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Chapter 10: Problem 84

A straight road rises with an inclination of 0.20 radian from the horizontal. Find the slope of the road and the change in elevation over a one-mile stretch of the road.

Short Answer

Expert verified
The slope of the road is approximately 0.2027, and the change in elevation over a one-mile stretch is approximately 326.22 meters.

Step by step solution

01

Calculate the Slope

The main formula to recall for this calculation is slope = tan(胃), where 胃 is the angle of inclination. Substituting the given value, we find tan(0.20). Use a calculator to find the value of the tangent of 0.20, which equals approximately 0.2027.
02

Calculate the Change in Elevation

The change in elevation, or vertical distance, can be found by multiplying the slope by the horizontal distance. Here, the horizontal distance is one mile, which is approximately 1.60934 kilometers, or 1609.34 meters. Multiply this by the slope: 0.2027 * 1609.34 = 326.22 meters. This is the change in elevation over a one-mile stretch of the road.
03

Summarize the Findings

The slope of the road is 0.2027, and the change in elevation over a one-mile (1609.34 meters) stretch is approximately 326.22 meters.

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Most popular questions from this chapter

In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. $$r=8 \cos \theta$$

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=\sin \theta$$

Converting a Polar Equation to Rectangular Form In Exercises \(117-126,\) convert the polar equation to rectangular form. Then sketch its graph. $$r=4 \cos \theta$$

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=1-2 \sin \theta$$

In Exercises \(59-64,\) use a graphing utility to graph the polar equation. Find an interval for \(\theta\) for which the graph is traced only once. $$r=2 \cos \left(\frac{3 \theta}{2}\right)$$
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