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dybincka [34]
3 years ago
15

In a mall, a shopper rides up an escalator between floors. at the top of the escalator, the shopper turns right and walks 9.09 m

to a store. the magnitude of the shopper's displacement from the bottom of the escalator to the store is 16.0 m. the vertical distance between the floors is 4.89 m. at what angle is the escalator inclined above the horizontal?

Mathematics
1 answer:
Semenov [28]3 years ago
5 0
Let x represent the horizontal displacement of the top of the escalator from its bottom. The geometry of the problem and the Pythagorean theorem tell you
  x² + 4.89² + 9.09² = 16.0²
  x² = 149.4598
  x ≈ 12.22 . . . meters

Then the tangent of the angle of interest is
  tan(α) = (4.89 m)/(12.22 m)
  α = arctan(4.89/12.22) ≈ 21.8°

The escalator is inclined 21.8° above the horizontal.

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Which two tables represent the same function?
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Answer:

The 1st and the 5th tables represent the same function

Step-by-step explanation:

* Lets explain how to solve the problem

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- The form of the equation of a line whose endpoints are (x1 , y1) and

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∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7

∴ \frac{y-8}{x-4}=\frac{7-8}{6-4}

∴ \frac{y-8}{x-4}=\frac{-1}{2}

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# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)

∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4

∴ \frac{y-5}{x-4}=\frac{4-5}{6-4}

∴ \frac{y-5}{x-4}=\frac{-1}{2}

- By using cross multiplication

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∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides

∴ x + 2y = 14 ⇒ (2)

# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)

∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5

∴ \frac{y-8}{x-2}=\frac{5-8}{8-2}

∴ \frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}

- By using cross multiplication

∴ 2(y - 8) = -1(x - 2) ⇒ simplify

∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides

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# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)

∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14

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∴ x - y = -8 ⇒ (4)

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- Equations (1) and (5) are the same

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