Reminder 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
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?
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder 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_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 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_forward
- 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 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 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 to two decimal places unless otherwise indicated. Finding Poles Find the poles of y=2x5x2+4x+3.arrow_forward
- Reminder Round all answers two decimals places unless otherwise indicated. A Cathedral Ceiling A cathedral ceiling shown in Figure 3.18 is 8 feet high at the west wall of a room. As you go from the west wall toward the east wall the ceiling slants upward. Three feet from the west wall, the ceiling is 10.5 feet high. a. What is the slope of the ceiling? b. The width of the room the distance from the west wall to the east wall is 17 feet. How high is the ceiling at the east wall? c. You want to install a light in the ceiling as far away from the west wall as possible. You intend to change the bulb, when required, by standing near the top of your small stepladder. If you stand on the highest safe step of your stepladder, you can reach 12 feet high. How far from the west wall should you install the light?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. 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. Quadratic Formula Use the quadratic formula to solve 2x2x1=0.arrow_forwardReminder Round all answers two decimals places unless otherwise indicated. A Ramp to a Building The base of a ramp sits on the ground see Figure 3.17.) Its slope is 0.4, and it extends to the top of the front steps of a building 15 horizontal feet away. a. How high is the ramp 1 horizontal foot towards the building from the base of the ramp? b. How high is the top of the steps relative to the ground?arrow_forwardReminder Round all answers to two decimals places unless otherwise indicated. A Wheelchair Service Ramp The Americans with Disabilities Act ADA requires, among other things, that wheelchair service ramps have a slope not exceeding 1/12. a. Suppose the front steps of a building are 2 feet high. You want to make a ramp conforming to ADA standards that reaches from the ground to the top of the steps. How far away from the building is the base of the ramp? b. Another way to give specifications on a ramp is to give allowable inches of rise per foot of run. In these terms, how many inches of rise does the ADA requirement allow in 1 foot of run?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,