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2 years ago

Please help and i have many more points!

Mathematics

1 answer:

Slav-nsk [51]2 years ago

8 0

Answer:

its A im pretty sure

Step-by-step explanation:

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A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo

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Answer:

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

$y - k = C \cdot (x-h)^{2}$

Where:

$h$ - Horizontal component of the vertix, measured in inches.

$k$ - Vertical component of the vertix, measured in inches.

$C$ - Parabola constant, dimensionless. (Where vertix is an absolute maximum when $C < 0$ or an absolute minimum when $C > 0$ )

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

$V (x,y) = (0, 32)$ (Vertix)

$A (x, y) = (-28, 0)$ (x-Intercept)

$B (x,y) = (28. 0)$ (x-Intercept)

The following equation are constructed from the definition of a parabola:

$0-32 = C \cdot (28 - 0)^{2}$

$-32 = 784\cdot C$

$C = -\frac{2}{49}$

The parabolic shape of the door is represented by $y - 32 = -\frac{2}{49}\cdot x^{2}$ . Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

$y -32 = -\frac{2}{49} \cdot x^{2}$