Deck 18: Mathematics in Engineering

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

Answer 1

Nonlinear model

Question 2

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

Answer 2

True

Question 3

Answer 3

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.

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

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.

Question 7

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

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

Question 8

The path of flight (trajectory) of a football thrown by a quarterback is described by the

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.

Question 10

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

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.

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

Question 14

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

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

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

Question 16

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

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

Question 18

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

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

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?

Question 20

The path of flight (trajectory) of a football thrown by a quarterback is described by the

Question 21

Perform the following operations on the given matrices:

Question 22

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 23

A movie theater advertises one ticket at the regular price o with a coupon for a second
ticket at half price.The theater sold 50 tickets for a tota ow many coupons were
redeemed?

Question 24

Find the derivative of

Question 25

At Snacks-R-Us, caramel corn wor 0 per pound is mixed with cashews wor r
pound in order to get 20 pounds of a mixture wor pound.How much of each snack
is used?

Question 26

Find the derivative of

Question 27

Perform the following operations on the given matrices:

Question 28

The future worth of a present value is modeled using the following function:

Question 29

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

Question 30

Perform the following operations on the given matrices:

Question 31

Solve the following set of equations using matrices:

Question 32

Solve the following set of equations using the Gaussian method:

Question 33

Minn Kota offers its sales representatives a choice between being paid a commission of 8% of sales or being paid a monthly salary of plus a commission of 1% of sales.For what
monthly sales do the two plans pay the same amount?

Question 34

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

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

Question 35

Calculate the average rate of change for the following functions:

Question 36

The loudness of sound, in decibels (dB), is dependent upon the sound intensity I according
to the following equation: is the original intensity and I is the new
intensity.By how many decibels does the loudness increase when the intensity doubles?

Question 37

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

Question 38

Question 39

Calculate the average rate of change for the following functions: and

Question 40

Calculate the average rate of change for the following functions:

Question 41

Evaluate:

Question 42

Find the derivative of

Question 43

Find the derivative of

Question 44

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

Question 45

Evaluate:

Question 46

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 47

Find the derivative of

Question 48

Find the derivative of

Question 49

What kind of mathematical model contains derivatives of functions?

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