Chapter 1: Fundamentals

Find the equation of the circle shown in figure

Sketch the region given by the set

$\left\{\left(x,y\right)\left|x\ge 4\text{or}y\ge 2\right.\right\}$

Find the real solutions of the equation$\sqrt{5-x}+1=x-2$.

A clothing manufacturer finds that the cost of producing x shirts is $500+6x+0.01x^2$dollars.

(a) Explain why the average cost per shirt is given by the rational expression

$A=\frac{500+6x+0.01x^2}{x}$

(b) Complete the table by calculating the average cost per shirt for the given values of x.

A set of real numbers is graphed. Find an inequality involving an absolute value that describes the set.

A set of real numbers is graphed. Find an inequality involving an absolute value that describes the set.

The rational expression$\frac{x^2-9}{x-3}$is not defined for $x=3$. Complete the tables, and determine what value the expression approaches as x gets closer and closer to 3. Why is this reasonable? Factor the numerator of the expression and simplify to see why

Factor the expression completely.

$x^2-2x-8$

Find the real solutions of the equation $2x+\sqrt{x+1}=8$.

The average ocean depth is $3.7\times {10}^3\mathrm{m}$and the area of the oceans is$3.6\times {10}^{14}{\mathrm{m}}^2$. What is the total volume of the ocean in liters? (one cubic meter contain 1000 liters)