F(x)=4x+1 g(x)=−4x−1 Write g in terms of f
1 answer:
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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, = 520 gallons
At t = 6 the volume in the tank, y = Minimum volume, = 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
Answer:
Teena is 14.5 years old and her brother is 17.5 years old.
Step-by-step explanation:
Let her brother's agebe the base unit (1 unit)
Therefore, Teena's age will be 1u - 3
Total age: 1u + 1u - 3 = 2u - 3
2u - 3 = 32
2u = 35
1u = 17.5
Her brother is 17.5 years old, and Teena is 17.5 - 3 = 14.5 years old.
