Chapter 9: Problem 33
List the terms of the expression. $$-3+x$$
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Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$4 x^{2}-3=57$$
Use a calculator to solve the equation or write no solution. Round the results to the nearest hundredth. $$5 a^{2}+10=20$$
In parts (a)-(d), a batter hits a pitched baseball when it is 3 feet off the ground. After it is hit, the height \(h\) (in feet) of the ball at time \(t\) (in seconds) is modeled by$$h=-16 t^{2}+80 t+3$$where \(t\) is the time (inseconds). a.Find the time when the ball hits the ground in the outfield. b.Write a quadratic equation that you can use to find the time when the baseball is at its maximum height of 103 feet. Solve the quadratic equation. c.Use a graphing calculator to graph the function. Use the zoom feature to approximate the time when the baseball is at its maximum height. Compare your results with those you obtained in part (b). d.What factors change the path of a baseball? What factors would contribute to hitting a home run?
CHANGING C-VALUES In Exercises 21-23, find values of \(c\) so that the equation will have two solutions, one solution, and no real solution. Then sketch the graph of the equation for each value of \(c\) that you chose. $$2 x^{2}+3 x+c=0$$
In Exercises 25 and 26 , use the vertical motion model \(\boldsymbol{h}=-\mathbf{1 6 t}^{2}+\boldsymbol{v t}+\boldsymbol{s}(\mathbf{p} . \mathbf{5 3 5})\) and the following information. You and a friend are playing basketball. You can jump with an initial velocity of 12 feet per second. You need to jump 2.2 feet to dunk a basketball. Your friend can jump with an initial velocity of 14 feet per second. Your friend needs to jump 3.4 feet to dunk a basketball. Can you dunk the ball? Can your friend? Justify your answers.
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