Reminder Round all answers two decimals places unless otherwise indicated.
The Umbra of the Moon This is a continuation of Exercise 23. A total eclipse of the sun occurs when we are in the umbra of the moon. The size of the moon’s umbra on Earth’s surface is so small
23. Earth’s Umbra Earth has a shadow in space, just as people do on a sunny day. The darkest part
Trending nowThis is a popular solution!
Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
College Algebra (5th Edition)
Intermediate Algebra for College Students (7th Edition)
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
A Graphical Approach to College Algebra (6th Edition)
College Algebra with Modeling & Visualization (5th Edition)
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
- Reminder Round all answers to two decimals places unless otherwise indicated. Earths Umbra Earth has a shadow in space, just as people do on a sunny day. The darkest part 1 of that shadow is a conical region in space known as the umbra. A representation of Earths umbra is shown in Figure 3.24. Earth has radius of about 3960 miles, and the umbra ends at a point about 860,000 miles from Earth. The moon is about 239,000 miles from Earth and has a radius of about 1100 miles. Consider a point on the opposite side of Earth from the sun and at a distance from Earth equal to the moons distance from Earth. What is the radius of the umber at that point? Can the moon fit inside Earths umbra? What celestial event occurs when this happens?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 two decimals places unless otherwise indicated. An Ice Cream Cone An ice cream cone is 4 inches deep and 2 inches across the top. See Figure 3.16.) If we wanted to make a king-size cone that has the same shape but is 2.5 inches across the top, how deep would the cone be?arrow_forward
- Reminder 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. 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. 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_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. NoteSome of the formulas below use the special number e, which was presented in the Prologue. Mitscherlichs EquationAn important agriculture problem is to determine how a quantity of nutrient, such as nitrogen, affects the growth of plants. We consider the situation wherein sufficient quantities of all but one nutrient are present. One boule of a nutrient is the amount needed to produce 50 of maximum possible yield. In 1990, E.A. Mitscherlichs proposed the following relation, which is known as Mitscherlichs Equation: Y=10.5b. Here b is the number of baules of nutrient applied, and Y is the percentage as a decimal of maximum yield produced. a.Verify that the formula predicts that 50 of maximum yield will be produced if 1 baule of nutrient is applied. b.Use functional notation to express the percentage of maximum yield produced by 3 baule of nutrient, and calculate the value. c.The exact value of a baule depends on the nutrient in question. For nitrogen, 1 baule is 223 pounds per acre. What percentage of maximum yield will be produced if 500 pounds of nitrogen per acre is present?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. Ship Propellers An ideal diameter d, in feet, of a ships propeller is given by the formula d=ch1/5r3/5. Here h is the horsepower of the engine driving the propeller. r is the maximum number of revolutions per minute of the propeller, and c is a constant. In both parts, give your answer in terms of a percentage. a. If the horsepower is increased by 20 while the number of revolutions per minute remains the same, how is the propeller diameter affected? b. If the horsepower remains the same while the number of revolutions per minute is increased by 20, how is the propeller diameter affected?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below use the special number e, which was presented in the Prologue. A Roast is taken from the refrigerator where it had been for several days and placed immediately in a preheated oven to cook. The temperature R=R(t) of the roast t minutes after being placed in the oven is given by R=325280e0.005tdegreesFahrenheit a. What is the temperature of the refrigerator? b. Express the temperature of the roast 30 minutes after being put in the oven in functional notation, and then calculate its value. c. By how much did the temperature of the roast increase during the first 10 minutes of cooking? d. By how much did the temperature of the roast increase from the first hour to 10 minutes after the first hour of cooking?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_forwardReminder Round all answers to two decimal places unless otherwise indicated. 6. Lanes on a Curved Track On a curved track, the lanes are arcs of circles, but each with a different radius. For a typical 100-meter curved track with several lanes, the inner radius of the nth lane is R(n)=100+1.22(n1) In meters. a. What is the radius of first plane? b. What is the width of each lane? c. It is more difficult to run in a lane with a small radius. If you wish to run in a lane with a radius of at least 35 meters, which lane should you pick?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning