Reminder Round all answers to two decimal places unless otherwise indicated.
Binary Stars Binary stars are pairs of stars that orbit each other. The period
Here
a. Alpha Centauri, the nearest star to the sun, is in fact a binary star. The separation of the pair is
b. How would the mass change if the separation angle were doubled, but the parallax and period remained the same as for the Alpha Centauri system?
c. How would the mass change if the parallax angle were doubled. but the separation and period remained the same?
d. How would the mass change if the period doubled, but the parallax angle and separation remained the same?
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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. 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_forwardReminder 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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. TravelIng in a CarMake graphs of location and velocity for each of the following driving events. In each case, assume that the car leaves from home moving west down a straight road and that position is given as the distance west from home. a. A vacation: Being eager to begin your overdue vacation, you set your cruise control and drive faster than you should to the airport. You park your car there and get on an airplane to Spain. When you fly back 2 weeks later, you are tired, and you drive back home at a leisurely pace. Note: Here we are talking about the location of your car, not of the airplane. b. On a country road: A car driving down a country road encounters a deer. The driver slams on the brakes, and the deer runs away. The journey is cautiously resumed. c. At the movies: In a movie chase scene, our hero is driving his car rapidly toward the bad guys. When the danger is spotted, he does a Hollywood 180-degree turn and speeds off in the opposite direction.arrow_forwardReminder Round all answers to two decimals places unless otherwise indicated. A Topographical Map In making a topographical map, it is not practical to measure the heights of structures such as mountains directly. This exercise illustrates how some such measurements are taken. A surveyor whose eye is 6 feet above the ground views a mountain peak that is 2 horizontal miles distant. See Figure 3.15 on the next page. Directly in his line of sight is the top of a surveying pole that is 10 horizontal feet distant and 8 feet high. How tall is the mountain peak? Note: One mile is 5280 feet.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Looking over a Wall Twenty horizontal feet north of a 50-foot building is a 35-foot wall see Figure 3.22). A man 6 feet tall wishes to view the top of the building from the north side of the wall. How far north of the wall must he stand in order to view the top if the building?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Parallax AngleIf we view a star now, and then view it again 6 months later, our position will have changed by the diameter of the Earths orbit around the sun. See Figure 5.47. For stars that are within about 100 light-years of Earth, the change in viewing location is sufficient to make the star appear to be in a different location in the sky. Half of the angle from one location to the next is known as the parallax angle. Even for nearby stars, the parallax angle is very small 43 and is normally measured in seconds of arc. The distance to a star can be determined from the parallax angle. The table on next page gives the parallax angle p measured in seconds of arc and the distance d from the sun in light years. Star Parallax angle Distance Markab 0.030 109 Al Nair 0.051 64 Alderamin 0.063 52 Altair 0.198 16.5 Vega 0.123 26.5 Rasalhague 0.056 58 a.Make a power function model of the data for d in terms of p. b.If one star has a parallax angle that is twice that of a second, how do their distances compare? c.The star Mergez has a parallax angle of 0.052second of arc. Use functional notation to express how far way Mergez is, and then calculate that value. d.The star Sabik is 69 light-years from the sun. What is its parallax angle?arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. From New York to Miami AgainThe city of Richmond, Virginia, is about halfway between New York and Miami. A Richmond resident might locate the airplane in Example 6.1 using distance north of Richmond. Make the graphs of location and velocity of the airplane from this perspective. EXAMPLE 6.1 FROM NEW YORK TO MIAMI An airplane leaves Kennedy Airport in New York and flies to Miami, where it is serviced and receives new passengers before returning to New York. Assume that the trip is uneventful and that after each takeoff, the airplane accelerates to its standard cruising speed, which it maintains until it decelerates prior to landing. Part 1 Describe what the graph of distance south of New York looks like during the period when the airplane is maintaining its standard cruising speed on the way to Miami. Part 2 Say we locate the airplane in terms of its distance south of New York. Make possible graphs of its distance south of New York versus time and of the velocity of the airplane versus time. Part 3 Say we locate the airplane in terms of its distance north of Miami. Make possible graphs of its distance north of Miami versus time and of the velocity of the airplane versus time.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. View from the Top Your office window is 35 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is 600 horizontal feet from your office. You know that the statue is 125 feet from the building. How tall is the statue? See Figure 3.14.)arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. A Cold Front At 4P.M. on a winter day, an arctic air mass moved from Kansas into Oklahoma, causing temperatures to plummet. The temperature T=T(h) in degrees Fahrenheit h hours after 4P.M. in Stillwater, Oklahoma, on that day is recorded in the following table. h=Hourssince4P.M. T=Temperature 0 62 1 59 2 38 3 26 4 22 a. Use functional notation to express the temperature in Stillwater at 5:30P.M., and then estimate its value. b. What was the average rate of change per minute in temperature between 5P.M. and 6P.M.? What was the average decrease per minute over that time interval? c. Estimate the temperature at 5:12P.M. d. At about what time did the temperature reach the freezing point? Explain your reasoning.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Surveying Vertical CurvesWhen 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. Its 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 100feet apart. To link a straight grade of g1 to a straight grade of g2, the elevations of the stations are given by y=g2g12Lx2+g1x+Eg1L2. Here y is the elevation of the vertical curve in feet, g1 and g2 are percents, L is the length of the vertical curve in hundreds of feet, x is the number of the station, and E is the elevation in feet of the intersection where the two grades would meet.See Figure 5.72. The station x=0 is the very beginning of the vertical curve, so the station x=0 lies where the straight section with grade g1 meets the vertical curve. The last station of the vertical curve is x=L, which lies where the vertical curve meets the straight section with grade g2. Figure 5.72 Assume that the vertical curve you want to design goes over a slight rise, joining a straight section of grade 1.35 to a straight section of grade 1.75. Assume that the length of the curve is to be 500feet so L=5 and that the elevation of the intersection is 1040.63feet. a.What is the equation for the vertical curve described above? Dont 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.arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Coxs Formula Assume that a long horizontal pipe connects the bottom of a reservoir with a drainage area. Coxs formula provides a way of determining the velocity v of the water flowing through the pipe: HdL=4v2+5v21200. Here H is the depth of the reservoir in feet, d is the pipe diameter in inches, L is the length of the pipe in feet, and the velocity v of the water is in feet per second. See Figure 5.71. a. Graph the quadratic function 4v2+5v2, using a horizontal span from 0 to 10. b. Judging on the basis of Coxs formula, is it possible to have a velocity of 0.25 foot per second? c. Find the velocity of the water in the pipe if the pipes diameter is 4 inches, its length is 1000 feet, and the reservoir is 50 feet deep. d. If the water velocity is too high, there will be erosion problems. Assuming that the pipe length is 1000 feet and the reservoir is 50 feet deep, determine the largest pipe diameter that will ensure that the water velocity does not exceed 10 feet per second.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning