Question 1

The position of an object subjected to constant acceleration can be described by the following $$\begin{array} { l } 
\text { function: } \quad x ( t ) = x _ { 0 } + v _ { 0 } t + \frac { 1 } { 2 } a t ^ { 2 } \
\text { where } x = \text { position } ( \mathrm { m } ) \
x _ { 0 } = \text { initial position } ( \mathrm { m } ) \
v _ { 0 } = \text { initial velocity } ( \mathrm { m } / \mathrm { s } ) \
a = \text { acceleration } \left( \mathrm { m } / \mathrm { s } ^ { \wedge } 2 \right) \
t = \text { time } ( \mathrm { sec } )
\end{array}$$ Which type of mathematical model is used here to describe the object's position?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Trigonometric model

Accepted Answer

The equation includes a quadratic term ($\frac{1}{2} a t^2$), making it a nonlinear model.

Question 2

In general, engineering problems are mathematical models of physical situations.

Accepted Answer

Engineering problems involve using mathematical models to describe physical situations, so they are closely related to mathematics.

Question 3

$$\text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. }$$

Accepted Answer

First, express $4 x + 6 y + 5 = 0$ in the basic form $y = m x + b$
$$\begin{array} { l } 
6 y = - 4 x - 5 \
y = - \frac { 2 } { 3 } x - \frac { 5 } { 6 } \
m = - \frac { 2 } { 3 }
\end{array}$$
Perpendicular lines have negative reciprocal slopes
$$\begin{array} { l } 
m = \frac { 3 } { 2 } \
2 = \frac { 3 } { 2 } ( 5 ) + b ~~~~~~\quad b = 2 - \frac { 15 } { 2 } = - \frac { 11 } { 2 } \
y = \frac { 3 } { 2 } x - \frac { 11 } { 2 }
\end{array}$$

Question 4

The simplest form of equations commonly used to describe a wide range of engineering situations is
A)linear models.
B)nonlinear models.
C)exponential models.
D)logarithmic models.

Accepted Answer

Linear models are the simplest form of equations commonly used in engineering, as they involve only straight lines and can be easily solved using basic algebraic methods. Nonlinear, exponential, and logarithmic models are more complex and involve curves or other nonlinear relationships, making them more difficult to work with and requiring more sophisticated mathematical techniques. Therefore, option A is the best choice.

Question 5

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: $$y ( x ) = - \left( \frac { g } { 2 v _ { 0 } ^ { 2 } \cos ^ { 2 } \theta } \right) x ^ { 2 } + ( \tan \theta ) x + y _ { 0 }$$ where $y =$ vertical position of football relative to the ground
$y _ { 0 } =$ vertical launch position of football relative to the ground 
$x =$ horizontal position of football relative to launch position
$g =$ magnitude of gravitational acceleration
$v _ { 0 } =$ launch speed
$\theta =$ launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Trigonometric model

Accepted Answer

The function is a quadratic equation in terms of $x$, which makes it a nonlinear model.

Question 6

Greek alphabetic characters quite commonly are used to express angles, dimensions, and
physical variables in drawings and in mathematical equations and expressions.It is therefore
very important to be familiar with these characters in order to communicate with other engineers.

Accepted Answer

Greek alphabetic characters are commonly used in engineering for expressing angles, dimensions, and physical variables in drawings and mathematical equations. Being familiar with these characters is important for communication with other engineers.

Question 7

What is the name of the following Greek alphabetic character? $$\omega$$
A)Omega
B)Mu
C)Gamma
D)Lambda

Accepted Answer

Omega is the last letter of the Greek alphabet, and it is represented by the symbol $$\omega$$.

Question 8

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: $\quad y ( x ) = - 0.002 x ^ { 2 } + 0.7 x + 7$
where $y =$ vertical position of football relative to the ground $( \mathrm { m } )$
$x =$ horizontal position of football relative to launch position (m)
How high above the ground is the football when it is 30 yards downfield from the quarterback?
a. $17.05 \mathrm {~m}$
b. $17.5 \mathrm {~m}$
c. $8.95 \mathrm {~m}$
d. $34.1 \mathrm {~m}$

Accepted Answer

The answer of The path of flight (trajectory) of a...

Question 9

For many engineering situations, exponential and logarithmic models are used to describe the
relationships between dependent and independent variables because they predict the actual
relationships more accurately than linear models do.

Accepted Answer

Exponential and logarithmic models often better capture nonlinear relationships between variables, whereas linear models only capture linear relationships.

Question 10

$$\text { Find an equation of the line through } ( 1 , - 3 ) \text { with slope } - 1 / 2 \text {. }$$

Accepted Answer

The answer of \[\text { Find an equation of the...

Question 11

The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as a. the $x$-intercept.
b. the $y$-intercept.
c. the dependent intercept.
d. the slope.

Accepted Answer

The answer of The quantity or numerical value within a...

Question 12

For many engineering situations, nonlinear models are used to describe the relationships
between dependent and independent variables because they predict the actual relationships more
accurately than linear models do.

Accepted Answer

Nonlinear models are often preferred in engineering because they can better capture the complexities of real-world systems and predict relationships more accurately than linear models.

Question 13

Hooke's Law describes the relationship between force F and elastic deflection x in a spring according to the following equation: $F ^ { = } k x$ .Which type of mathematical model is used in
Hooke's Law?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Logarithmic model

Accepted Answer

Hooke's Law is a linear model because the force is directly proportional to the displacement, represented by a straight line equation $F = kx$.

Question 14

What is the name of the following Greek alphabetic character? $$\mu$$
A)Omega
B)Mu
C)Gamma
D)Lambda

Accepted Answer

Mu is the 12th letter of the Greek alphabet.

Question 15

The gravitational force between two masses is modeled using the following function: $$F _ { g } ( r ) = G \frac { m _ { 1 } m _ { 2 } } { r ^ { 2 } }$$
where $F _ { g } =$ gravitational force (newtons)
$$\begin{array} { l } 
G = 6.673 ^ { \times } 10 ^ { - 11 } \frac { \mathrm { N.m } ^ { 2 } } { \mathrm {~kg} ^ { 2 } } \
m _ { 1 } = \text { mass number } 1 \text { (kilograms) } \
m _ { 2 } = \text { mass number } 2 \text { (kilograms) } \
r = \text { distance between centers of masses (meters) }
\end{array}$$ Which type of mathematical model is used here to describe the gravitational force?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Trigonometric model

Accepted Answer

The gravitational force equation is a nonlinear model because it involves the inverse square of the distance $ r $.

Question 16

Find the slope of the line that passes thru the points (2,1) and (8,5).

Accepted Answer

The answer of Find the slope of the line that...

Question 17

The velocity of an object under constant acceleration can be modeled using the following function: $$v ( t ) = v _ { 0 } + a t$$ where $v =$ velocity
$v _ { 0 } =$ initial velocity
$a =$ acceleration
$t =$ time Which type of mathematical model is used to describe velocity in this application?
A)Linear model
B)Nonlinear model
C)Exponential model
D)Logarithmic model

Accepted Answer

The answer of The velocity of an object under constant...

Question 18

What is the name of the following Greek alphabetic character? $$\gamma$$
A)Epsilon
B)Zeta
C)Gamma
D)Lambda

Accepted Answer

Gamma is the third letter of the Greek alphabet.

Question 19

The pitch of a roof refers to its "steepness" and is expressed in terms of the number of
millimeters the roof rises for each 1000 mm of run.For example, an 750-1000 pitch means that
the roof rises 750 mm vertically for each 1000 mm of horizontal run.What is the slope of a roof
with an 750-1000 pitch?

Accepted Answer

The answer of The pitch of a roof refers to...

Question 20

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: $\quad y ( x ) = - 0.002 x ^ { 2 } + 0.7 x + 7$
where $y =$ vertical position of football relative to the ground $( \mathrm { m } )$
$$x = \text { horizontal position of football relative to launch position (m) }$$
How high above the ground is the football as it leaves the quarterback's hand?
a. $0.002 \mathrm {~m}$
b. $0.7 \mathrm {~m}$
c. $7 \mathrm {~m}$
d. $7.7 \mathrm {~m}$

Accepted Answer

The answer of The path of flight (trajectory) of a...

Quiz 18: Mathematics in Engineering

In general, engineering problems are mathematical models of physical situations.

$\text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. }$

The simplest form of equations commonly used to describe a wide range of engineering situations is

Greek alphabetic characters quite commonly are used to express angles, dimensions, and physical variables in drawings and in mathematical equations and expressions.It is therefore very important to be familiar with these characters in order to communicate with other engineers.

What is the name of the following Greek alphabetic character? $\omega$

For many engineering situations, exponential and logarithmic models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

$\text { Find an equation of the line through } ( 1 , - 3 ) \text { with slope } - 1 / 2 \text {. }$

The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as a. the $x$ -intercept. b. the $y$ -intercept. c. the dependent intercept. d. the slope.

For many engineering situations, nonlinear models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

Hooke's Law describes the relationship between force F and elastic deflection x in a spring according to the following equation: $F ^ { = } k x$ .Which type of mathematical model is used in Hooke's Law?

What is the name of the following Greek alphabetic character? $\mu$

Find the slope of the line that passes thru the points (2,1) and (8,5).

The velocity of an object under constant acceleration can be modeled using the following function: $v ( t ) = v _ { 0 } + a t$ where $v =$ velocity $v _ { 0 } =$ initial velocity $a =$ acceleration $t =$ time Which type of mathematical model is used to describe velocity in this application?

What is the name of the following Greek alphabetic character? $\gamma$

Quiz 18: Mathematics in Engineering

In general, engineering problems are mathematical models of physical situations.

Find an equation of the line through (5,2) that is parallel to the line 4x+6y+5=0. \text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. } Find an equation of the line through (5,2) that is parallel to the line 4x+6y+5=0.

The simplest form of equations commonly used to describe a wide range of engineering situations is

Greek alphabetic characters quite commonly are used to express angles, dimensions, and physical variables in drawings and in mathematical equations and expressions.It is therefore very important to be familiar with these characters in order to communicate with other engineers.

What is the name of the following Greek alphabetic character? ω\omegaω

For many engineering situations, exponential and logarithmic models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

Find an equation of the line through (1,−3) with slope −1/2. \text { Find an equation of the line through } ( 1 , - 3 ) \text { with slope } - 1 / 2 \text {. } Find an equation of the line through (1,−3) with slope −1/2.

The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as a. the xxx -intercept. b. the yyy -intercept. c. the dependent intercept. d. the slope.

For many engineering situations, nonlinear models are used to describe the relationships between dependent and independent variables because they predict the actual relationships more accurately than linear models do.

Hooke's Law describes the relationship between force F and elastic deflection x in a spring according to the following equation: F=kxF ^ { = } k xF=kx .Which type of mathematical model is used in Hooke's Law?

What is the name of the following Greek alphabetic character? μ\muμ

Find the slope of the line that passes thru the points (2,1) and (8,5).

What is the name of the following Greek alphabetic character? γ\gammaγ

$\text { Find an equation of the line through } ( 5,2 ) \text { that is parallel to the line } 4 x + 6 y + 5 = 0 \text {. }$

What is the name of the following Greek alphabetic character? $\omega$

$\text { Find an equation of the line through } ( 1 , - 3 ) \text { with slope } - 1 / 2 \text {. }$

The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as a. the $x$ -intercept. b. the $y$ -intercept. c. the dependent intercept. d. the slope.

Hooke's Law describes the relationship between force F and elastic deflection x in a spring according to the following equation: $F ^ { = } k x$ .Which type of mathematical model is used in Hooke's Law?

What is the name of the following Greek alphabetic character? $\mu$

What is the name of the following Greek alphabetic character? $\gamma$