91Ó°ÊÓ

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{r-9}{\sqrt{r}-3} $$

The coefficient of self-induction \(L\) (in henrys), the energy P stored in an electronic circuit (in joules), and the current I (in amps) are related by the formula $$ I=\sqrt{\frac{2 P}{L}} $$ Find \(I\) if \(P=100\) and \(L=40 .\)

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt[6]{y^{5}} \cdot \sqrt[3]{y^{2}} $$

Find each power of i. $$i^{-17}$$

Simplify. Assume that all variables represent positive real numbers. \(\sqrt[3]{-81 m^{4} n^{10}}\)

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{4}{\sqrt{x}-2 \sqrt{y}} $$

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \frac{\sqrt[3]{t^{4}}}{\sqrt[5]{t^{4}}} $$

Gives a method of finding the area of a triangle if the lengths of its sides are known. Suppose that \(a, b\), and \(c\) are the lengths of the sides. Let s denote one-half of the perimeter of the triangle (called the semiperimeter) - that is, $$ s=\frac{1}{2}(a+b+c) $$ Then the area of the triangle is given by $$ \mathscr{A}=\sqrt{s(s-a)(s-b)(s-c)} $$ Use Heron's formula to solve each problem. Find the area of the Bermuda Triangle, to the nearest thousand square miles, if the "sides" of this triangle measure approximately \(960 \mathrm{mi}, 1030 \mathrm{mi}\), and \(1030 \mathrm{mi}\).

Rationalize each denominator. Assume that all variables represent positive real numbers and that no denominators are 0. $$ \frac{5}{3 \sqrt{r}+\sqrt{s}} $$

Find each power of i. $$i^{-27}$$