91Ó°ÊÓ

Evaluate the discriminant for each equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or non real complex. Do not solve the equation. $$8 x^{2}-72=0$$

Solve each equation. $$625 x^{-4}-125 x^{-2}+4=0$$

Solve each problem. The industrial process that is used to convert methanol to gasoline is carried out at a temperature range of \(680^{\circ} \mathrm{F}\) to \(780^{\circ} \mathrm{F}\). Using \(F\) as the variable, write an absolute value inequality that corresponds to this range.

A projectile is fired straight up from ground level. After \(t\) seconds, its height above the ground is \(s\) feet, where $$s=-16 t^{2}+220 t$$ For what time period is the projectile at least \(624 \mathrm{ft}\) above the ground?

Find the values of \(a, b,\) and \(c\) for which the quadratic equation $$ a x^{2}+b x+c=0 $$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) $$-3,2$$

Solve each equation for the indicated variable. Assume all denominators are nonzero. $$\frac{1}{R}=\frac{1}{r_{1}}+\frac{1}{r_{2}}, \quad \text { for } R$$