Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Surveying Vertical Curves When a road is being built, it usually has straight sections, all with the same grade, that must be linked to each other by curves. (By this we mean curves up and down rather than side to side, which would be another matter.) It’s important that as the road changes from one grade to another, the rate of change of grade between the two be constant. The curve linking one grade to another grade is called a vertical curve.
Surveyors mark distances by means of stations that are
Here
Figure 5.72
Assume that the vertical curve you want to design goes over a slight rise, joining a straight section of grade
a. What is the equation for the vertical curve described above? Don’t round the coefficients.
b. What are the elevations of the stations for the vertical curve?
c. Where is the highest point of the road on the vertical curve? (Give the distance along the vertical curve and the elevation.)
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Walking and Running You live east of campus, and you are walking from campus toward your home at a constant speed. When you get there, you rest for 5minutes and then run back west at a rapid speed. After a few minutes, you reach your destination, and then you rest for 10minutes. Measure your location as your distance west of your home, and make graphs of your location and velocity.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Gravity on Earth and on MarsThe acceleration due to gravity near the surface of a planet depends on the mass of the planet; larger planets impart greater acceleration than smaller ones. Mars is much smaller than Earth. A rock is dropped from the top of a cliff on each planet. Give its location as the distance down from the top of the cliff. a.On the same coordinate axes, make a graph of distance down for each of the rocks. b.On the same coordinate axes, make a graph of velocity for each of the rocks.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The Rock with a Changed Reference Point Make graphs of position and velocity for a rock tossed upward from ground level as it might be viewed by someone standing atop a tall building. Thus, the location of the rock is measured by its distance down from the top of the building.arrow_forward
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- Reminder Round all answers to two decimal places unless otherwise indicated. Market Supply and demand The quality of wheat, in billions of bushels, that wheat suppliers are willing to produce in a year and offer for sale is called the quantity supplied and is denoted by S. The quantity supplied and is determined by the price P of wheat, in dollars per bushel, and the relation is P=2.13S0.75. The quantity of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year is called the quantity demanded and is denoted by D. The quantity demanded is also determined by the price P of wheat, and the relation is P=2.650.55D. At the equilibrium price, the quality supplied and the quality demanded are the same. Find the equilibrium price for wheat.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Protein Content of Wheat GrainProtein content of wheat grain is affected by soil moisture and the amount of available nitrogen among other things. Figure 1.45 shows" the percent of protein content of wheat grain versus pounds of nitrogen per acre applied in three separate situations. In each case, soil moisture refers to moisture at the soil depth of 2 inches to 12 inches. Situation 1: Irrigation was used when soil moisture dropped to 49. Situation 2: Irrigation was used when soil moisture dropped to 34. Situation 3: Irrigation was used when soil moisture dropped to 1. a. If irrigation begins when soil moisture reaches 49, what application of nitrogen will result in the lowest percentage of protein in wheat grain? b. If irrigation begins when soil moisture reaches 34, what application of nitrogen will result in the same protein content of wheat grain as beginning irrigation when soil moisture reaches 1? c. If you irrigate when soil moisture reaches 34, how much nitrogen should you apply to achieve a 13 protein content in wheat grain? d. Does Figure 1.45 indicate that, for nitrogen levels at 45 pounds per acre or higher, increased protein content in wheat grain is associated with higher or lower soil moisture? FIGURE 1.45 Protein content versus availability of nitrogenarrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. The MacArthur-Wilson Theory of Biogeography Consider an island that is separated from the mainland, which contains a pool of potential colonizer species. The MacArthur-Wilson theory of biogeography hypothesizes that some species from the mainland will migrate to the island, but that increasing competition on the island will lead to species extinction. It further hypothesizes that both the rate of migration and the rate of extinction of species are exponential functions, and that an equilibrium occurs when the rate of extinction matches the rate of immigration. This equilibrium point is thought to be the point at which immigration and extinction stabilize. Suppose that, for a certain island near the mainland, the rate of immigration of new species is given by I=4.20.93tspeciesperyear and that the rate of species extinction on the island is given by E=1.51.1tspeciesperyear. According, to the MacArthur-Wilson theory, how long will be required for stabilization to occur, and what will be the immigration and extinction rates at that time?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning