Question

the volume in a tank varies periodically. At t=0 is at its maximum of 520 gallomns and at t=6 it is at its miximum of 170 gallons. A function in the form y=Acos(Bx)+C can be used to model this situation.Based on the information given determine the values of A,B and C

Answer 1

Answer:

A = 175, B = π/6, C = 345

Step-by-step explanation:

The given variation of the volume in the tank and time includes are;

At t = 0 the volume in the tank, y = Maximum volume, $y_{max}$ = 520 gallons

At t = 6 the volume in the tank, y = Minimum volume, $y_{min}$ = 170 gallons

The function that models the situation is y = A·cos(B·x) + C

Given that the function that models the situation is the cosine function, we have;

A = The amplitude = (The maximum - The minimum)/2

∴ A = (520 - 170)/2 = 175

A = 175

The period = The time to change from maximum to minimum = 2 × The time to change from maximum (t = 0) to minimum (t = 6)

∴ The period = 2 × (6 - 0) = 12

The period = 12 seconds = 2·π/B

∴ B = 2·π/12 = π/6

B = π/6

C = The vertical shift = Th minimum + A = (The maximum + The minimum)/2

∴ C = (520 + 170)/2 = 345

C = 345