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Chapter 8: Problem 7
Graph each inequality. $$y>2 x-1$$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y<12\), it's not necessary for me to graph the linear equation \(3 x-4 y=12\) because the inequality contains a \(<\) symbol, in which equality is not included.
An object moves in simple harmonic motion described by \(d=6 \cos \frac{3 \pi}{2} t,\) where \(t\) is measured in seconds and \(d\) in inches. Find: a. the maximum displacement b. the frequency c. the time required for one cycle. (Section \(5.8, \text { Example } 8)\)
An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of \(x\) and \(y\) for which the maximum occurs. Objective Function Constraints $$\begin{aligned} &z=3 x+2 y\\\ &\left\\{\begin{array}{c} {x \geq 0, y \geq 0} \\ {2 x+y \leq 8} \\ {x+y \geq 4} \end{array}\right. \end{aligned}$$
Use the two steps for solving a linear programming problem, given in the box on page \(888,\) to solve the problems. A theater is presenting a program for students and their parents on drinking and driving. The proceeds will be donated to a local alcohol information center. Admission is 2.00 for parents and 1.00 for students. However, the situation has two constraints: The theater can hold no more than 150 people and every two parents must bring at least one student. How many parents and students should attend to raise the maximum amount of money?
For the linear function \(f(x)=m x+b, f(-3)=23\) and \(f(2)=-7 .\) Find \(m\) and \(b\).
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