Group Chat
1. Dmitri loves guitar and needs to play a base amount of 80 minutes� per week. He also notices that for every minute of VLE lesson that � he is part of, he needs ¼ of a minute of additional time playing the � guitar, in order to remain sane. �a. Using proper notation, write this as a function. Define each variable.�b. Write a reasonable domain for a week of VLE.� Based on this domain, state the range. �c. Use your function to find the hours of guitar playing that � he will need to do after a VLE week during which he � attended twelve and a half full classes.
2. Your parents left for a holiday in Spain and left you with 512 boxes of frozen � pelmeņi in the freezer. You eat one box of pelmeņi for each meal, every day.�a. Using proper notation, write this as a function of boxes � remaining dependent on days. Define each variable.�b. Write a reasonable domain and range for this function.�c. Use your function to calculate what day of the week it is� if your parents left on a Monday morning and, when you � check your Pelmeni supply, you find that there are 201 left.
1. Dmitri loves guitar and needs to play a base amount of 80 minutes� per week. He also notices that for every minute of VLE lesson that � he is part of, he needs ¼ of a minute of additional time playing the � guitar, in order to remain sane. �a. Using proper notation, write this as a function. Define each variable.�b. Write a reasonable domain for a week of VLE.� Based on this domain, state the range. �c. Use your function to find the hours of guitar playing that � he will need to do after a VLE week during which he � attended twelve and a half full classes.
2. Your parents left for a holiday in Spain and left you with 512 boxes of frozen � pelmeņi in the freezer. You eat one box of pelmeņi for each meal, every day.�a. Using proper notation, write this as a function of boxes � remaining dependent on days. Define each variable.�b. Write a reasonable domain and range for this function.�c. Use your function to calculate what day of the week it is� if your parents left on a Monday morning and, when you � check your Pelmeni supply, you find that there are 201 left.
TODAY: � Two applied problems that combine � functions and quadratics -- great stuff ! ☺
Problem 1: � Kenzo Watanabe and the Akashi-Kaikyo Bridge
1. Use the given points to create a model for the suspension cable.� Change the model from y = …x form to function form, � using h(d) where h is height and d is horizontal distance
1. Use the given points to create a model for the suspension cable.� Change the model from y = …x form to function form, � using h(d) where h is height and d is horizontal distance
2. Given that the two bridge towers are 283 meters in height, use your model to � find the length of the bridge span between the two towers. � ����Explain whether this solution makes sense in the context of the real-life situation.� (refer to the diagram on the graph above)
�Explain whether this solution makes sense in the context of the real-life situation.� (refer to the diagram on the graph above)
4. Kenzo runs at an average speed of 19 kilometers per hour. Find how many calories � Kenzo will burn when running the span between the two towers (one way).
4. Kenzo runs at an average speed of 19 kilometers per hour. Find how many calories � Kenzo will burn when running the span between the two towers (one way).
5. The entire length of the bridge is more than just the span between the two towers. Kenzo’s full runs are from one end of the bridge to the other end and back again. During such a run, he can burn 378 calories. Using the same average speed as above and the calorie burning model, find the full length of the Akashi-Kaikyo Bridge.
Justify your solution by using the fact that the suspension cables beyond each bridge tower are symmetrical to the suspension cable between the two towers.
5. The entire length of the bridge is more than just the span between the two towers. Kenzo’s full runs are from one end of the bridge to the other end and back again. During such a run, he can burn 378 calories. Using the same average speed as above and the calorie burning model, find the full length of the Akashi-Kaikyo Bridge.
Justify your solution by using the fact that the suspension cables beyond each bridge tower are symmetrical to the suspension cable between the two towers.
6. One evening, Kenzo sneaks onto the Akashi-Kaikyo Bridge suspension cable. He decides to run the full length of the parabolic suspension cable. Given the formula below for the length of a parabolic arc, find the calories that Kenzo will burn when he runs one full length of the suspension cable.�
6. One evening, Kenzo sneaks onto the Akashi-Kaikyo Bridge suspension cable. He decides to run the full length of the parabolic suspension cable. Given the formula below for the length of a parabolic arc, find the calories that Kenzo will burn when he runs one full length of the suspension cable.�
Problem 2:� Kristaps Porzingis, Latvian NBA Star
On the evening of December 16, 2019, Latvian basketball star Kristaps Porzingis led the Dallas Mavericks to a 120-116 victory over the Milwaukee Bucks, ending the Bucks’ 18-game winning streak. During the game, Porzingis scored 4 of 8 three point shots, several of them from far beyond the 3-point line. ��One of his three point shots was made from 31 feet away from the basketball hoop. �That’s more than 7 feet beyond the 3-point line!�
The height dependent on distance from hoop graph of this shot is given below. �Be careful: this is NOT the same as the previous height dependent on time graph!��
5. Using the information given in the introduction of this problem and what you have calculated � in questions 1.-3., approximate the coordinates of three points on the parabola below.
The height dependent on distance from hoop graph of this shot is given below. �Be careful: this is NOT the same as the previous height dependent on time graph!��
4. Using the information given in the introduction of this problem and what you have calculated � in questions 1.-3., approximate the coordinates of three points on the parabola below.
5. Create a quadratic model, h(d) for the height dependent on distance from hoop graph.
5. Create a quadratic model, h(d) for the height dependent on distance from hoop graph.
6. State a reasonable domain and range for the function h(d).
6. State a reasonable domain and range for the function h(d).
7. Apply the model to find: �� a) The height of the ball when it is 11 feet from Porzingis.��� b) The height of the ball when it is 33 feet from Porzingis.�� c) The distance from Porzingis when the ball is at a height of 13 feet.
7. Apply the model to find: �� a) The height of the ball when it is 11 feet from Porzingis.��� b) The height of the ball when it is 33 feet from Porzingis.�� c) The distance from Porzingis when the ball is at a height of 13 feet.