West of a city, a certain eastbound route is straight and makes a steep descent toward the city. The highway has a 11% grade, which means that its slope is − 11 100 . Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance in miles? (Round your answer to two decimal places.) mi

The change in horizontal distance is 1.72 mi

Step-by-step explanation:

From the question, the highway has a 11% grade, which means that its slope is -11 / 100.

The negative sign indicates that the road is descending.

Hence, slope (m) = 11/100

The slope m, is given by

Where Δy is the change in vertical distance and

Δx is the change in horizontal distance

Now, from the question, you have descended a distance of 1000 ft, that is

Δy = 1000 ft

Then, to determine the change in the horizontal distance Δx,

From

, then

∴

Δx = 9090.91 ft

This is the change in horizontal distance in ft, Now to convert it to miles

1 mile = 5280 ft

Hence, 1 ft = 1/5280 miles

If 1 ft = 1/5280 miles

Then, 9090.91 ft = x miles

x = 9090.91 × 1/5280

x = 1.72 miles

Hence, the change in horizontal distance in miles is 1.72 mi

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step-by-step explanation: