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The length of the roller coaster track from the top of a hill to the bottom of the hill is 125 feet at a 53°C angle with the vertical. If the position at the top of the hill is (x, y) , use function notation to describe the translation to the bottom of the hill. Round to the nearest foot.

Respuesta :

(x + 100, y - 75) is the function notation used to characterise the translation to a bottom of the hill.

What is defined as Pythagorean Theorem?

The Pythagorean theorem states that the sum of a squares on a legs of a right triangle equals the square on hypotenuse (this same side opposite this same right angle)—or, in recognizable algebraic notation, a² + b² = c².

Now, as per the given question;

From the shown diagram,

AC  = b

Ab  = c

We must find the coordinates of a point B. If C(x,y), then the coordinates of points A and B are:

A(x, y−b) and B(x+c, y−b)

We need to figure out b and c. To find c, we should use sine function.

sinC = perpendicular/hypotenuses

sinC = c/BC

​Thus, c = BC sinC

c = 125sin53°

  =125⋅0.79863551

c ≈100

To find b, we are using the Pythagorean Theorem.

BC² = AC² + AB²

125² = b² + 100²

b² = 125² - 100²

b = √5625

b = 75

The coordinates of a point B are as follows:

B(x+c, y−b)

B(x+100, y−75).

Therefore, the translation to the bottom of the hill defined by the function notation is B(x+100, y−75).

To know more about the Pythagorean Theorem, here

https://brainly.com/question/343682

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