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Chapter 7: Problem 11
Write an equation that expresses each relationship. Then solve the equation for \(y .\) \(x\) varies jointly as \(y\) and \(z\)
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A company that manufactures wheelchairs has fixed costs of \(\$ 500,000 .\) The average cost per wheelchair, \(C,\) for the company to manufacture \(x\) wheelchairs per month is modeled by the formula $$ C=\frac{400 x+500,000}{x} $$ Use this mathematical model to solve Exercises \(69-70\). How many wheelchairs per month can be produced at an average cost of \(\$ 450\) per wheelchair?
Factor completely: \(x^{4}+2 x^{3}-3 x-6 .\) (Section 6.1 Example 8 )
Perform the indicated operation or operations. Simplify the result, if possible. $$\frac{7 y-2}{y^{2}-y-12}+\frac{2 y}{4-y}+\frac{y+1}{y+3}$$
In Exercises \(87-90\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. All real numbers satisfy the equation \(\frac{3}{x}-\frac{1}{x}=\frac{2}{x}\)
We have seen that Young's rule $$ C=\frac{D A}{A+12} $$ can be used to approximate the dosage of a drug prescribed for children. In this formula, \(A=\) the child's age, in years, \(D=\)an adult dosage, and \(C=\)the proper child's dosage. Use this formula to solve Exercises \(73-74\) When the adult dosage is 1000 milligrams, a child is given 500 milligrams. What is that child's age?
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