Height from Slope and Horizontal Distance The base of a ladder is
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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.arrow_forwardSlope from the Rise and Run One end of a ladder is on the ground. The top of the ladder rests at the top of an 8-foot wall. The wall is 2 horizontal feet from the base of the ladder. What is the slope of the line made by the ladder? Assume that the positive direction points from the base of the ladder toward the wall.arrow_forwardHeight from Slope and Horizontal Distance The base of a ladder is 4 horizontal feet from the wall where its top rests. The slope of the line made by the ladder is 1.7. What is the vertical height of the top of the ladder? Assume that the positive direction points from the base of the ladder toward the wall.arrow_forward
- 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?arrow_forwardHorizontal Distance from Height and Slope A ladder leans against a wall so that its slope is 1.75. The top of the ladder is 9 vertical feet above the ground. What is the approximate horizontal distance from the base of the ladder to the wall? Assume that the positive direction points from the base of the ladder toward the wall.arrow_forwardHorizontal Distance from Height and Slope A ladder leans against a wall so that its slope is 2.1. The top of the ladder is 12 vertical feet above the ground. What is the horizontal distance from the base of the ladder to the wall? Assume that the positive direction points from the base of the ladder toward the wall.arrow_forward
- 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?arrow_forwardRailroad 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?arrow_forwardSlope 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?arrow_forward
- 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?arrow_forwardA 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.arrow_forwardRoad 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?arrow_forward
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