Deck 18: Mathematics in Engineering

Question 1

Find an equation of the line through (1,-3) with a slope of .

Answer 1

Question 2

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

Answer 2

True

Question 3

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.

Answer 3

True

Question 4

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

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

Question 5

What is the name of the following Greek alphabetic character?

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

Question 6

For nonlinear models (equations) the slope is constant.

Question 7

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 8

In the spring equation F = k x, the spring force, F is called

A)a dependent variable
B)an independent variable
C)none of the above

Question 9

What is the name of the following Greek alphabetic character?

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

Question 10

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 11

Mathematics is a language that has its own symbols and terminology.As an engineering student, you need to learn mathematical symbols and their meanings.

Question 12

Find an equation of the line that passes through the points (-1,2) and (3,-4).

Question 13

Find an equation of the line through (5,2) that is perpendicular to the line .

Question 14

Find an equation of the line through (5,2) that is parallel to the line .

Question 15

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 16

What is the name of the following Greek alphabetic character?

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

Question 17

In the spring equation F = k x, the deformation of the spring, x is called

A)a dependent variable
B)an independent variable
C)none of the above

Question 18

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

A)linear equations.
B)nonlinear equations.
C)exponential equations.
D)logarithmic equations.

Question 19

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

Question 20

The pitch of a roof refers to its "steepness" and is expressed in terms of the number of inches the roof rises for each 12 inches of run.For example, an 8-12 pitch means that the roof rises 8 inches vertically for each 12 inches of horizontal run.What is the slope of a roof with an 8-12 pitch?

Question 21

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground (m) x = 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 m
B)0.2 m
C)2 m
D)7.7 m

Question 22

The term rate of change always refers to how a physical quantity varies with time.

Question 23

Solve the following set of equations using matrices:

Question 24

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground (m) x = horizontal position of football relative to launch position (m)
How high above the ground is the football when it is 30 meters downfield from the quarterback?

A)1.1 m
B)2.2 m
C)28 m
D)7.9 m

Question 25

Solve the following set of equations using the Gaussian method:

Question 26

Given the following matrix: find .

Question 27

Given the following matrix: calculate the determinant of .

Question 28

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

Question 29

Calculate the average rate of change for the following function: between and

Question 30

The velocity of an object under constant acceleration can be modeled using the following function: v(t) = v0 + at where v = velocity
V0 = 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 31

Given the following matrix: calculate the determinant of .

Question 32

Perform the following operations on the given matrices:

Question 33

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 34

The position of an object subjected to constant acceleration can be described by the following function: where position (m) initial position (m) initial velocity (m/s) acceleration (m/s^2) time (sec) 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 35

Perform the following operations on the given matrices:

Question 36

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

Question 37

Calculate the average rate of change for the following function: between and

Question 38

Perform the following operations on the given matrices:

Question 39

A company advertises a gadget at the regular price of $8, with a coupon for a second gadget at half price.The company sold 50 gadgets for a total of $364.How many coupons were redeemed?

Question 40

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground y0 = vertical launch position of football relative to the ground
X = horizontal position of football relative to launch position
G = magnitude of gravitational acceleration
V0 = launch speed
Θ = 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 41

Find the derivative of .

Question 42

Find the derivative of .

Question 43

Evaluate:

Question 44

Find the derivative of .

Question 45

What kind of mathematical model contains derivatives of functions?

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

Question 46

Boundary conditions provide information about what is happening physically at the boundaries of a problem.

Question 47

Evaluate:

Question 48

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

Question 49

Initial conditions tell us about the initial conditions of a system (at time t = 0), before a disturbance or a change is introduced.

Question 50

Find the derivative of .