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A section of a railway has a slope of approximately 0.37. In this section, a vertical change of one unit corresponds to a horizontal change of what length? Round your answer to the nearest hundredth.

Verified Answer :

bartdrinksmalk

Slope \(\frac{dy}{dx}=0.37\)

We are given \(dy=1\)
So \(\frac{1}{dx}=0.37\)
⇒\(dx=\frac{1}{0.37}\)≈2.70

fichoh

The horizontal change in length which is obtained using the slope formula is 2.70 units.

The slope can defined as the ratio of rise to the run ; which is the ratio of the vertical change to the horizontal change.

Hence ; \(slope = \frac{vertical \:change}{horizontal \:change}\)

Given a vertical change = 1 unit

\(0.37 = \frac{1}{horizontal \:change}\)

\(Horizontal change = \frac{1}{0.37}\)

\(Horizontal change = 2.702\)

Therefore, the length of the horizontal change is 2.70 units (rounded to the nearest hundredth)

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