2. A large dam both gains and loses water. The graph below shows the net rate...

 

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2. A large dam both gains and loses water. The graph below shows the net rate at which the reservoir gains water. The units are megalitres/day R(t) = net gain of water by reservoir 4 t ( days ) -2 1 2 3 4 5 7 8 10 The formula for the graph is R(t) 2 2 cos(t) - 3 sin(0.2t) a) Does the reservoir gain or lose water from the start of day 0 to the end of day 2 (you can see this from the graph) ? b) Write down the integral that represents the net gain of water from the start of day 0 to the end of day 8 (be careful of the limits). Evaluate this integral. 2. A large dam both gains and loses water. The graph below shows the net rate at which the reservoir gains water. The units are megalitres/day R(t) = net gain of water by reservoir 4 t ( days ) -2 1 2 3 4 5 7 8 10 The formula for the graph is R(t) 2 2 cos(t) - 3 sin(0.2t) a) Does the reservoir gain or lose water from the start of day 0 to the end of day 2 (you can see this from the graph) ? b) Write down the integral that represents the net gain of water from the start of day 0 to the end of day 8 (be careful of the limits). Evaluate this integral.