Question

An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?

A. 8 units
B. 6 units
C. 5 units
D. 3 units

Answer 1

The answer is 6

Explanation:

Answer 2

To solve this problem you must apply the proccedure shown below:

1. You have that the the archway is modeled by the equation y=-2x^2+8x and the angle mentioned in the problem is defined by the equation x−2.23y+10.34=0.

2. Therefore, you must susbtitute y=-2x^2+8x into x−2.23y+10.34=0, as below:

x−2.23(-2x^2+8x)+10.34=0

3. When you apply the distributive property, you obtain:

x−2.23(-2x^2+8x)+10.34=0
x+4.46x^2-17.84x+10.34=0
4.46x^2-16.84x+10.34=0

4. When you solve the quadratic equation, you obtain:

x=3 units

Therefore, the answer is the option D: D. 3 units.