Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

CHAPTER 1 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

The absolute value of any real number is positive.
$16 - 4 \div 2 = 14$ $16 - 4 \div 2 = 14$
For approximate numbers, $26.7 - 15 = 11.7.$ $26.7 - 15 = 11.7.$
$2 a^{3} = 8 a^{3}$ $2 a^{3} = 8 a^{3}$
$0.237 = 2.37 \times 10^{- 1}$ $0.237 = 2.37 \times 10^{- 1}$
$- \sqrt{- 4} = 2$ $- \sqrt{- 4} = 2$
$4 x - (2 x + 3) = 2 x + 3$ $4 x - (2 x + 3) = 2 x + 3$
${(x - 7)}^{2} = 49 - 14 x + x^{2}$ ${(x - 7)}^{2} = 49 - 14 x + x^{2}$
$\frac{6 x + 2}{2} = 3 x$ $\frac{6 x + 2}{2} = 3 x$
If $5 x - 4 = 0, x = 5/4$ $5 x - 4 = 0, x = 5/4$
If $a - b c = d, c = (d - a) / b$ $a - b c = d, c = (d - a) / b$
In setting up the solution to a word problem involving numbers of gears, it would be sufficient to “let $x = the$ $x = the$ first gear.”

PRACTICE AND APPLICATIONS

In Exercises 13–24, evaluate the given expressions.

$- 2 + (- 5) - 3$ $- 2 + (- 5) - 3$
$6 - 8 - (- 4)$ $6 - 8 - (- 4)$
$\frac{(- 5) (6) (- 4)}{(- 2) (3)}$ $\frac{(- 5) (6) (- 4)}{(- 2) (3)}$
$\frac{(- 9) (- 12) (- 4)}{24}$ $\frac{(- 9) (- 12) (- 4)}{24}$
$- 5 - | 2 (- 6) | + \frac{- 15}{3}$ $- 5 - | 2 (- 6) | + \frac{- 15}{3}$
$3 - 5 | - 3 - 2 | - \frac{| - 4 |}{- 4}$ $3 - 5 | - 3 - 2 | - \frac{| - 4 |}{- 4}$
$\frac{18}{3 - 5} - {(- 4)}^{2}$ $\frac{18}{3 - 5} - {(- 4)}^{2}$
$- {(- 3)}^{2} - \frac{- 8}{(- 2) - | - 4 |}$ $- {(- 3)}^{2} - \frac{- 8}{(- 2) - | - 4 |}$
$\sqrt{16} - \sqrt{64}$ $\sqrt{16} - \sqrt{64}$
$- \sqrt{81 + 144}$ $- \sqrt{81 + 144}$
${(\sqrt{7})}^{2} - \sqrt{38}$ ${(\sqrt{7})}^{2} - \sqrt{38}$
$- \sqrt{416} + {(\sqrt{6})}^{2}$ $- \sqrt{416} + {(\sqrt{6})}^{2}$

In Exercises 25–32, simplify the given expressions. Where appropriate, express results with positive exponents only.

${(- 2 r t^{2})}^{2}$ ${(- 2 r t^{2})}^{2}$
${(3 a^{0} b^{- 2})}^{3}$ ${(3 a^{0} b^{- 2})}^{3}$
$- 3 m n^{- 5} t (8 m^{- 3} n^{4})$ $- 3 m n^{- 5} t (8 m^{- 3} n^{4})$
$\frac{15 p^{4} q^{2} r}{5 p q^{5} r}$ $\frac{15 p^{4} q^{2} r}{5 p q^{5} r}$
$\frac{- 16 N^{- 2} (N T^{2})}{- 2 N^{0} T^{- 1}}$ $\frac{- 16 N^{- 2} (N T^{2})}{- 2 N^{0} T^{- 1}}$
$\frac{- 35 x^{- 1} y (x^{2} y)}{5 x y^{- 1}}$ $\frac{- 35 x^{- 1} y (x^{2} y)}{5 x y^{- 1}}$
$\sqrt{45}$ $\sqrt{45}$
$\sqrt{9 + 36}$ $\sqrt{9 + 36}$

In Exercises 33–36, for each number, (a) determine the number of significant digits and (b) round off each to two significant digits.

8000
21,490
9.050
0.7000

In Exercises 37–40, evaluate the given expressions. All numbers are approximate.

$37.3 - 16.92 {(1.067)}^{2}$ $37.3 - 16.92 {(1.067)}^{2}$
$\frac{8.896 \times 10^{- 12}}{- 3.5954 - 6.0449}$ $\frac{8.896 \times 10^{- 12}}{- 3.5954 - 6.0449}$
$\frac{\sqrt{0.1958 + 2.844}}{3.142 {(65)}^{2}}$ $\frac{\sqrt{0.1958 + 2.844}}{3.142 {(65)}^{2}}$
$\frac{1}{0.03568} + \frac{37, 466}{{29.63}^{2}}$ $\frac{1}{0.03568} + \frac{37, 466}{{29.63}^{2}}$

In Exercises 41–46, make the indicated conversions.

875 Btu to joules
18.4 in. to meters
65 km/h to ft/s
$12.25 g / L to lb / {ft}^{3}$ $12.25 g / L to lb / {ft}^{3}$
225 hp to joules per minute
$89.7 lb / {in.}^{2} to N / {cm}^{2}$ $89.7 lb / {in.}^{2} to N / {cm}^{2}$

In Exercises 47–78, perform the indicated operations.

$a - 3 a b - 2 a + a b$ $a - 3 a b - 2 a + a b$
$x y - y - 5 y - 4 x y$ $x y - y - 5 y - 4 x y$
$6 L C - (3 - L C)$ $6 L C - (3 - L C)$
$- (2 x - b) - 3 (- x - 5 b)$ $- (2 x - b) - 3 (- x - 5 b)$
$(2 x - 1) (5 + x)$ $(2 x - 1) (5 + x)$
$(C - 4 D) (D - 2 C)$ $(C - 4 D) (D - 2 C)$
${(x + 8)}^{2}$ ${(x + 8)}^{2}$
${(2 r - 9 s)}^{2}$ ${(2 r - 9 s)}^{2}$
$\frac{2 h^{3} k^{2} - 6 h^{4} k^{5}}{2 h^{2} k}$ $\frac{2 h^{3} k^{2} - 6 h^{4} k^{5}}{2 h^{2} k}$
$\frac{4 a^{2} x^{3} - 8 a x^{4}}{- 2 a x^{2}}$ $\frac{4 a^{2} x^{3} - 8 a x^{4}}{- 2 a x^{2}}$
$4 R - [2 r - (3 R - 4 r)]$ $4 R - [2 r - (3 R - 4 r)]$
$- 3 b - [3 a - (a - 3 b)] + 4 a$ $- 3 b - [3 a - (a - 3 b)] + 4 a$
$2 x y - {3 z - [5 x y - (7 z - 6 x y)]}$ $2 x y - {3 z - [5 x y - (7 z - 6 x y)]}$
$x^{2} + 3 b + [(b - y) - 3 (2 b - y + z)]$ $x^{2} + 3 b + [(b - y) - 3 (2 b - y + z)]$
$(2 x + 1) (x^{2} - x - 3)$ $(2 x + 1) (x^{2} - x - 3)$
$(x - 3) (2 x^{2} + 1 - 3 x)$ $(x - 3) (2 x^{2} + 1 - 3 x)$
$- 3 y {(x - 4 y)}^{2}$ $- 3 y {(x - 4 y)}^{2}$
$- s {(4 s - 3 t)}^{2}$ $- s {(4 s - 3 t)}^{2}$
$3 p [(q - p) - 2 p (1 - 3 q)]$ $3 p [(q - p) - 2 p (1 - 3 q)]$
$3 x [2 y - r - 4 (x - 2 r)]$ $3 x [2 y - r - 4 (x - 2 r)]$
$\frac{12 p^{3} q^{2} - 4 p^{4} q + 6 p q^{5}}{2 p^{4} q}$ $\frac{12 p^{3} q^{2} - 4 p^{4} q + 6 p q^{5}}{2 p^{4} q}$
$\frac{27 s^{3} t^{2} - 18 s^{4} t + 9 s^{2} t}{- 9 s^{2} t}$ $\frac{27 s^{3} t^{2} - 18 s^{4} t + 9 s^{2} t}{- 9 s^{2} t}$
$(2 x^{2} + 7 x - 30) \div (x + 6)$ $(2 x^{2} + 7 x - 30) \div (x + 6)$
$(4 x^{2} - 41) \div (2 x + 7)$ $(4 x^{2} - 41) \div (2 x + 7)$
$\frac{3 x^{3} - 7 x^{2} + 11 x - 3}{3 x - 1}$ $\frac{3 x^{3} - 7 x^{2} + 11 x - 3}{3 x - 1}$
$\frac{w^{3} + 7 w - 4 w^{2} - 12}{w - 3}$ $\frac{w^{3} + 7 w - 4 w^{2} - 12}{w - 3}$
$\frac{4 x^{4} + 10 x^{3} + 18 x - 1}{x + 3}$ $\frac{4 x^{4} + 10 x^{3} + 18 x - 1}{x + 3}$
$\frac{8 x^{3} - 14 x + 3}{2 x + 3}$ $\frac{8 x^{3} - 14 x + 3}{2 x + 3}$
$- 3 {(r + s - t) - 2 [(3 r - 2 s) - (t - 2 s)]}$ $- 3 {(r + s - t) - 2 [(3 r - 2 s) - (t - 2 s)]}$
$(1 - 2 x) (x - 3) - (x + 4) (4 - 3 x)$ $(1 - 2 x) (x - 3) - (x + 4) (4 - 3 x)$
$\frac{2 y^{3} - 7 y + 9 y^{2} + 5}{2 y - 1}$ $\frac{2 y^{3} - 7 y + 9 y^{2} + 5}{2 y - 1}$
$\frac{6 x^{2} + 5 x y - 4 y^{2}}{2 x - y}$ $\frac{6 x^{2} + 5 x y - 4 y^{2}}{2 x - y}$

In Exercises 79–90, solve the given equations.

$3 x + 1 = x - 8$ $3 x + 1 = x - 8$
$4 y - 3 = 5 y + 7$ $4 y - 3 = 5 y + 7$
$\frac{5 x}{7} = \frac{3}{2}$ $\frac{5 x}{7} = \frac{3}{2}$
$\frac{2 (4 - N)}{- 3} = \frac{5}{4}$ $\frac{2 (4 - N)}{- 3} = \frac{5}{4}$
$- 6 x + 5 = - 3 (x - 4)$ $- 6 x + 5 = - 3 (x - 4)$
$- 2 (- 4 - y) = 3 y$ $- 2 (- 4 - y) = 3 y$
$2 s + 4 (3 - s) = 6$ $2 s + 4 (3 - s) = 6$
$2 | x | - 1 = 3$ $2 | x | - 1 = 3$
$3 t - 2 (7 - t) = 5 (2 t + 1)$ $3 t - 2 (7 - t) = 5 (2 t + 1)$
$- (8 - x) = x - 2 (2 - x)$ $- (8 - x) = x - 2 (2 - x)$
$2.7 + 2.0 (2.1 x - 3.4) = 0.1$ $2.7 + 2.0 (2.1 x - 3.4) = 0.1$
$0.250 (6.721 - 2.44 x) = 2.08$ $0.250 (6.721 - 2.44 x) = 2.08$

In Exercises 91–100, change numbers in ordinary notation to scientific notation or change numbers in scientific notation to ordinary notation. (See Appendix B for an explanation of the symbols that are used.)

A certain computer has 60,000,000,000,000 bytes of memory.
The escape velocity (the velocity required to leave the Earth’s gravitational field) is about 25,000 mi/h.
In 2015, the most distant known object in the solar system, a dwarf planet named V774104, was discovered. It was 15,400,000,000 km from the sun.
Police radar has a frequency of $1.02 \times 10^{9} Hz .$ $1.02 \times 10^{9} Hz .$
Among the stars nearest the Earth, Centaurus A is about $2.53 \times 10^{13}$ $2.53 \times 10^{13}$ mi away.
Before its destruction in 2001, the World Trade Center had nearly $10^{7} {ft}^{2}$ $10^{7} {ft}^{2}$ of office space.
The faintest sound that can be heard has an intensity of about $10^{- 12} W / m^{2} .$ $10^{- 12} W / m^{2} .$
An optical coating on glass to reduce reflections is about 0.00000015 m thick.
The maximum safe level of radiation in the air of a home due to radon gas is $1.5 \times 10^{- 1} Bq / L .$ $1.5 \times 10^{- 1} Bq / L .$ (Bq is the symbol for bequerel, the metric unit of radioactivity, where $1 Bq = 1 decay / s .$ $1 Bq = 1 decay / s .$ )
A certain virus was measured to have a diameter of about 0.00000018 m.

In Exercises 101–114, solve for the indicated letter. Where noted, the given formula arises in the technical or scientific area of study.

$V = π r^{2} L,$ $V = π r^{2} L,$ for L (oil pipeline volume)
$R = \frac{2 G M}{c^{2}},$ $R = \frac{2 G M}{c^{2}},$ for G (astronomy: black holes)
$P = \frac{π^{2} E I}{L^{2}},$ $P = \frac{π^{2} E I}{L^{2}},$ for E (mechanics)
$f = p (c - 1) - c (p - 1),$ $f = p (c - 1) - c (p - 1),$ for p (thermodynamics)
$P p + Q q = R r,$ $P p + Q q = R r,$ for q (moments of forces)
$V = I R + I r,$ $V = I R + I r,$ for R (electricity)
$d = (n - 1) A,$ $d = (n - 1) A,$ for n (optics)
$m u = (m + M) v,$ $m u = (m + M) v,$ for M (physics: momentum)
$N_{1} = T (N_{2} - N_{3}) + N_{3},$ $N_{1} = T (N_{2} - N_{3}) + N_{3},$ for $N_{2}$ $N_{2}$ (mechanics: gears)
$Q = \frac{k A t (T_{2} - T_{1})}{L},$ $Q = \frac{k A t (T_{2} - T_{1})}{L},$ for $T_{1}$ $T_{1}$ (solar heating)
$R = \frac{A (T_{2} - T_{1})}{H},$ $R = \frac{A (T_{2} - T_{1})}{H},$ for $T_{2}$ $T_{2}$ (thermal resistance)
$Z^{2} (1 - \frac{λ}{2 a}) = k,$ $Z^{2} (1 - \frac{λ}{2 a}) = k,$ for $λ$ $λ$ (radar design)
$d = k x^{2} [3 (a + b) - x],$ $d = k x^{2} [3 (a + b) - x],$ for a (mechanics: beams)
$V = V_{0} [1 + 3 a (T_{2} - T_{1})],$ $V = V_{0} [1 + 3 a (T_{2} - T_{1})],$ for $T_{2}$ $T_{2}$ (thermal expansion)

In Exercises 115–120, perform the indicated calculations.

A computer’s memory is $5.25 \times 10^{13} bytes,$ $5.25 \times 10^{13} bytes,$ and that of a model 30 years older is $6.4 \times 10^{4} bytes .$ $6.4 \times 10^{4} bytes .$ What is the ratio of the newer computer’s memory to the older computer’s memory?
The time (in s) for an object to fall h feet is given by the expression $0.25 \sqrt{h} .$ $0.25 \sqrt{h} .$ How long does it take a person to fall 66 ft from a sixth-floor window into a net while escaping a fire?
The CN Tower in Toronto is 0.553 km high. The Willis Tower (formerly the Sears Tower) in Chicago is 442 m high. How much higher is the CN Tower than the Willis Tower?
The time (in s) it takes a computer to check n cells is found by evaluating ${(n / 2650)}^{2} .$ ${(n / 2650)}^{2} .$ Find the time to check $4.8 \times 10^{3}$ $4.8 \times 10^{3}$ cells.
The combined electric resistance of two parallel resistors is found by evaluating the expression $\frac{R_{1} R_{2}}{R_{1} + R_{2}} .$ $\frac{R_{1} R_{2}}{R_{1} + R_{2}} .$ Evaluate this for $R_{1} = 0.0275 Ω$ $R_{1} = 0.0275 Ω$ and $R_{2} = 0.0590 Ω .$ $R_{2} = 0.0590 Ω .$
The distance (in m) from the Earth for which the gravitational force of the Earth on a spacecraft equals the gravitational force of the sun on it is found by evaluating $1.5 \times 10^{11} \sqrt{m / M},$ $1.5 \times 10^{11} \sqrt{m / M},$ where m and M are the masses of the Earth and sun, respectively. Find this distance for $m = 5.98 \times 10^{24} kg$ $m = 5.98 \times 10^{24} kg$ and $M = 1.99 \times 10^{30} kg .$ $M = 1.99 \times 10^{30} kg .$

In Exercises 121–124, simplify the given expressions.

One transmitter antenna is $(x - 2 a) ft$ $(x - 2 a) ft$ long, and another is $(x + 2 a)$ $(x + 2 a)$ yd long. What is the sum, in feet, of their lengths?
In finding the value of an annuity, the expression $(A i - R) {(1 + i)}^{2}$ $(A i - R) {(1 + i)}^{2}$ is used. Multiply out this expression.
A computer analysis of the velocity of a link in an industrial robot leads to the expression $4 (t + h) - 2 {(t + h)}^{2} .$ $4 (t + h) - 2 {(t + h)}^{2} .$ Simplify this expression.
When analyzing the motion of a communications satellite, the expression $\frac{k^{2} r - 2 h^{2} k + h^{2} r v^{2}}{k^{2} r}$ $\frac{k^{2} r - 2 h^{2} k + h^{2} r v^{2}}{k^{2} r}$ is used. Perform the indicated division.

In Exercises 125–136, solve the given problems.

Does the value of $3 \times 18 \div (9 - 6)$ $3 \times 18 \div (9 - 6)$ change if the parentheses are removed?
Does the value of $(3 \times 18) \div 9 - 6$ $(3 \times 18) \div 9 - 6$ change if the parentheses are removed?
In solving the equation $x - (3 - x) = 2 x - 3,$ $x - (3 - x) = 2 x - 3,$ what conclusion can be made?
In solving the equation $7 - (2 - x) = x + 2,$ $7 - (2 - x) = x + 2,$ what conclusion can be made?
For $x = 2$ $x = 2$ and $y = - 4,$ $y = - 4,$ evaluate (a) $2 | x | - 2 | y |;$ $2 | x | - 2 | y |;$ (b) $2 | x - y | .$ $2 | x - y | .$
If $a < 0,$ $a < 0,$ write the value of $| a |$ $| a |$ without the absolute value symbols.
If $3 - x < 0,$ $3 - x < 0,$ solve $| 3 - x | + 7 = 2 x$ $| 3 - x | + 7 = 2 x$ for x.
Solve $| x - 4 | + 6 = 3 x$ $| x - 4 | + 6 = 3 x$ for x. (Be careful!)
Show that ${(x - y)}^{3} = - {(y - x)}^{3} .$ ${(x - y)}^{3} = - {(y - x)}^{3} .$
Is division associative? That is, is it true (if $b \neq 0, c \neq 0$ $b \neq 0, c \neq 0$ ) that $(a \div b) \div c = a \div (b \div c) ?$ $(a \div b) \div c = a \div (b \div c) ?$
What is the ratio of $8 \times 10^{- 3}$ $8 \times 10^{- 3}$ to $2 \times 10^{4} ?$ $2 \times 10^{4} ?$
What is the ratio of $\sqrt{4 + 36}$ $\sqrt{4 + 36}$ to $\sqrt{4} ?$ $\sqrt{4} ?$

In Exercises 137–154, solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.

A certain engine produces 250 hp. What is this power in kilo-watts (kW)?
The pressure gauge for an automobile tire shows a pressure of $32 lb / {in .}^{2} .$ $32 lb / {in .}^{2} .$ What is this pressure in $N / m^{2} ?$ $N / m^{2} ?$
A certain automobile engine produces a maximum torque of $110 N \cdot m .$ $110 N \cdot m .$ Convert this to foot pounds.
A typical electric current density in a wire is $1.2 \times 10^{6} A / m^{2}$ $1.2 \times 10^{6} A / m^{2}$ (A is the symbol for ampere). Express this in $mA / {cm}^{2} .$ $mA / {cm}^{2} .$
Two computer software programs cost $190 together. If one costs $72 more than the other, what is the cost of each?
A sponsor pays a total of $9500 to run a commercial on two different TV stations. One station charges $1100 more than the other. What does each charge to run the commercial?
Three chemical reactions each produce oxygen. If the first produces twice that of the second, the third produces twice that of the first, and the combined total is ${560 cm}^{3},$ ${560 cm}^{3},$ what volume is produced by each?
In testing the rate at which a polluted stream flows, a boat that travels at 5.5 mi/h in still water took 5.0 h to go downstream between two points, and it took 8.0 h to go upstream between the same two points. What is the rate of flow of the stream?
The voltage across a resistor equals the current times the resistance. In a microprocessor circuit, one resistor is $1200 Ω$ $1200 Ω$ greater than another. The sum of the voltages across them is 12.0 mV. Find the resistances if the current is $2.4 μ A$ $2.4 μ A$ in each.
An air sample contains 4.0 ppm (parts per million) of two pollutants. The concentration of one is four times the other. What are the concentrations?
One road crew constructs 450 m of road bed in 12 h. If another crew works at the same rate, how long will it take them to construct another 250 m of road bed?
The fuel for a two-cycle motorboat engine is a mixture of gasoline and oil in the ratio of 15 to 1. How many liters of each are in 6.6 L of mixture?
A ship enters Lake Superior from Sault Ste. Marie, moving toward Duluth at 17.4 km/h. Two hours later, a second ship leaves Duluth moving toward Sault Ste. Marie at 21.8 km/h. When will the ships pass, given that Sault Ste. Marie is 634 km from Duluth?
A helicopter used in fighting a forest fire travels at 105 mi/h from the fire to a pond and 70 mi/h with water from the pond to the fire. If a round-trip takes 30 min, how long does it take from the pond to the fire? See Fig. 1.23.

Fig. 1.23
One grade of oil has 0.50% of an additive, and a higher grade has 0.75% of the additive. How many liters of each must be used to have 1000 L of a mixture with 0.65% of the additive?
Each day a mining company crushes 18,000 Mg of shale-oil rock, some of it 72 L/Mg and the rest 150 L/Mg of oil. How much of each type of rock is needed to produce 120 L/Mg?
An architect plans to have 25% of the floor area of a house in ceramic tile. In all but the kitchen and entry, there are ${2200 ft}^{2}$ ${2200 ft}^{2}$ of floor area, 15% of which is tile. What area can be planned for the kitchen and entry if each has an all-tile floor?
A karat equals 1/24 part of gold in an alloy (for example, 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200 g of 14-karat gold?
In calculating the simple interest earned by an investment, the equation $P = P_{0} + P_{0} r t$ $P = P_{0} + P_{0} r t$ is used, where P is the value after an initial principal $P_{0}$ $P_{0}$ is invested for t years at interest rate r. Solve for r, and then evaluate r for $P = $7625, P_{0} = $6250,$ $P = $7625, P_{0} = $6250,$ and $t = 4.000 years .$ $t = 4.000 years .$ Write a paragraph or two explaining (a) your method for solving for r, and (b) the calculator steps used to evaluate r, noting the use of parentheses.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for CHAPTER 1 REVIEW EXERCISES

Create new playlist

Sign In

Sign Up

Table of Contents for
CHAPTER 1 REVIEW EXERCISES