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TEST FOR UNDERSTANDING FOR EXAMPLE
Find a formula for the path of the cannonball if the slope of the angle of elevation is
EXAMPLE
A cannonball fired from a cannon will follow the path of the parabola that is the graph of
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Simply Supported Beam A simply supported 20-foot beam supports a uniformly distributed load of 1000 pounds per foot. The bending moment M (in foot - pounds) x feet from one end of the beam is given by M=500x(20x). (a) Where is the bending moment zero? (b) Use a graphing utility to graph the equation. (c) Use the graph to determine the point on the beam where the bending moment is the greatest.arrow_forwardOrbit of a Satellite A satellite is in orbit around the moon. A coordinate plane containing the orbit is set up with the center of the moon at the origin, as shown in the following graph, with distances measured in megameters (Mm). The equation of the satellites orbit is (x3)225+y216=1 a From the graph, determine the closest to and the farthest from the center of the moon that the satellite gets. b There are two points in the orbit with y-coordinates 2. Find the x-coordinates of these points, and determine their distances to the center of the moon.arrow_forwardTEST YOUR UNDERSTANDING | FOR EXAMPLE 5.12 Find a formula for the roof line in the example if the center height is 8feet above the outside wall rather than 4feet. EXAMPLE 5.12ROOF LINES The outside wall of a house is 10feet high. From the western wall, the roof rises 4feet over a horizontal span of 16feet and then descends at the same rate another horizontal span of 16feet to the eastern wall see Figure 5.55arrow_forward
- Reminder Round all the answers to two decimal places unless otherwise indicated. Using the Quadratic Formula Solve part 1 of Example 5.14 using the quadratic formula. EXAMPLE 5.14FLIGHT OF A CANNONBALL A cannonball fired from a cannon will follow the path of the parabola that is the graph of y=y(x), where y=16(1+s2)(x/v0)2+sx feet. Here s is the slope of inclination of the cannon barrel, v0 is the initial velocity in feet per second, and the variable x is the distance downrange in feet. Suppose that a cannon is elevated with a slope of 0.5 corresponding to an angle of inclination of about 27 degrees and the cannonball is given an initial velocity of 250 feet per second. See Figure 5.62. Part 1 How far will the cannonball travel?arrow_forwardTemperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where x = 0 corresponds to 6 a.m. These data can be approximated by the model y=0.026x31.03x2+10.2x+34,0x24 Use a graphing utility to create a scatter plot of the data. Then graph the model in the same viewing window. How well does the model fit the data? Use the graph to approximate the times when the temperature was increasing and decreasing. Use the graph to approximate the maximum and minimum temperatures during this 24-hour period. Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?arrow_forwardTangent Line to a Circle Find an equation for the line tangent to the circle x2+y2=25 at the point (3,4).see the figure. At what other point on the circle will a tangent line be parallel to the tangent line in part a?arrow_forward
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