91Ó°ÊÓ

Manufacturing Company manufactures steel rods. Suppose the rods ordered by a customer are manufactured to a specification of \(0.5\) in. and are acceptable only if they are within the tolerance limits of \(0.49\) in. and \(0.51\) in. Letting \(x\) denote the diameter of a rod, write an inequality using absolute value to express a criterion involving \(x\) that must be satisfied in order for a rod to be acceptable.

Rationalize the denominator of the expression. $$ \frac{y}{\sqrt[3]{x^{2} z}} $$

Use the discriminant to determine the number of real solutions of the equation. $$ 4 x^{2}+12 x+9=0 $$

Rationalize the denominator of the expression. $$ \frac{2 x}{\sqrt[3]{x y^{2}}} $$

The diameter \(x\) (in inches) of a batch of ball bearings manufactured by PAR Manufacturing satisfies the inequality $$ |x-0.1| \leq 0.01 $$ What is the smallest diameter a ball bearing in the batch can have? The largest diameter?

Use the discriminant to determine the number of real solutions of the equation. $$ 25 x^{2}-80 x+64=0 $$

Use the discriminant to determine the number of real solutions of the equation. $$ \frac{6}{k^{2}}+\frac{1}{k}-2=0 $$

Write the expression in simplest radical form. $$ \sqrt{\frac{16}{3}} $$

Use the discriminant to determine the number of real solutions of the equation. $$ (2 p+1)^{2}-3(2 p+1)+4=0 $$

Write the expression in simplest radical form. $$ -\sqrt{\frac{8}{3}} $$