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The vessel is filled with 1000 litres of...

The vessel is filled with 1000 litres of water at 8 a.m. The volume of water in this vessel at t hours after it is filled is observed to be `v(t=1000-200t+5t^(2)`. What is the rate of change of volume (i) at 8:a .m. (ii) at noon (12:00 p.m.)?

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To solve the problem, we need to find the rate of change of volume of water in the vessel at two specific times: at 8 a.m. (t = 0) and at noon (t = 4 hours). The volume of water in the vessel is given by the function: \[ v(t) = 1000 - 200t + 5t^2 \] ### Step 1: Differentiate the Volume Function To find the rate of change of volume with respect to time, we need to differentiate the volume function \( v(t) \) with respect to \( t \): \[ ...
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