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Chapter 5: Problem 53
Explain what is meant by the partial fraction decomposition of a rational expression.
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Bottled water and medical supplies are to be shipped to survivors of an earthquake by plane. The bottled water weighs 20 pounds per container and medical kits weigh 10 pounds per kit. Each plane can carry no more than \(80,000\) pounds. If \(x\) represents the number of bottles of water to be shipped per plane and \(y\) represents the number of medical kits per plane, write an inequality that models each plane's \(80,000\)-pound weight restriction.
In Exercises 106-109, determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing a linear inequality, I should always use \((0,0)\) as a test point because it's easy to perform the calculations when 0 is substituted for each variable.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Partial fraction decomposition involves finding a single rational expression for a given sum or difference of rational expressions.
Exercises 37-39 will help you prepare for the material covered in the first section of the next chapter. Solve the system: $$\left\\{\begin{aligned}w-x+2 y-2 z &=-1 \\\x-1 y+z &=1 \\\y-z &=1 \\\z-&-3\end{aligned}\right.$$ Express the solution set in the form \(\\{(\boldsymbol{x}, \boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z})\\} .\) What makes it fairly easy to find the solution?
What is a constraint in a linear programming problem? How is a constraint represented?
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