The amount of water that flows from the tank during the first 35 minutes is 4550 liters.
To find the amount of water that flows from the tank during the first 35 minutes, we need to calculate the definite integral of the rate function r(t) over the interval [0, 35].
Here's how we can solve it:
Step 1: Define the definite integral.
We want to find the amount of water that flows from the tank between time t = 0 and t = 35. Therefore, the definite integral is written as:
∫(200 - 4t) dt from 0 to 35
Step 2: Evaluate the definite integral.
We can integrate the function using the power rule:
∫(200 - 4t) dt = 200t - 2t^2 from 0 to 35
Now, we substitute the limits of integration:
(200 * 35 - 2 * 35^2) - (200 * 0 - 2 * 0^2) = 7000 - 2450 = 4550
Therefore, the amount of water that flows from the tank during the first 35 minutes is 4550 liters.
Complete question:
Water flows from the bottom of a storage tank at a rate of r(t) = 200 − 4t liters per minute, where 0 ≤ t ≤ 50. find the amount of water that flows from the tank during the first 35 minutes.