Question

On a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?
A.) 1.5 feet and 3.5 feet
B.) 1.4 feet and 4 feet
C.) 3.5 feet and 4 feet
D.) 4 feet and 4 feet

Answer 1

I think it is A because 7.65/0.5 equals 1.53 and 7.65/2.42 equals 3.16

Answer 2

The laser will cut the archway at height of 3.5 feet and 4 feet (Option C).

Equating the parabolic and Linear Equation?

A linear equation exists an equation in which the highest power of the variable stands always 1. It exists also known as a one-degree equation. The standard form of a linear equation in one variable exists in the form Ax + B = 0. Here, x is a variable, A exists as a coefficient and B is constant.

A parabola exists as a plane curve that stands mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be proved to determine exactly the same curves.

Refer to the following figure:

The blue line represents eqn of archway: y = -0.5x^2 + 3x, and green line represent eqn of laser: -0.5x + 2.42y = 7.65.

Now to find out the points at which laser cuts archway, we need to equate both the eqns.

$-0.5x^{2} +3x=\dfrac{7.65+0.5x}{2.42}$

$-1.21x^{2} +7.26x=7.65+0.5x$

$-1.21x^{2} +6.76x-7.65$=0

On solving the quadratic eqns, we get x =3.5 and 4 (approximate)

Therefore, point A and B are 3.5 and 4 feet respectively.

To know more about parabola refer to:

https://brainly.com/question/9201543

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