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Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 46

Solution of Equations Consisting of Combined Operations and Rearrangement of Formulas - all with Video Answers

Educators

Chapter Questions

02:15

Problem 1

Solve $\sqrt[3]{x}=\frac{1}{5}$. Express the answer as both a common fraction and a decimal fraction.

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
00:24

Problem 2

Solve the equation $-75.4=5.2 C$ for the unknown value $C$.

Grace Muhihu
Grace Muhihu
Numerade Educator
03:06

Problem 3

Find the unknown value of $b$ in the equation $\frac{b}{5}-6=12.1$.

Karuna Ramroop
Karuna Ramroop
Numerade Educator
00:44

Problem 4

Multiply $\left(4 x^2+3\right)\left(4 x^2-3\right)$.

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:56

Problem 5

Use a digital micrometer to measure the thickness of one of your hairs. Be careful not to crush the hair.

Vipender Rao
Vipender Rao
Numerade Educator

Problem 6

Read the metric height gage measurement for this setting in Figure 46-8.

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00:41

Problem 7

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$5 x-33=12$

Ethan Somes
Ethan Somes
Numerade Educator
01:07

Problem 8

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$10 M+5+4 M=89$

Ethan Somes
Ethan Somes
Numerade Educator
01:27

Problem 9

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$8 E-14=2 E+28$

Coach Rye
Coach Rye
Numerade Educator
02:04

Problem 10

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$4 B-7=B+21$

M S
M S
Numerade Educator
02:05

Problem 11

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$7 T-14=0$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:38

Problem 12

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$6 N+4=84+N$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
00:53

Problem 13

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$2.5 A+8=15-4.5$

Nick Johnson
Nick Johnson
Numerade Educator
01:32

Problem 14

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$12-(-x+8)=18$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:54

Problem 15

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$3 H+(2-H)=20$

Amanda Stone
Amanda Stone
Numerade Educator
01:32

Problem 16

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$12=-(2+C)-(4+2 C)$

Thomas Emment
Thomas Emment
Numerade Educator
01:40

Problem 17

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$-5(R+6)=10(R-2)$

Bailey Radel
Bailey Radel
Numerade Educator
01:41

Problem 18

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$0.29 E=9.39-0.01 E$

Km Neeraj
Km Neeraj
Numerade Educator
00:44

Problem 19

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$7.2 F+5(F-8.1)=0.6 F+15.18$

Tiffany Tran
Tiffany Tran
Numerade Educator
00:57

Problem 20

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$\frac{P}{7}+8=6.3$

Casey Evans
Casey Evans
Numerade Educator
09:06

Problem 21

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$\frac{1}{4} W+(W-8)=\frac{3}{4}$

Alejandro Ruiz
Alejandro Ruiz
Numerade Educator
06:21

Problem 22

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$\frac{1}{8} D-3(D-7)=5 \frac{1}{8} D-3$

Debasish Das
Debasish Das
Numerade Educator
00:50

Problem 23

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$0.58 y=18.3-0.02 y$

Victor Salazar
Victor Salazar
Numerade Educator
01:01

Problem 24

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$2 H^2-20=(H+4)(H-4)$

Casey Evans
Casey Evans
Numerade Educator
00:31

Problem 25

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$4 A^2+3 A+36=8 A^2+3 A$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
02:27

Problem 26

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$x(4+x)+20=x^2-(x-5)$

James Kiss
James Kiss
Numerade Educator
01:10

Problem 27

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$\left(\frac{b}{2}\right)^3+34=42$

Victor Salazar
Victor Salazar
Numerade Educator

Problem 28

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$3 F^3+F(F+8)=8 F+F^2+81$

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00:41

Problem 29

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$9+y^2=(y-4)(y-1)$

Victor Salazar
Victor Salazar
Numerade Educator
02:32

Problem 30

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$\frac{1}{4}(2 B-12)+B^2=\frac{1}{2} B+22$

Kayleah Tsai
Kayleah Tsai
Numerade Educator
01:44

Problem 31

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$-4(y-1.5)=2 \sqrt{y}-4 y$

Vishal Parmar
Vishal Parmar
Numerade Educator
06:06

Problem 32

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$14 \sqrt{x}=6(\sqrt{x}+8)+16$

James Kiss
James Kiss
Numerade Educator
00:37

Problem 33

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$8.12 P^2+6.83 P+5.05$ $=16.7 P^2+6.83 P$

Sherrie Fenner
Sherrie Fenner
Numerade Educator
04:36

Problem 34

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$7.3 \sqrt{x}=3(\sqrt{x}+8.06)-4.59$

James Kiss
James Kiss
Numerade Educator
00:46

Problem 35

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$\sqrt{B^2}-2.53 B=-2.53(B-3.95)$

Nick Johnson
Nick Johnson
Numerade Educator
00:49

Problem 36

Solve for the unknown and check each of the following combined operations equations. Round answers to 2 decimal places where necessary.
$(2 y)^3-2.80(5.89+3 y)$ $=23.87-8.40 y$

James Kiss
James Kiss
Numerade Educator

Problem 37

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$F=2.380 P+0.250$
Given: $F=2.375$.
Solve for $P$.

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01:20

Problem 38

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$a=3 H \div 8$
Given: $a=0.1760$.
Solve for $H$.

Aribah Ali
Aribah Ali
Numerade Educator
01:24

Problem 39

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
H.P. $=0.000016 \mathrm{MN}$
Given: $\quad H . P .=22, N=50.8$.
Solve for $M$.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:48

Problem 40

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$N=0.707 D P_n$
Given: $\quad N=24, P_n=8$.
Solve for $D$.

Alison Rodriguez
Alison Rodriguez
Numerade Educator

Problem 41

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$S=T-\frac{1.732}{N}$
Given: $\quad S=0.4134, N=20$.
Solve for $T$.

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03:18

Problem 42

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$a=\frac{D_2-D_1}{2}$
Given: $a=0.250, D_1=0.875$.
Solve for $D_2$.

Goutam Chand
Goutam Chand
Numerade Educator
03:09

Problem 43

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$S=\frac{0.290 W}{t^2}$
Given: $\quad S=1000, t=0.750$.
Solve for $W$.

Naman Kumar
Naman Kumar
Numerade Educator
03:09

Problem 44

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$W=S t\left(0.55 d^2-0.25 d\right)$
Given: $\quad W=1150, d=0.750$.
Solve for $S t$.

Naman Kumar
Naman Kumar
Numerade Educator

Problem 45

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$M=E-0.866 P+3 W$
Given: $\quad M=3.3700, E=3.2000, P=0.125$.
Solve for $W$.

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00:38

Problem 46

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$S=\frac{L_1}{L_2}\left[\frac{1}{2}\left(D_1-D_2\right)\right]$
Given: $\quad S=\frac{1}{4}, L_1=16, L_2=4, D_2=2 \frac{1}{2}$.
Solve for $D_1$.

Mariam Saleh-Esa
Mariam Saleh-Esa
Numerade Educator

Problem 47

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$C=\frac{\pi D N}{12}$
Given: $\quad C=210, D=6, \pi=3.1416$.
Solve for $N$.

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01:15

Problem 48

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$D_o=\frac{P_c(N+2)}{\pi}$
Given: $\quad D_o=4.3750, \pi=3.1416, P_c=0.3927$.
Solve for $N$. $\qquad$

Brad Thornton
Brad Thornton
Numerade Educator
00:50

Problem 49

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$S=\sqrt{\frac{d^2}{4}+h^2}$
Given: $\quad S=12.700, d=6$.
Solve for $h$. $\qquad$

Brad Thornton
Brad Thornton
Numerade Educator
01:01

Problem 50

The following formulas are used in the machine trades. Substitute the given values in each formula and solve for the unknown. Round the answers to 3 decimal places where necessary.
$C=2 \sqrt{h(2 r-h)}$
Given: $\quad C=7.600, h=3.750$.
Solve for $r$. $\qquad$

Brad Thornton
Brad Thornton
Numerade Educator
00:36

Problem 51

The dimensions shown can be found using these two formulas.
(1) $A=a b$
(2) $d=\sqrt{a^2+b^2}$
a. Solve formula (1) for $a$.
b. Solve formula (1) for $b$.
c. Solve formula (2) for $a$.
d. Solve formula (2) for $b$.

AM
August Miller
Numerade Educator
01:21

Problem 52

The radii shown in this figure can be found using these two formulas.
(1) $R=1.155 r$
(2) $A=2.598 R^2$
a. Solve formula (1) for $r$.
b. Solve formula (2) for $R$.

James Kiss
James Kiss
Numerade Educator
00:44

Problem 53

The dimensions shown can be found using these two formulas.
(1) $F W=\sqrt{D_o^2-D^2}$
(2) $D_0=2 C-d+2 a$
a. Solve formula (1) for $D_{\text {。 }}$.
b. Solve formula (1) for $D$.
c. Solve formula (2) for $d$.
d. Solve formula (2) for $a$.

Aribah Ali
Aribah Ali
Numerade Educator
02:56

Problem 54

$A=\pi\left(R^2-r^2\right)$
a. Solve for $R$.
b. Solve for $r$.

Debasish Das
Debasish Das
Numerade Educator
03:31

Problem 55

$M=D-1.5155 P+3 W$
a. Solve for $D$.
b. Solve for $P$.
c. Solve for W.

Debasish Das
Debasish Das
Numerade Educator
01:04

Problem 56

$\angle A+\angle B+\angle C=180^{\circ}$
a. Solve for $\angle A$.
b. Solve for $\angle B$.
c. Solve for $\angle C$.

Monica Miller
Monica Miller
Numerade Educator
01:07

Problem 57

$L=3.14(0.5 D+0.5 d)+2 x$
a. Solve for $D$.
b. Solve for $d$.
c. Solve for $X$.

Sriram Soundarrajan
Sriram Soundarrajan
Numerade Educator
02:04

Problem 58

$\operatorname{By}(F-1)=C x$
a. Solve for $x$.
b. Solve for $B$.
c. Solve for $C$.

Allison Knapp
Allison Knapp
Numerade Educator
00:38

Problem 59

$C a=S(C-F)$
a. Solve for $S$.
b. Solve for $C$.

AG
Ankit Gupta
Numerade Educator
02:17

Problem 60

The horsepower of an electric motor is found with this formula.
$$
\begin{aligned}
& \mathrm{hp}=\frac{6.2832 T(\mathrm{rpm})}{33,000} \quad \text { where } \mathrm{hp}=\text { horsepower } \\
& T=\text { torque in pound-feet }(\mathrm{lb}-\mathrm{ft}) \\
& \mathrm{rpm}=\text { revolutions per minute } \\
&
\end{aligned}
$$

Solve for $T$ when $h p=1.50$ and $\mathrm{rpm}=2250$. Round the answer to 2 decimal places.

Paul Gabriel
Paul Gabriel
Numerade Educator
01:17

Problem 61

A tapered pin is shown.
a. Solve for $h$ when $R=2.38 \mathrm{~cm}, r=1.46 \mathrm{~cm}$, and $V=69.5 \mathrm{~cm}^3$. Round the answer to 2 decimal places.
$$
V=1.05\left(R+R r+r^2\right) h
$$
b. Solve for $h$ when $S=0.875 \mathrm{in}, R=0.420 \mathrm{in}$, and $r=0.200 \mathrm{in}$. Round the answer to 3 decimal places.
$$
S=\sqrt{(R-r)^2+h^2}
$$

Nick Johnson
Nick Johnson
Numerade Educator
01:09

Problem 62

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{10}{x}=\frac{5 x}{8}$

AG
Ankit Gupta
Numerade Educator
00:53

Problem 63

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{A}{12.5}=\frac{4.761}{5 A}$

Raushan Kumar
Raushan Kumar
Numerade Educator
02:18

Problem 64

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{11}{8}=\frac{E+3}{12}$

Km Neeraj
Km Neeraj
Numerade Educator
00:28

Problem 65

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{M-5}{12}=\frac{15}{8}$

Liuxi Sun
Liuxi Sun
Numerade Educator
00:26

Problem 66

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{5-B}{4.38}=\frac{B+9.2}{11.71}$

Elizabeth Xu
Elizabeth Xu
Numerade Educator

Problem 67

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{E-15}{E+7.53}=\frac{0.36}{1.86}$

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03:22

Problem 68

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{6.08}{3 H^2-12}=\frac{5.87}{12.53}$

Mitchell Cutler
Mitchell Cutler
Numerade Educator
01:11

Problem 69

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{12.8}{5-3 C^2}=\frac{7.43}{-31.29}$

Nick Johnson
Nick Johnson
Numerade Educator
00:32

Problem 70

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{8.62 M+23.30}{12.36}=\frac{7.62 M+0.05}{0.86}$

Katelyn Chen
Katelyn Chen
Numerade Educator
03:26

Problem 71

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{P^2-186.73}{5.65 P}=\frac{-23.30 P}{3.04}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
01:30

Problem 72

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{B+1}{B-2}=\frac{B+3}{B-5}$

Mitchell Cutler
Mitchell Cutler
Numerade Educator
02:20

Problem 73

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{C+4}{C-3}=\frac{C-1}{C+6}$

Brian Lin
Brian Lin
Numerade Educator
01:30

Problem 74

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{N^3-4}{3}=\frac{N^3}{6}$

Mitchell Cutler
Mitchell Cutler
Numerade Educator
00:37

Problem 75

Solve for the unknown value in each of the following proportions. Check each answer. Round the answers to 3 decimal places where necessary.
$\frac{2 A^3+7 A-5}{7}=\frac{A^3+5 A+8}{5}$

Amy Jiang
Amy Jiang
Numerade Educator