Photo AI
The graph below gives the volume, in litres, of water in a container / seconds after the water starts to fill the container - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 2
Question 21
The graph below gives the volume, in litres, of water in a container / seconds after the water starts to fill the container. (a) Calculate an estimate for the gradi... show full transcript
Worked Solution & Example Answer:The graph below gives the volume, in litres, of water in a container / seconds after the water starts to fill the container - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 2
Step 1
Calculate an estimate for the gradient of the graph when t = 17.5
Answer
To estimate the gradient at t = 17.5 seconds, we first identify the coordinates of the point on the graph at this time. Observing the graph, we can approximate that when t = 17.5, the volume V is around 20 litres.
Next, we will estimate the gradient using two points near t = 17.5 seconds, for example, (15 seconds, 17 litres) and (20 seconds, 22 litres).
The formula for gradient between two points (x1, y1) and (x2, y2) is:
Substituting the points:
- (x1, y1) = (15, 17)
- (x2, y2) = (20, 22)
The calculation is:
Thus, the estimated gradient at t = 17.5 seconds is 1 litre per second.
Step 2
Describe fully what the gradient in part (a) represents.
Answer
The gradient of the graph represents the rate of change of volume with respect to time. In this context, since the volume is measured in litres and time is measured in seconds, the gradient provides the flow rate of water into the container.
Specifically, a gradient of 1 litre per second indicates that at t = 17.5 seconds, water is flowing into the container at a rate of 1 litre every second.