Question

Water flows from a hose into an empty bucket at a rate of f(t) = for each question, round your answer to 3 decimal places. v(t) = 5 gallons/minute, beginning at t = 1. (a) How much water has flowed into the bucket at time t = 5? (Remember the water starts flowing at t = 1) gallons (b) If the volume of the bucket is 5 gallons, at what time t will the bucket be full of water? t = minutes. Submit answer Q Search ᵃ) 20.833 gallons; 2.708 minutes

b) 25.833 gallons; 3.708 minutes
c) 22.500 gallons; 3.000 minutes
d) 20.000 gallons; 2.500 minutes

Answer 1

Assuming the flow rate is a constant 5 gallons per minute starting from t = 1 minute, 20.000 gallons of water would have flowed into the bucket by t = 5 minutes, and the bucket would be full at t = 2 minutes.

Step-by-step explanation:

There seems to be a typo in the given function for the water flow rate; however, based on the context, let's assume that f(t) = 5 gallons/minute starting at t = 1 minute. To find out how much water has flowed into the bucket by t = 5 minutes, we integrate the flow rate from t = 1 to t = 5.

1. Calculate the total volume of water: V = ∫_1^5 f(t) dt = ∫_1^5 5 dt = 5(t)|_1^5 = 5(5) - 5(1) = 20 gallons
2. To determine when the bucket will be full, we need to find t when V = 5 gallons. Since the flow rate is constant, V = f(t) ∙ (t - 1), setting V equal to the bucket's volume and solving for t: 5 = 5 ∙ (t - 1), so t - 1 = 1 which implies t = 2 minutes.

Therefore, (a) the bucket has 20.000 gallons of water at t = 5 minutes, and (b) the bucket will be full at t = 2 minutes.