91Ó°ÊÓ

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt{81}$$

The formula occurs in the indicated application. Solve for the specified variable. \(\frac{1}{f}=\frac{1}{p}+\frac{1}{q}\) for \(q\) (lens equation)

Solve the equation or inequality. Express the solutions in terms of intervals whenever possible. $$\frac{3}{2 x+3}<\frac{1}{x-2}$$

The number of hydrogen atoms in a mole is Avogadro's number, \(6.02 \times 10^{23} .\) If one mole of the gas has a mass of 1.01 grams, estimate the mass of a hydrogen atom.

Simplify the expression. $$\frac{\frac{3}{x-1}-\frac{3}{a-1}}{x-a}$$

The population dynamics of many fish are characterized by extremely high fertility rates among adults and very low survival rates among the young. A mature halibut may lay as many as 2.5 million eggs, but only \(0.00035 \%\) of the offspring survive to the age of 3 years. Use scientific form to approximate the number of offspring that live to age 3

The formula occurs in the indicated application. Solve for the specified variable. \(\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\) for \(R_{2}\) (three resistors connected in parallel)

Solve the equation or inequality. Express the solutions in terms of intervals whenever possible. $$\frac{x+1}{x^{2}-25} \leq 0$$

Simplify the expression. $$\frac{\frac{x+2}{x}-\frac{a+2}{a}}{x-a}$$

Simplify the expression, and rationalize the denominator when appropriate. $$\sqrt[3]{-125}$$