Question
The graph shows stopping distances for motorcycles at various speeds on dry roads and on wet roads.model a motorcycle’s stopping distance, f(x) or g(x), in feet, traveling at x miles per hour. Function f models stopping distance on dry pavement and function g models stopping distance on wet pavement.a. Use function g to find the stopping distance on wet pavement for a motorcycle traveling at 35 miles per hour. Round to the nearest foot. Does your rounded answer overestimate or underestimate the stopping distance shown by the graph? By how many feet?b. Use function f to determine speeds on dry pavementrequiring stopping distances that exceed 267 feet.
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Typically, this function is derived from data points on the graph. Assume the function g(x) has been modeled as \( g(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants determined from the graph. Show more…
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The graph shows stopping distances for motorcycles at various speeds on dry roads and on wet roads. Stopping Distances for Motorcycles at Selected Speeds. Dry Pavement. Wet Pavement. Speed (miles per hour). Source: National Highway Traffic Safety Administration. The functions f(x) = 0.125x^2 - 0.8x + 99 and g(x) = 0.125x^2 + 2.3x + 27 model a motorcycle's stopping distance, f(x) or g(x), in feet, traveling at x miles per hour. Function f models stopping distance on dry pavement and function g models stopping distance on wet pavement. a. Use function g to find the stopping distance on wet pavement for a motorcycle traveling at 35 miles per hour. Round to the nearest foot. Does your rounded answer overestimate or underestimate the stopping distance shown by the graph? By how many feet? b. Use function f to determine speeds on dry pavement requiring stopping distances that exceed 267 feet.
$\{x | x \geq 30\} .$ Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. a. Use the given functions at the bottom of the previous page to find the stopping distance on dry pavement and the stopping distance on wet pavement for a car traveling at 55 miles per hour. Round to the nearest foot. b. Based on your answers to part (a), which rectangular coordinate graph shows stopping distances on dry pavement and which shows stopping distances on wet pavement? c. How well do your answers to part (a) model the actual stopping distances shown in Figure 3.43 on page $431 ?$ d. Determine speeds on wet pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet. Round to the nearest mile per hour. How is this shown on the appropriate graph of the models? (GRAPH CANNOT COPY)
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$\{x | x \geq 30\} .$ Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. a. Use the given functions at the bottom of the previous page to find the stopping distance on dry pavement and the stopping distance on wet pavement for a car traveling at 35 miles per hour. Round to the nearest foot. b. Based on your answers to part (a), which rectangular coordinate graph shows stopping distances on dry pavement and which shows stopping distances on wet pavement? c. How well do your answers to part (a) model the actual stopping distances shown in Figure 3.43 on page $431 ?$ d. Determine speeds on dry pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet. Round to the nearest mile per hour. How is this shown on the appropriate graph of the models? (GRAPH CANNOT COPY)
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