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.)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter9: Real Numbers And Right Triangles

Section9.5: The Distance And Midpoint Formulas

Problem 52E

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Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

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 ft
8 ft
3 ft
17 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 feet
high. How far from the west wall should you install the light? (Round your answer to one decimal place.)
ft

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