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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?

Respuesta :

Answer:

1.721 miles

Explanation:

Given:

Grade = 11%

i.e for every 11 ft of descend horizontal distance is 100 ft

or

for every 1 ft of descend horizontal distance is [tex]\frac{\textup{100}}{\textup{11}}[/tex]  ft

therefore,

For the descend of 1000 ft horizontal distance = [tex]1000\times\frac{\textup{100}}{\textup{11}}[/tex]  ft

or

= 9090.90 ft

Also,

1 mile = 5280 ft

or

1 ft = 0.000189394 miles

therefore,

9090.90 ft = 9090.90 ft × 0.000189394 miles

= 1.721 miles

The change in the horizontal distance would be as follows:

[tex]1.721[/tex] miles

Find the distance

Given that,

Grade of the highway [tex]= 11[/tex]%

Distance for every horizontal descent measuring 11 ft [tex]= 100 ft.[/tex]

Distance for every horizontal descent measuring 1 ft [tex]= 100/11[/tex]

Distance for every horizontal descent measuring 1000 ft[tex]= 1000[/tex] × [tex]100/11[/tex]

[tex]= 9090.90 ft[/tex]

Since,

[tex]1 mile = 5280 ft[/tex]

&

[tex]1 ft. = 0.000189394 miles[/tex]

So,

∵ [tex]9090.90 ft[/tex] [tex]= 9090.90 ft[/tex] × [tex]0.000189394 miles[/tex]

[tex]= 1.721 miles[/tex]

Thus, [tex]1.721[/tex] miles is the correct answer.

Learn more about "Distance" here:

brainly.com/question/989117

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