A cathedral ceiling shown in the figure below 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.10.5 ft8 ft3 ft17 ft(a) What is the slope of the ceiling? (Round your answer to four decimal places.)ft per ft(b) The width of the room (the distance from the west wall to the east wall) is 17 feet. How high is the ceiling at the east wall? (Round your answer to two decimal places.)ft(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 20 feethigh. How far from the west wall should you install the light? (Round your answer to one decimal place.)ft

(a) Let x be the distance from the west wall Let y be the height of the ceiling at a distance x from…

A cathedral ceiling shown in the figure below 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. 17A (a) What is the slope of the ceiling? (Round your answer to four decimal places.) ft per ft (b) The width of the room (the distance from the west wall to the east wall) is 17 feet. How high is the ceilling at the east wall? (Round your answer to two decimal places.) ft (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 20 feet high. How far from the west wall should you install the light? (Round your answer to one decimal place.)

A cathedral ceiling shown in the figure below 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. 17A (a) What is the slope of the ceiling? (Round your answer to four decimal places.) ft per ft (b) The width of the room (the distance from the west wall to the east wall) is 17 feet. How high is the ceilling at the east wall? (Round your answer to two decimal places.) ft (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 20 feet high. How far from the west wall should you install the light? (Round your answer to one decimal place.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.1: The Geometry Of Lines

Problem 12SBE: More on the Circus Tent Assume that the roof of the circus tent in Exercise S- 11 extends in a...

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A Ramp A ramp runs from the ground level to a building entrance that is 3 feet high and 12 feet from the base of the ramp. If we think of the base of the ramp as the origin and the building is located on the positive horizontal axis as shown in Figure 3.26), find the slope of the line representing the ramp.
Railroad Grade A train travels 3.5 kilometers on a straight track with a grade of 1.2 (see figure). What is the vertical rise of the train in that distance?
More on the Circus Tent Assume that the roof of the circus tent in Exercise S- 11 extends in a straight line to the ground. How far from the center of the tent does the roof meet the ground? A Circus Tent You are at the center of a circus tent, where the height is 22 feet see Figure 3.29). You are facing due west, which you take to be the positive direction. The slope of the tent line is 0.8. If you walk 7 feet west, how high is the tent?
Road Grade From the top of a mountain road, a surveyor takes several horizontal measurements x and several vertical measurements y, as shown in the table ( x and y are measured in feet). (a) Sketch a scatter plot of the data. (b) Use a straightedge to sketch the line that you think best fits the data. (c) Find an equation for the line you sketched in part (b). (d) Interpret the meaning of the slope of the line in part (c) in the context of the problem. (e) The surveyor needs to put up a road sign that indicates the steepness of the road. For example, a surveyor would put up a sign that states 8grade on a road with a downhill grade that has a slope of 8100. What should the sign state for the road in this problem?
Slides A company manufactures slides. The top of the slide is 5 feet high. The bottom is 7 feet away, as shown in Figure 3.11. a. If the coordinate axes are chosen as shown in the figure, find the slope of the slide. b. A child complains that the trip down the slide is not fast enough. How should the slope be adjusted to accommodate the unhappy child?
Continuation of Exercise S-9 If you move 5 additional feet west, what is the height of the roof above the place where you stand? S-9. Slope from Two Points Take west to be the positive direction. The height of a sloped roof above the place where you stand is 12 feet see Figure 3.28). If you move 3 feet west, the height is 10 feet. What is the slope?
Slope of a roof. An easy way to determine the slope of a roof is to set one end of a 12 inch level on the roof surface and hold it level. Then take a tape measure or ruler and measure from the other end of the level down to the roof surface. This will give you the slope of the roof. Builders, sometimes, refer to this as pitch and state it as an “x pitch” meaning w x12 , where x isthe measurement from the roof to the level—the rise.It is also sometimes stated as an “x -in-12 pitch”. (a) What is the slope of the roof in this picture? (b) What is the pitch in construction terms?
A Rope A rope is stretched from the top of a 4-foot high wall, which we use to determine the vertical axis. The end of the rope is attached to the ground at a point 20 horizontal feet away at a point on the positive horizontal axis. What is the slope of the line representing the rope? Suggestions: Be careful about the sign.
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The following problems review material we covered in Section 3.5. Linear Velocity A point moving on the circumference of a circle covers 5 feet every 20 seconds. Find the linear velocity of the point.
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