Finsler Steepest Descent with Applications to Piecewise-regular
EXAMPLE 1 Finding Slope The Mount Pilatus Railway in the Swiss Alps is the steepest cogwheel railway...
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Transcript of EXAMPLE 1 Finding Slope The Mount Pilatus Railway in the Swiss Alps is the steepest cogwheel railway...
EXAMPLE 1 Finding Slope
The Mount Pilatus Railway in the Swiss Alps is the steepest cogwheel railway in the world. The track rises about 20 feet vertically for every 50 feet it runs horizontally. How can you describe the steepness of the track?
Cogwheel Railway
EXAMPLE 1 Finding Slope
The diagram shows the rise and the run of the Mount Pilatus Railway described above.
slope = runrise
= 50 ft20 ft 2
5=
ANSWER
The track has a slope of .25
5
2
GUIDED PRACTICE for Example 1
slope = runrise 1
3=
ANSWER
The track has a slope of .13
3
1
1. Using slope, describe the steepness of a ramp that rises 6 feet vertically for every 18 feet it reaches horizontally.
Ramps
= 18 ft6 ft
EXAMPLE 2 Positive and Negative Slope
Find the slope of the line.
m = runrise
=y2 – y1x2 – x1
= 7 – 25 – 1
54
=
m = runrise
=y2 – y1x2 – x1
= 3 – 64 – 2
–32
= 32
or –
EXAMPLE 3 Zero and Undefined Slope
Find the slope of the line.
m = runrise
=y2 – y1x2 – x1
= 3 – 36 – 2
04
=
=y2 – y1x2 – x1
4 – (–2)1 – 1=
0= The slope is undefined
m = runrise
= 60
GUIDED PRACTICE for Examples 2 and 3
Find the slope of the line passing through the points.
2. (2, 1), (6, 4)
m = runrise
= 4 – 16 – 2
34
=
3. (0, 6), (10, 0)
m = runrise
=y2 – y1x2 – x1
= 0 – 610 – 0 10
= –6
4. (– 3, – 4), (5, 2)
m = runrise
=y2 – y1x2 – x1 4
= 3= 2 – (–4)5 – (–3)
=y2 – y1x2 – x1
5= –3
GUIDED PRACTICE for Examples 2 and 3
m = runrise
=y2 – y1x2 – x1
0=
6. (1, 6), (1, 2)
m = runrise
=y2 – y1x2 – x1
= 2 – 61 – 1
7. (– 8, 3), (8, 3)
m = runrise
=y2 – y1x2 – x1
= 3 – 38 – (–8)
5. (1, 5), (– 3, 5)
= 0
= – 40
undefined
= 5 – 5–3 – 1