Chapter 2

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. (a) \(i^{43}\) (b) \(i^{-20}\)

Solve the equation. $$\frac{3}{y}+\frac{6}{y}-\frac{1}{y}=11$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 25 x^{2}-9 x<0 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ (3,7) $$

Exer. 1-50: Solve the equation. $$ \sqrt[3]{6-s^{2}}+5=0 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. (a) \(i^{92}\) (b) \(i^{-33}\)

Exer. 15-16: Determine whether the two equations are equivalent. (a) \(x^{2}=25, x=5\) (b) \(x=\sqrt{64}, x=8\)

Two children, who are 224 meters apart, start walking toward each other at the same instant at rates of \(1.5 \mathrm{~m} / \mathrm{sec}\) and \(2 \mathrm{~m} / \mathrm{sec}\), respectively (see the figure). (a) When will they meet? (b) How far will each have walked?

Solve the equation. $$(3 x-2)^{2}=(x-5)(9 x+4)$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 16 x^{2} \geq 9 x $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ [4, \infty) $$

Exer. 1-50: Solve the equation. $$ \sqrt[5]{2 x^{2}+1}-2=0 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. (a) \(i^{73}\) (b) \(i^{-46}\)

A runner starts at the beginning of a runners' path and runs at a constant rate of \(6 \mathrm{mi} / \mathrm{hr}\). Five minutes later a second runner begins at the same point, running at a rate of \(8 \mathrm{mi} / \mathrm{hr}\) and following the same course. How long will it take the second runner to reach the first?

Solve the equation. $$(x+5)^{2}+3=(x-2)^{2}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 16 x^{2}>9 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ (-3, \infty) $$

Exer. 1-50: Solve the equation. $$ \sqrt[4]{2 x^{2}-1}=x $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. (a) \(i^{66}\) (b) \(i^{-55}\)

At 6 A.M. a snowplow, traveling at a constant speed, begins to clear a highway leading out of town. At \(8 \mathrm{~A} . \mathrm{M}\). an automobile begins traveling the highway at a speed of \(30 \mathrm{mi} / \mathrm{hr}\) and reaches the plow \(30 \mathrm{minutes}\) later. Find the speed of the snowplow.

Solve the equation. $$(5 x-7)(2 x+1)-10 x(x-4)=0$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{4}+5 x^{2} \geq 36 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ (-\infty,-5) $$

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

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

Two children own two-way radios that have a maximum range of 2 miles. One leaves a certain point at 1:00 P.M., walking due north at a rate of \(4 \mathrm{mi} / \mathrm{hr}\). The other leaves the same point at 1:15 P.M., traveling due south at \(6 \mathrm{mi} / \mathrm{hr}\). When will they be unable to communicate with one another?

Solve the equation. $$(2 x+9)(4 x-3)=8 x^{2}-12$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{4}+15 x^{2}<16 $$

Exer. 13-20: Express the interval as an inequality in the variable \(x\). $$ (-\infty, 2] $$

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

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{5}{2-7 i} $$

Solve the equation. $$\frac{3 x+1}{6 x-2}=\frac{2 x+5}{4 x-13}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{3}+2 x^{2}-4 x-8 \geq 0 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 3 x-2>14 $$

Exer. 1-50: Solve the equation. $$ 3 \sqrt{2 x-3}+2 \sqrt{7-x}=11 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{1-7 i}{6-2 i} $$

A salesperson purchased an automobile that was advertised as averaging \(25 \mathrm{mi} / \mathrm{gal}\) in the city and \(40 \mathrm{mi} / \mathrm{gal}\) on the highway. A recent sales trip that covered 1800 miles required 51 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city?

Solve the equation. $$\frac{5 x+2}{10 x-3}=\frac{x-8}{2 x+3}$$

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

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

Exer. 1-50: Solve the equation. $$ \sqrt{2 x+15}-2=\sqrt{6 x+1} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{2+9 i}{-3-i} $$

A bullet is fired horizontally at a target, and the sound of its impact is heard \(1.5\) seconds later. If the speed of the bullet is \(3300 \mathrm{ft} / \mathrm{sec}\) and the speed of sound is \(1100 \mathrm{ft} / \mathrm{sec}\), how far away is the target?

Solve the equation. $$\frac{2}{5}+\frac{4}{10 x+5}=\frac{7}{2 x+1}$$

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

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

Exer. 1-50: Solve the equation. $$ x=4+\sqrt{4 x-19} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{-4+6 i}{2+7 i} $$

A woman begins jogging at \(3: 00\) P.M., running due north at a 6-minute-mile pace. Later, she reverses direction and runs due south at a 7-minute-mile pace. If she returns to her starting point at \(3: 45\) P.M., find the total number of miles run.

Solve the equation. $$\frac{-5}{3 x-9}+\frac{4}{x-3}=\frac{5}{6}$$