Chapter 2

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{\left(x^{2}+1\right)(x-3)}{x^{2}-9} \geq 0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 3-5 x<11 $$

Exer. 1-50: Solve the equation. $$ x=3+\sqrt{5 x-9} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{-3-2 i}{5+2 i} $$

A farmer plans to use 180 feet of fencing to enclose a rectangular region, using part of a straight river bank instead of fencing as one side of the rectangle, as shown in the figure on the next page. Find the area of the region if the length of the side parallel to the river bank is (a) twice the length of an adjacent side. (b) one-half the length of an adjacent side. (c) the same as the length of an adjacent side.

Solve the equation. $$\frac{3}{2 x-4}-\frac{5}{3 x-6}=\frac{3}{5}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x^{2}-x}{x^{2}+2 x} \leq 0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 2 x+5<3 x-7 $$

Exer. 1-50: Solve the equation. $$ x+\sqrt{5 x+19}=-1 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{4-2 i}{-5 i} $$

Exer. 25-26: Determine the value or values of \(d\) that complete the square for the expression. (a) \(x^{2}+9 x+d\) (b) \(x^{2}-8 x+d\) (c) \(x^{2}+d x+36\) (d) \(x^{2}+d x+\frac{49}{4}\)

Solve the equation. $$\frac{9}{2 x+6}-\frac{7}{5 x+15}=\frac{2}{3}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{(x+3)^{2}(2-x)}{(x+4)\left(x^{2}-4\right)} \leq 0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x-8>5 x+3 $$

Exer. 1-50: Solve the equation. $$ x-\sqrt{-7 x-24}=-2 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{-2+6 i}{3 i} $$

Exer. 25-26: Determine the value or values of \(d\) that complete the square for the expression. (a) \(x^{2}+13 x+d\) (b) \(x^{2}-6 x+d\) (c) \(x^{2}+d x+25\) (d) \(x^{2}+d x+\frac{81}{4}\)

Solve the equation. $$2-\frac{5}{3 x-7}=2$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x-2}{x^{2}-3 x-10} \geq 0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 9+\frac{1}{3} x \geq 4-\frac{1}{2} x $$

Exer. 1-50: Solve the equation. $$ \sqrt{7-2 x}-\sqrt{5+x}=\sqrt{4+3 x} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (2+5 i)^{3} $$

Solve the equation. $$\frac{6}{2 x+11}+5=5$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x+5}{x^{2}-7 x+12} \leq 0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{1}{4} x+7 \leq \frac{1}{3} x-2 $$

Exer. 1-50: Solve the equation. $$ 4 \sqrt{1+3 x}+\sqrt{6 x+3}=\sqrt{-6 x-1} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (3-2 i)^{3} $$

Exer. 27-30: Solve by completing the square. (Note: See the discussion after Example 5 for help in solving Exercises 29 and 30 .) $$ x^{2}-8 x+11=0 $$

A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height \(h\) of the silo that will result in a capacity of \(11,250 \pi \mathrm{ft}^{3}\).

Solve the equation. $$\frac{1}{2 x-1}=\frac{4}{8 x-4}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{-3 x}{x^{2}-9}>0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ -3<2 x-5<7 $$

Exer. 1-50: Solve the equation. $$ \sqrt{11+8 x}+1=\sqrt{9+4 x} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (2-\sqrt{-4})(3-\sqrt{-16}) $$

Exer. 27-30: Solve by completing the square. (Note: See the discussion after Example 5 for help in solving Exercises 29 and 30 .) $$ 4 x^{2}-12 x-11=0 $$

Solve the equation. $$\frac{4}{5 x+2}-\frac{12}{15 x+6}=0$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{2 x}{16-x^{2}}<0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 4 \geq 3 x+5>-1 $$

Exer. 1-50: Solve the equation. $$ 2 \sqrt{x}-\sqrt{x-3}=\sqrt{5+x} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ (-3+\sqrt{-25})(8-\sqrt{-36}) $$

Exer. 27-30: Solve by completing the square. (Note: See the discussion after Example 5 for help in solving Exercises 29 and 30 .) $$ 4 x^{2}+20 x+13=0 $$

It takes a boy 90 minutes to mow the lawn, but his sister can mow it in 60 minutes. How long would it take them to mow the lawn if they worked together, using two lawn mowers?

Solve the equation. $$\frac{7}{y^{2}-4}-\frac{4}{y+2}=\frac{5}{y-2}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x+1}{2 x-3}>2 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 3 \leq \frac{2 x-3}{5}<7 $$

Exer. 1-50: Solve the equation. $$ \sqrt{2 \sqrt{x+1}}=\sqrt{3 x-5} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{4+\sqrt{-81}}{7-\sqrt{-64}} $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ 6 x^{2}-x=2 $$

With water from one hose, a swimming pool can be filled in 8 hours. A second, larger hose used alone can fill the pool in 5 hours. How long would it take to fill the pool if both hoses were used simultaneously?

Solve the equation. $$\frac{4}{2 u-3}+\frac{10}{4 u^{2}-9}=\frac{1}{2 u+3}$$