tex], then the given function have period [tex]\frac{2\pi }{\frac{\pi}{2}}[/tex] = 4.

So, entire cycle takes 4 hours.

Thus, option C is correct.