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The function f(t) = 65 sin (pi over 5t) + 35 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?

User Parakleta
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6 votes
Maximum: 100°; minimum: −30°; period: 10 hours
sin(πt/5) varies between -1 and 1, so f(t) varies between -30 and 100. P=2π/π/5=10
User Maulik Modi
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7.5k points
3 votes

Answer:

  1. Minimum and maximum temperatures are
    -30,100
  2. Time taken to complete one complete cycle is 10 hours.

Explanation:

The general sinusoidal periodic function is,


f(t)=a\sin (b(t+c))+d

here,

  1. amplitude = a,
  2. period =
    (2\pi)/(b),
  3. horizontal or phase shift = c,
  4. vertical shift = d,

Comparing this with the given function
f(t)=65\sin(\pi)/(5)x+35, we get

  1. amplitude = a = 65,
  2. period =
    (2\pi)/((\pi)/(5)) = 10,
  3. vertical shift = d = 35, so the axis of symmetry will be,
    y=35

The maximum and minimum temperatures will be,


=35\pm 65


=-30,100

Time taken to complete one complete cycle is the period, so it is 10 hours.

The function f(t) = 65 sin (pi over 5t) + 35 models the temperature of a periodic-example-1
User Surya Sasidhar
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8.7k points

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