Rose climbs down the mountain while Lucy climbs up. The equation and the table represent the
elevations of the climbers in feet, y, as functions of time in minutes, z.
Find Rose and Lucy's climbing speeds.
Rose's speed
feet per minute
Lucy's speed
? feet per minute
Rose's climb:
y=-11a +900
Lucy's climb:
Minutes, z
1
2
3
4
5
Elevation, y
900
890
880
870
860
Rose's speed: -11 feet per minute
Lucy's speed: 10 feet per minute
To find Rose and Lucy's climbing speeds, we need to analyze the given information.
From the equation, Rose's climb can be represented as:
y = -11a + 900
To find Rose's climbing speed, we need to determine the slope of her climb equation. The slope represents the rate of change of elevation with respect to time. In this case, the slope is equal to the coefficient of 'a', which is -11.
Therefore, Rose's climbing speed is 11 feet per minute.
Now, we need to analyze Lucy's climb represented in the table:
| Minutes, z | Elevation, y |
|------------|--------------|
| 1 | ? |
| 2 | ? |
Unfortunately, we don't have the values for Lucy's elevation at minutes 1 and 2. Without this information, it is not possible to calculate Lucy's climbing speed.
To find Rose and Lucy's climbing speeds, we need to determine the rate at which their elevations change with respect to time. This rate of change is known as the derivative.
Given the equation for Rose's climb: y = -11z + 900, we can clearly see that the coefficient of z, which is -11, represents Rose's climbing speed. Therefore, Rose's climbing speed is 11 feet per minute.
For Lucy's climb, we need more information. The table provided only shows the minutes, z, and not the corresponding elevations, y. To calculate Lucy's climbing speed, we need at least two data points that include both z and y values.
Please provide additional data points for Lucy's climb, and we can calculate her climbing speed.