Mathematical Problems Involving Graphs and Equations

The content includes a set of mathematical problems related to graphs, equations, and modeling of paths using given equations. These problems involve finding distances, heights, and intersection points based on the provided graph representations. The scenarios involve water sprinklers watering lawns, with questions on distances, heights, and potential impact points on a man standing near the sprinkler. The problems utilize equations to model the paths of the water jets and require mathematical calculations and interpretations for solutions.

• Mathematics
• Graphs
• Equations
• Modeling
• Water Sprinkler

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Uploaded on Sep 25, 2024 | 0 Views

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1. Each graph below crosses the x axis twice like the diagram to the right Find the length of the GREEN line -this is the distance between the two x-intercepts. 0 Find the length of the GREEN line y = (x 5)(x + 3) y = (x 2)(x + 6) y = (x + 5)(x + 3) y = (x + 2)(x + 6) y = (x + 5)(x 3) y = (x + 2)(x 6) y = (x 5)(x 3) y = (x 5)(x + 2) y = (x 2)(x 6)

2. Match the equation with the graph 3 2 2 1 y = (x 2)(x 4) 1 0 0 2 4 6 -8 -6 -4 -2 -1 -1 y = (x + 2)(x + 4) y = (x + 2)(x + 4) y = (x 2)(x 4)

3. A water sprinkler is used to water a lawn. It creates a path modelled by the equation 8m y = 0.5(4 x)(4 + x) Both scales on the graph are in metres 1) How far away does the water land from that water sprinkler? Water jet 0 8m 2) What is the highest point the water sprinkler can reach? 3) A man, 1.7 metres tall is standing 0.5 metres from the water jet, will he be hit by the water jet?

4. A water sprinkler is used to water a lawn. It creates a path modelled by the equation 10 8 y = 0.5(4 x)(4 + x) 6 Both scales on the graph are in metres 4 1) What is the furthest distance the water can reach from the water sprinkler? 2 Water jet 4 3 2 1 0 1 2 3 4 2) What is the highest point the water sprinkler can reach? 2 4 3) A man, 1.7 metres tall is standing 0.5 metres from the water sprinkler, will he be hit by the water sprinkler? 6

5. A water sprinkler is used to water a lawn. The water is released from a pump h metres from the ground. It lands 7.5m from where it released. It creates a path modelled by the equation Water jet y = 0.5(4 x)(4 + x) Both scales on the graph are in metres h 0 7.5 1) Find h 2) What is the highest point the water sprinkler can reach?

6. A water sprinkler is used to water a lawn. The water is released from a pump h metres from the ground. It lands 7.5m from where it released. It creates a path modelled by the equation Water jet y = 0.5(4 x)(4 + x) Both scales on the graph are in metres h 0 7.5 1) Find h 2) What is the highest point the water sprinkler can reach?