Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Parallax Angle If we view a star now, and then view it again
Star | Parallax angle | Distance |
Markab |
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Al Na’ir |
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Alderamin |
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Altair |
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Vega |
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Rasalhague |
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a. Make a power function model of the data for
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
d. The star Sabik is
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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. 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Rubber Ball A rubber ball is dropped from the top of a building. The ball lands on concrete and bounces once before coming to rest on the grass. Measure the location of the ball as its distance up from the ground. Make graphs of the location and velocity of the ball.arrow_forward
- 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. 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_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. Looking Up The constant g32feetpersecondpersecond is the downward acceleration due to gravity near the surface of the Earth. If we stand on the surface of the Earth and locate objects using their distance up from the ground, then the positive direction is up, so down is the negative direction. With this perspective, the equation of change in velocity for a freely falling object would be expressed as dVdt=g. We measure upward velocity V in feet per second and time t in seconds. Consider a rock tossed upward from the surface of the Earth with an initial velocity of 40feetpersecond upward. a. Use a formula to express the velocity VV(t) as a linear function. Hint: You get the slope of V from the equation of change. The vertical intercept is the initial value. b. How many seconds after the toss does the rock reach the peak of its flight? Hint: What is the velocity of the rock when it reaches its peak? c. How many seconds after the toss does the rock strike the ground? Hint: How aces me time it takes for the rock to rise to its peak compare with the time it takes for it to fall hack to the ground?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Binary Stars Binary stars are pairs of stars that orbit each other. The period p of such a pair is the time, in years, required for a single orbit. The separation s between such a pair is measured in seconds of arc. The parallax angle a also in seconds of arc for any stellar object is the angle of its apparent movement as the Earth moves through one half of its orbit around the sun. Astronomers can calculate the total mass M of a binary system using M=s3a3p2 Here M is the number of solar masses. a. Alpha Centauri, the nearest star to the sun, is in fact a binary star. The separation of the pair is s=17.6 seconds of arc, its parallax angle is a=0.76 second of arc, and the period of the pair is 80.1years. What is the mass of the Alpha Centauri pair? 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?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A Wrap Skirt Figure 3.13 shows a simplified pattern for a wrap skirt that is 20 inches long. The bottom hem for this pattern has a length of 63 inches. Suppose you decide to alter the pattern to make a skirt that is 24 inches long. What should be the length of the bottom hem?arrow_forward
- Reminder 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_forwardReminderRound all answers to two decimal places unless otherwise indicated. Falling with a parachuteWhen an average-sized man with a parachute jumps from an airplane, he will fall S=12.5(0.2t1)+20t feet in t seconds. a.Plot the graph of S versus t over at least the first 10seconds of the fall. b.How far does the parachutist fall in 2seconds? c.Calculate dSdt at 2seconds into the fall and explain what the number you calculated means in practical terms.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Wind ChillThe graph in Figure 1.40 shows the temperature T = Tv adjusted for wind chill as a function of the velocity v of the wind when the thermometer reads 30 degrees Fahrenheit. The adjusted temperature T shows the temperature that has an equivalent cooling power when there is no wind. a. At what wind speed is the temperature adjusted for wind chill equal to 0? b. Your answer in part a is the solution of an equation involving Tv. Which equation? c. At what value of v would a small increase in v have the greatest effect on Tv? In other words, at what wind speed could you expect a small increase in wind speed to cause the greatest change in wind chill? Explain your reasoning. d. Suppose the wind speed is 45 miles per hour. Judging from the shape of the graph, how significant would you expect the effect on Tv to be if the wind speed increased? FIGURE 1.40 Temperature adjusted for wind chill when the thermometer reads 30 degrees Fahrenheit.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning