Question

PLEASE HELP HURRY

Matt wants to start zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint? Use specific numbers from the situation to justify or refute whether Matt’s design meets the slope constraint.

slope constraint: the slope of the zip line should be 6 to 8 feet of vertical change for every 100 feet of horizontal change

Answer 1

Okay, let's calculate the slope for Matt's proposed zip line design to determine if it meets the constraints:

* Starting height in first tree: 16 ft

* Ending height in second tree: 10 ft

* Difference in height between trees: 16 ft - 10 ft = 6 ft

* Matt needs to determine the horizontal distance between the trees. Let's assume this is 100 ft for the calculation.

* Vertical change (difference in height): 6 ft

* Horizontal change (distance between trees): 100 ft

* Slope = (Vertical change) / (Horizontal change)

= (6 ft) / (100 ft)

= 0.06

So with a starting height of 16 ft and ending height of 10 ft, over a 100 ft horizontal distance between the trees, the slope works out to 0.06.

This meets the slope constraint of 6 to 8 ft of vertical change for every 100 ft of horizontal change.

Therefore, Matt's designed zip line with a 16 ft starting height and 10 ft ending height, over 100 ft between the trees, should meet the necessary slope requirements for a safe and enjoyable zip line ride.

Please let me know if you have any other questions! I'm happy to help further in explaining the calculations.

Answer 2

Explanation:

To determine whether Matt's design meets the slope constraint, we need to calculate the slope of the zip line using the given height difference and the horizontal distance between the two trees.

Let's assume that the horizontal distance between the two trees is 100 feet. Then, the vertical change of the zip line would be:

16 feet - 10 feet = 6 feet

This means that the slope of the zip line is:

6 feet of vertical change / 100 feet of horizontal change = 0.06

To express the slope as a ratio, we can simplify:

0.06 = 6/100 = 3/50

Therefore, the slope of the zip line is 3/50.

According to the slope constraint, the slope of the zip line should be between 6/100 and 8/100, or:

0.06 ≤ slope ≤ 0.08

Since 3/50 is less than 6/100, the slope of the zip line is not sufficient to meet the slope constraint. Therefore, Matt's design does not meet the slope constraint and would need to be modified to meet the safety requirements.