The rate of water flowing into a tank is given by $R(t) = 5t - t^2$ litres per minute, where $t$ is the time in minutes from when the flow starts. Initially, the tank contains 10 litres of water.
a. Find an expression for the volume of water, $V(t)$, in the tank at time $t$ minutes.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Application of intergration. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
application of integration to problems involving finding a function from a known rate of change given a boundary condition, calculation of the area of a region under a curve and simple cases of areas between curves, average value of a function and other situations.
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