The water level of a strait is changing at a rate of (3)/(2)sin(2-(t)/(2)) centimeters per hour (where t is the hours since midnight). By approximately how many centimeters does the water level change between t=1 and t=4 ? Choose 1 answer: (A) 1.4 (B) 1.5 (C) 2.8 (D) 3.0

Question

The water level of a strait is changing at a rate of  (3)/(2)sin(2-(t)/(2)) centimeters per hour (where  t is the hours since midnight). By approximately how many centimeters does the water level change between  t=1 and  t=4 ? Choose 1 answer: (A) 1.4 (B) 1.5 (C) 2.8 (D) 3.0

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We are given the rate of change of the water level as a function of time, which is (3/2)sin(2-(t/2)) centimeters per hour. We need to find the total change in water level from t=1 to t=4.Calculate initial change: Calculate the change in water level at the start time t=1. We substitute t=1 into the rate function to find the water level change rate at that time. Change rate at t=1: (3/2)sin(2-(1/2)) = (3/2)sin(1.5)Calculate final change: Calculate the change in water level at the end time t=4. We substitute t=4 into the rate function to find the water level change rate at that time. Change rate at t=4: (3/2)sin(2-(4/2)) = (3/2)sin(0)Identify mistake: Realize a mistake in the approach. The values calculated in Step 2 and Step 3 are the rates of change at specific times, not the total change in water level over the time interval. We need to integrate the rate function from t=1 to t=4 to find the total change in water level.

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