An archway is modeled by the equation y = -2x2 + 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

Question

An archway is modeled by the equation y = -2x2 + 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

ty188 · Answer

can anyone help

welshfella · Answer

you need to solve the system of equations
y = -2x^2 + 8x  
x - 2.23y + 10.34 = 0

ty188 · Answer

ok @welshfella

welshfella · Answer

use substitution
from the second equation 
x = 2.23y - 10.34

Plug this into the first equation:-

y = 2(2.23y - 10.34)^2  + 8(2.23y - 10.34)

welshfella · Answer

which is very messy but can be done

welshfella · Answer

thats 
-2(2.23y - 10.34)^2  + 8(2.23y - 10.34)

I forgot the  negtive before the 2

welshfella · Answer

an easier way would be to plug in the values  given and see which one s fit . There should be 2 values which fit . The highest one wil l be the the height of B

ty188 · Answer

@welshfella I got it wrong lol

welshfella · Answer

the correct answer is  6 units  ( 5 98 to be exact)