Deck 20: Engineering Economics

Question 1

The rate of change refers to how a dependent variable changes with respect to an independent
variable.

Answer 1

True

Question 2

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.

Answer 2

True

Question 3

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

A) Epsilon
B) Zeta
C) Gamma
D) Lambda

Answer 3

Gamma

Question 4

The loudness $\beta$ of sound is dependent upon the sound intensity I according to the following equation: $\beta = 10 \log \left( I \times 10 ^ { 12 } \right)$ . Which type of mathematical model is used in this relationship?

A) Linear model
B) Nonlinear model
C) Exponential model
D) Logarithmic model

Question 5

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.

Question 6

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

A) Omega
B) Mu
C) Gamma
D) Lambda

Question 7

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

Question 8

The future worth of a present value is modeled using the following function: $F ( n ) = P ( 1 + i ) ^ { n }$ where $\begin{array} { l } F = \text { future worth } ( \$ ) \\P = \text { present value } ( \$ ) \\i = \text { interest rate (\%) } \\n = \text { length of investment (years) }\end{array}$ 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

Question 9

Calculus is commonly divided into two broad areas:

A) single variable and multivariable calculus.
B) differential and integral calculus.
C) vector and matrix calculus.
D) linear and nonlinear calculus.

Question 10

The velocity of an object under constant acceleration can be modeled using the following function: $\quad v ( t ) = v _ { 0 } + a t$
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

Question 11

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.

Question 12

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)
$\begin{array} { l } G = 6.673 \times 10 ^ { - 11 } \frac { \mathrm { N } \cdot \mathrm { m } ^ { 2 } } { \mathrm {~kg} ^ { 2 } } \\m _ { 1 } = \text { mass number } 1 \text { (kilograms) }\end{array}$ $m _ { 2 } = \text { mass number } 2 \text { (kilograms) }$
$r =$ distance between centers of masses (meters) 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

Question 13

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.

Question 14

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

A) 0.002 ft
B) 0.7 ft
C) 7 ft
D) 7.7 ft

Question 15

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

A) Omega
B) Mu
C) Gamma
D) Lambda

Question 16

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

Question 17

The position of an object subjected to constant acceleration can be described by the following function: $x ( t ) = x _ { 0 } + v _ { 0 } t + \frac { 1 } { 2 } a t ^ { 2 }$ where $\begin{array} { l } x = \text { position } ( \mathrm { m } ) \\x _ { 0 } = \text { initial position } ( \mathrm { m } ) \\v _ { 0 } = \text { initial velocity } ( \mathrm { m } / \mathrm { s } ) \\a = \text { acceleration } \left( \mathrm { m } / \mathrm { s } ^ { \wedge } 2 \right) \\t = \text { time } ( \mathrm { sec } )\end{array}$ 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

Question 18

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

Question 19

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

A) 26.2 ft
B) 29.8 ft
C) 13.8 ft
D) 53.8 ft

Question 20

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.

Question 21

What kind of mathematical model contains derivatives of functions?

A) nonlinear equation
B) differential equation
C) exponential equation
D) logarithmic equation

Question 22

Many engineering problems are modeled using differential equations with a set of
corresponding boundary and/or initial conditions.

Question 23

The drag force acting on a car can be modeled using the following function: $F_{d}=\frac{1}{2} C_{d} \rho V^{2} A$
where $F _ { d } =$ drag force
$C _ { d } =$ drag coefficient
$\rho =$ air density
$V =$ speed of car relative to air
$A =$ frontal area of car The power P required to overcome air resistance can be modeled according to $P = F _ { d } V .$ When analyzing power as a function of velocity P(V), what order is the resulting function?

A) first order
B) second order
C) third order
D) none of the above

Question 24

The term rate of change always refers to the physical quantity of time.