SOLUTION: A cathedral ceiling is 8 feet high at the west wall of a room. As you go from the west wall toward the east wall, the ceiling slants upward. Three feet from the west wall, the ceil

Question 1146783: A cathedral ceiling is 8 feet high at the west wall of a room. As you go from the west wall toward the east wall, the ceiling slants upward. Three feet from the west wall, the ceiling is 10.5 feet high.
(c) You want to install a light in the ceiling as far away from the west wall as possible. You intend to change the bulb, when required, by standing near the top of your small stepladder. If you stand on the highest safe step of your stepladder, you can reach 18 feet high. How far from the west wall should you install the light? (Round your answer to one decimal place.)
*I have already tried 10.8 and Rise/Run. Not sure how to complete this one..
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the distance from the west wall.
let y = the height of the ceiling at that distance from the west wall.

when x = 0, y = 8
when x = 3, y = 10.5

slope intercept form of the equation of a straight line is y = mx + b.
m is the slope and b is the y-intercept.

m is the change in y divided by the correspond change in x.

m is therefore equal to (10.5-8) / (3-0) = 2.5/3.

b is the value of y when x is equal to 0.
that makes b equal to 8.

the equation of the line represrenting the height of the ceiling is y = 2.5/3 * x + 8.

when x = 0, y = 8
when x = 3, y = 2.5/3 * 3 + 8 = 2.5 + 8 = 10.5

these values confirm the equation is an accurate model of the slant of the ceiling as it goes from the west wall to the east wall.

the highest you can reach is 18 feet.
the equation of y = 2.5/3 * x + 8 becomes 18 = 2.5/3 * x + 8
subtract 8 from both sides to get 10 = 2.5/3 * x
multiply both sides by 3/2.5 to get 10 * 3/2.5 = x
simplify to get 12 = x

the height of the ceiling is 18 feet when the distance from the west wall is 12 feet.

that's as far from the west wall that you can go, given that the maximum height you can reach is 18 feet.

that's your solution as best i can determine.
divide both sides by 2.5 to get 10 / 2.5 = x.

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