Reminder Round all answers to two decimals places unless otherwise indicated.
Earth’s Umbra Earth has a shadow in space, just as people do on a sunny day. The darkest part
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Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- 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_forwardReminder Round all answers to two decimals places unless otherwise indicated. An Overflow Pipeline An overflow pipeline for a pond is to run in a straight line from the pond at maximum water level a distance of 96 horizontal feet to a drainage area that is 5 vertical feet below the maximum water level see Figure 3.21. How much lower is the pipe at the end of each 12-foot horizontal stretch?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. The Photic Zone This is a continuation of Exercise 18. In the ocean, the photic zone is the region where there is sufficient light for photosynthesis to occur. See Figure 4.12. For marine phytoplankton, the photic zone extends from the surface of the ocean to a depth where the light intensity is about 1 of surface light. Near Cape Cod, Massachusetts, the depth of the photic zone is about 16meters. In waters near Cape Cod, by what percentage does light intensity decrease for each additional meter of depth?arrow_forwardReminder 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 moons umbra on Earths surface is so small 2 that we can consider that the umbra reaches its apex at Earths center. The sun is 93,498,600 miles away from Earth. What is the radius of the sun? The actual radius is 434,994 miles. Because of our simplified assumptions, you will get a slightly different, though relatively close, answer. 23. 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 sum 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 fir inside Earths umbra? What celestial event occurs when this happens?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
- Reminder Round all answers to two decimal places unless otherwise indicated. Poiseuilles law for fluid velocitiesPoiseuilles law describes the velocities of fluids flowing in a tube---for example, the flow of blood in a vein. See Figure 5.74 This law applies when the velocities are not too large----more specifically, when the flow has no turbulence. In this case, the flow is laminar, which means that the paths of the flow are parallel to the tube walls. The law states that v=k(R2r2), where v is the velocity, k is a constant which depends on the fluid, the tube, and the units used for measurement, R is the radius of the tube, and r is the distance from the centerline of the tube. Since k and R are fixed for any application, v is a function at a point of distance r from the centerline of the tube. a.What is r for a point along the walls of the tube? What is the velocity of the fluid along the walls of the tube? b.Where in the tube does the fluid flow most rapidly? c.Choose numbers for k and R, and make a graph of v as a function of r. Use a horizontal span of 0 to R. d.Describe your graph from part c. e.Explain why you needed to use a horizontal span of 0 to R in order to describe the flow throughout the tube.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. 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_forward
- Reminder 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_forwardReminder Round all answers to two decimal places unless otherwise indicated. Finding Poles Find the poles of y=2x5x2+4x+3.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