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Nutka1998 [239]
3 years ago
5

A stretch of highway has a 4% uphill grade. This means that the road rises 1 foot for every 25 feet of horizontal distance. The

beginning of the highway (x = 0) has an elevation of 2,225 feet. Write an equation for this stretch of roadway ini point-slope form.​
Mathematics
1 answer:
Sladkaya [172]3 years ago
3 0

Answer:

The equation for this stretch of roadway in point-slope form is y - 2225 = 0.04x

Step-by-step explanation:

Equation in point-slope form:

The equation of a line in point-slope form is given by:

y - y_0 = m(x - x_0)

In which (x_0,y_0) is the point and m is the slope.

A stretch of highway has a 4% uphill grade. This means that the road rises 1 foot for every 25 feet of horizontal distance.

This means that m = 0.04

The beginning of the highway (x = 0) has an elevation of 2,225 feet.

This means that (x_0,y_0) = (0,2255). So

y - y_0 = m(x - x_0)

y - 2225 = 0.04(x - 0)

y - 2225 = 0.04x

The equation for this stretch of roadway in point-slope form is y - 2225 = 0.04x

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Answer:

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Step-by-step explanation:  

It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...

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   AC^2 = 4^2 + 3^2 = 16 + 9 = 25

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And the scale factor to ∆BHC is ...  

  scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6  

Then the side AH is 0.8·AB = 0.8·4 = 3.2

And the side CH is 0.6·BC = 0.6·3 = 1.8  

These two side lengths should add to the length AC = 5, and they do.  

The remaining side BH can be found from either scale factor:    

  BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4

_____  

The sides of interest are ...  

  AH = 3.2

  CH = 1.8

  BH = 2.4

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