Question

When Kumu Akeo was a sophmore at Kamehameha Schools he was sent to exchange in Japan. One day his homestay family took him to a nearby mountain and it was his first time snowboarding. Mount Shibutsu (至仏山) is 7310 ft tall and is beautifully covered in snow even during the spring timeThe first time snowboarding you assume youʻre amazing and decide to try the triple diamond slope at the top of the mountain (triple diamond was the most difficult rating of this area.) It takes you 45 minutes to go down the 270 ft.Task 1: Restake the information given in this situationFind the rate of change for your descent in correct units. Please give an equation in slope intercept form to map your descent down the mountainPlease attach a graph of your equation

Kumu Akeo went down to Japan to go snowboarding. He went to the mountain, Mount Shibutsu (至仏山). Its 7310 ft tall and snows even during spring. He decided to go down the hard trail which takes 45 minutes to go down. It was 270 ft down. Given the information the rate of change isOkay that took a long time and your friend Pythagoras finds that you finally made it down to the double diamond slope after many ʻlearning fallsʻ as he called them. Pythagoran gives you some advice and youʻve figured out this whole snowboarding thing. This slope is also 270 ft and itʻs about 540 ft (horizontally) from the restaraunt where lunch will be servedTask 2Draw out this situation (optional 2pts)
Restake the information given in this new situation Find your new rate of descent in correct units. Please give an equation in standard form mapping your descent down the mountain Please attach a graph of your equation Now you have 2 graphs with different slopes. Talking about slopes Gauss is wondering which of these two graphs have a slope that is more likely to represent the slopes you were just shredding. Gauss wonders if you used your rate of descent in the second task how far laterally from your starting location will you end up?
Task 3 Restake the given information. Please give an equation in point slope form to represent the new graph. What does the y-intercept represent? What does the x-intercept represent?

Answer 1

The rate of change for your descent in the first task is 6 ft/min. The equation in slope-intercept form to map your descent down the mountain is y = 6x + b. In the second task, the rate of descent remains the same at 6 ft/min. The equation in standard form to map your descent down the mountain is Ax + By = C. In the third task, the slope for the rate of descent laterally was not provided, so we cannot determine the distance from the starting location.

Step-by-step explanation:

Task 1: Restating the information given in this situation:

- Mount Shibutsu is 7310 ft tall and is covered in snow even during the spring.

- The slope that you decided to snowboard down is a triple diamond, which is the most difficult rating in this area.

- It took you 45 minutes to descend the slope, which was 270 ft long.

To find the rate of change for your descent, we can divide the vertical distance traveled (270 ft) by the time it took (45 minutes), giving us 270 ft / 45 min = 6 ft/min.

The equation in slope-intercept form to map your descent down the mountain would be y = mx + b, where m is the slope (6 ft/min) and b is the y-intercept (the starting point on the mountain).

Task 2:

- The new situation involves going down a slope that is also 270 ft long.

- The slope is located 540 ft horizontally from the restaurant where lunch will be served.

To find the rate of descent in this situation, we can use the same formula as before: rate of descent = vertical distance / time.

Since the vertical distance and time remain the same, the rate of descent will also be 6 ft/min.

The equation in standard form to map your descent down the mountain would be Ax + By = C, where A, B, and C are constants representing the slope and intercepts.

Task 3:

- Given the information, we were not provided with the slope to determine the rate of descent laterally.

- An equation in point-slope form to represent the new graph would take the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

The y-intercept of the equation represents the starting point on the mountain, and the x-intercept represents the distance laterally from the starting location where you will end up.