91Ó°ÊÓ

Find the \(x\) and \(y\)-intercepts of the line, and draw its graph. \(5 x+2 y-10=0\)

Radicals Simplify the expression, and eliminate any negative exponents(s). Assume that all letters denote positive numbers. (a) \(\sqrt[5]{x^{3} y^{2}} \sqrt[19]{x^{4} y^{16}}\) (b) \(\frac{\sqrt[3]{8 x^{2}}}{\sqrt{x}}\)

Scientific Notation Write each number in scientific notation. (a) \(129,540,000\) (b) \(7,259,000,000\) (c) 0.0000000014 (d) 0.0007029

Find the area of the triangle formed by the coordinate axes and the line $$2 y+3 x-6=0$$

Use scientific notation, the Laws of Exponents, and a calculator to perform the indicated operations. State your answer rounded to the number of significant digits indicated by the given data. $$\frac{\left(3.542 \times 10^{-6}\right)^{9}}{\left(5.05 \times 10^{4}\right)^{12}}$$

Without using a calculator, determine which number is larger in each pair. (a) \(2^{1 / 2}\) or \(2^{1 / 3}\) (b) \(\left(\frac{1}{2}\right)^{1 / 2}\) or \(\left(\frac{1}{2}\right)^{1 / 3}\) (c) \(7^{1 / 4}\) or \(4^{1 / 3}\) (d) \(\sqrt[3]{5}\) or \(\sqrt{3}\)

If you had a million \(\left(10^{6}\right)\) dollars in a suitcase, and you spent a thousand (10 ) dollars each day, how many years would it take you to use all the money? Spending at the same rate, how many years would it take you to empty a suitcase filled with a billion ( \(10^{9}\) ) dollars?

Depth of a Well One method for determining the depth of a well is to drop a stone into it and then measure the time it takes until the splash is heard. If \(d\) is the depth of the well (in feet) and \(t_{1}\) the time (in seconds) it takes for the stone to fall, then \(d=16 t_{1}^{2},\) so \(t_{1}=\sqrt{d} / 4 .\) Now if \(t_{2}\) is the time it takes for the sound to travel back up, then \(d=1090 t_{2}\) because the speed of sound is 1090 ft's. So \(t_{2}=d / 1090\) Thus the total time elapsed between dropping the stone and hearing the splash is $$t_{1}+t_{2}=\frac{\sqrt{d}}{4}+\frac{d}{1090}$$ How deep is the well if this total time is 3 s? PICTURE CANT COPY

Use the Difference of Squares Formula \(A^{2}-B^{2}=(A+B)(A-B)\) to evaluate the following differences of squares in your head. Make up more such expressions that you can do in your head. (a) \(528^{2}-527^{2}\) (b) \(122^{2}-120^{2}\) (c) \(1020^{2}-1010^{2}\)