Chapter 1: Fundamentals

A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one-third the height of the entire structure. If the total volume of the structure is$1400\pi {\mathrm{ft}}^3$and its radius is$10\mathrm{ft}.$what is its height?

Determine whether the given value is a solution of the equation

$4x+7=9x-3$

(a)$x=-2$

(b)$x=2$

Life Expectancy The average life expectancy in the United States has been rising steadily over the past few decades, as shown in the table.

(a) Make a scatter plot of the data.

(b) Find and graph the regression line.

(c) Use the linear model you found in part (b) to predict the life expectancy in the year 2006.

(d) Search the Internet or your campus library to find the actual 2006 average life expectancy. Compare to your answer in part (c).

Perform the indicated operations, and write the result in the form

(a)$(3-2i)+(4+3i)$

(b)$(3-2i)-(4+3i)$

(c)$(3-2i)(4+3i)$

(d)$\frac{(3-2i)}{(4+3i)}$

(e)$i^{48}$

(f)$(\sqrt{2}-\sqrt{-2})(\sqrt{8}+\sqrt{-2})$

If the graph of an equation is symmetric with respect to both the x- and y-axes, is it necessarily symmetric with respect to the origin?

Express the given quantity in terms of the indicated variable.

The sum of three consecutive even integers; n = first integer of the three.

Find the domain of the expression.

$\frac{x^2-1}{x-3}$

9-10: Real Numbers: List the elements of the given set that are

1. Natural numbers
2. Integers
3. Rational numbers
4. Irrational numbers

$\left\{-1.5,0,\frac{5}{2},\sqrt{7},2.71,-\pi ,3.1\overline{4},100,-8\right\}$

Solution? Let $S=\left\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\right\}.$ Determine which elements of satisfying the inequality.

$1<2x-4\le 7$

Write each radical expression using exponents, and each exponential expression using radicals.

$\frac{1}{\sqrt{3}}$