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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 can take two points on the graph that are close to this time.
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Identify the point on the graph at t = 17.5 seconds. Here, we can approximate that the volume is around 22 litres.
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Choose another point for calculation, let’s say at t = 15 seconds where the volume is approximately 18 litres, and another point at t = 20 seconds where the volume is around 25 litres.
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The gradient ( ext{slope}) can be estimated using the formula:
ext{Gradient} = rac{ ext{Change in Volume}}{ ext{Change in Time}}
For the interval between 15 seconds (18 litres) and 20 seconds (25 litres):
ext{Gradient} = rac{25 - 18}{20 - 15} = rac{7}{5} = 1.4
Thus, the estimated gradient at t = 17.5 seconds is approximately 1.4 litres per second.
Step 2
Describe fully what the gradient in part (a) represents
Answer
The gradient of the graph represents the rate at which the volume of water in the container is increasing with respect to time. Specifically, a gradient of 1.4 litres per second indicates that at t = 17.5 seconds, the volume of water in the container is increasing by 1.4 litres for every additional second that passes. This means the water is being added to the container consistently at this rate at that specific moment.