anyone have answers to Geometry Sem 2 2.5.3 Practice: Modeling: Wildlife Sanctuary?
YOUR ASSIGNMENT: Wildlife Sanctuary You are designing a path for traveling to one of the animal habitats in the wildlife sanctuary. Which of the following regions did you choose? Lion Habitat Hippo Habitat Elephant Habitat Make Sense of the Problem (3 Points: 1 Point for each answer) What do you know about the requirements for your two paths? What do you want to find out? What kind of answer do you expect? Making Sense of the Problem: Below is a graph that represents the wildlife sanctuary. The Crocodile River is represented by the line y = 4, and the center of each habitat is represented by a point. Analyze the Data: Path 1: You want path 1 to be a continuous distance of 1.5 km from the center of the habitat. 1. Path 1 represents what mathematical object? (1 point) 2. What is the radius of path 1? (1 point) 3. Draw a rough sketch of path 1 on your graph. (1 point) 4. Will path 1 intercept the Crocodile River? (1 point) Use the Circle Tool on the activity page to help. 5. What is the maximum radius of path 1 before it intercepts the Crocodile River? Use the Circle Tool on the activity page to help. (1 point) Maximum radius = __________ km Path 2: You want path 2 to be equidistant from the Crocodile River and the habitat you chose. 6. Path 2 represents what mathematical object? (1 point) 7. What is the mathematical name for the object that is defined by the Crocodile River (1 point) 8. What is the mathematical name for the object that is defined by your selected region? (1 point) 9. Draw a line that represents the shortest distance between your habitat's center point and the river. What is the midpoint of this line? (2 points) 10. This midpoint is the vertex (or bottom point) of your parabolic path. Draw the midpoint on your graph, then sketch the parabola that represents path 2. (1 point) Solving the Problem: Consider a point (x, y) that is on the path. Use the Parabola Tool on the activity page to help you visualize this point. 11. Using the distance formula , find the distance from the center of your habitat to the point (x, y). Write this equation. Your answer will contain x- and y-terms. (1 point) 12. What is the distance from the directrix (the Crocodile River) to the point (x,y)? Write this equation. Your answer will contain a y-term. (2 points) 13. Set these two distances equal to each other. (1 point) 14. Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square root
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