Question

the mount washington cog railway un new hampshire is one of the steepest cog railways in the world. a section of the railway has a slope if approximately 0.37. in this section, a vertical change of 1 unit corresponds to a horizontal change of what length? round your answer to the nearest hundredth.

Answer 1

The horizontal change is 2.70.

(Rounded to the nearest hundredth)

Explanation:

To find the answer, we need to apply the definition of a slope, which is

`m=(\Delta y)/(\Delta x)`

That is, the slope is the quotient between the vertical change and the horizontal change, that's what gives the inclination.

So, in this case we know that the slope is approximately 0.37,
`m \approx 0.37`. The vertical change is 1,
`\Delta y = 1`. So, replacing these values we can find the horizontal variation

`m=(\Delta y)/(\Delta x)\\0.37=(1)/(\Delta x) \\\Delta x =(1)/(0.37)\\ \Delta x \approx 2.70`

Therefore, the horizontal change is 2.70.

Answer 2

A slope could be simply calculated as rise over run. Rise would mean the vertical step, while run is the horizontal step. Thus,

Slope = rise/run

Let x - horizontal change

0.37 = 1/x

0.37x = 1

X = 1/0.37

X = 0.63

Thus, the horizontal change is 0.63 units.

I hope I was able to answer your question. Have a good day.