Deck 18: Mathematics in Engineering

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سؤال
Find an equation of the line through (1,-3) with a slope of Find an equation of the line through (1,-3) with a slope of   .<div style=padding-top: 35px> .
استخدم زر المسافة أو
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لقلب البطاقة.
سؤال
In general, engineering problems are mathematical models of physical situations.
سؤال
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.
سؤال
Hooke's Law describes the relationship between force F and deflection x in a spring according to the following equation: <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Logarithmic model <div style=padding-top: 35px> .Which type of mathematical model is used in Hooke's Law?

A)Linear model
B)Nonlinear model
C)Exponential model
D)Logarithmic model
سؤال
What is the name of the following Greek alphabetic character? <strong>What is the name of the following Greek alphabetic character?  </strong> A)Omega B)Mu C)Gamma D)Lambda <div style=padding-top: 35px>

A)Omega
B)Mu
C)Gamma
D)Lambda
سؤال
For nonlinear models (equations) the slope is constant.
سؤال
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.
سؤال
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
سؤال
What is the name of the following Greek alphabetic character? <strong>What is the name of the following Greek alphabetic character?  </strong> A)Omega B)Mu C)Gamma D)Lambda <div style=padding-top: 35px>

A)Omega
B)Mu
C)Gamma
D)Lambda
سؤال
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.
سؤال
Mathematics is a language that has its own symbols and terminology.As an engineering student, you need to learn mathematical symbols and their meanings.
سؤال
Find an equation of the line that passes through the points (-1,2) and (3,-4).
سؤال
Find an equation of the line through (5,2) that is perpendicular to the line Find an equation of the line through (5,2) that is perpendicular to the line   .<div style=padding-top: 35px> .
سؤال
Find an equation of the line through (5,2) that is parallel to the line Find an equation of the line through (5,2) that is parallel to the line   .<div style=padding-top: 35px> .
سؤال
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.
سؤال
What is the name of the following Greek alphabetic character? <strong>What is the name of the following Greek alphabetic character?  </strong> A)Epsilon B)Zeta C)Gamma D)Lambda <div style=padding-top: 35px>

A)Epsilon
B)Zeta
C)Gamma
D)Lambda
سؤال
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
سؤال
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.
سؤال
Find the slope of the line that passes thru the points (2,1) and (8,5).
سؤال
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?
سؤال
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: <strong>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?</strong> A)0.002 m B)0.2 m C)2 m D)7.7 m <div style=padding-top: 35px> 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
سؤال
The term rate of change always refers to how a physical quantity varies with time.
سؤال
Solve the following set of equations using matrices: Solve the following set of equations using matrices:  <div style=padding-top: 35px>
سؤال
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: <strong>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?</strong> A)1.1 m B)2.2 m C)28 m D)7.9 m <div style=padding-top: 35px> 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
سؤال
Solve the following set of equations using the Gaussian method: Solve the following set of equations using the Gaussian method:  <div style=padding-top: 35px>
سؤال
Given the following matrix: Given the following matrix:   find   .<div style=padding-top: 35px> find Given the following matrix:   find   .<div style=padding-top: 35px> .
سؤال
Given the following matrix: Given the following matrix:   calculate the determinant of   .<div style=padding-top: 35px> calculate the determinant of Given the following matrix:   calculate the determinant of   .<div style=padding-top: 35px> .
سؤال
Calculate the average rate of change for the following functions: Calculate the average rate of change for the following functions:   between   and  <div style=padding-top: 35px> between Calculate the average rate of change for the following functions:   between   and  <div style=padding-top: 35px> and Calculate the average rate of change for the following functions:   between   and  <div style=padding-top: 35px>
سؤال
Calculate the average rate of change for the following function: Calculate the average rate of change for the following function:   between   and  <div style=padding-top: 35px> between Calculate the average rate of change for the following function:   between   and  <div style=padding-top: 35px> and Calculate the average rate of change for the following function:   between   and  <div style=padding-top: 35px>
سؤال
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
سؤال
Given the following matrix: Given the following matrix:   calculate the determinant of   .<div style=padding-top: 35px> calculate the determinant of Given the following matrix:   calculate the determinant of   .<div style=padding-top: 35px> .
سؤال
Perform the following operations on the given matrices: Perform the following operations on the given matrices:      <div style=padding-top: 35px> Perform the following operations on the given matrices:      <div style=padding-top: 35px> Perform the following operations on the given matrices:      <div style=padding-top: 35px>
سؤال
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.
سؤال
The position of an object subjected to constant acceleration can be described by the following function: <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> where <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> position (m) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> initial position (m) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> initial velocity (m/s) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> acceleration (m/s^2) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> 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
سؤال
Perform the following operations on the given matrices: Perform the following operations on the given matrices:      <div style=padding-top: 35px> Perform the following operations on the given matrices:      <div style=padding-top: 35px> Perform the following operations on the given matrices:      <div style=padding-top: 35px>
سؤال
The rate of change refers to how a dependent variable changes with respect to an independent variable.
سؤال
Calculate the average rate of change for the following function: Calculate the average rate of change for the following function:   between   and  <div style=padding-top: 35px> between Calculate the average rate of change for the following function:   between   and  <div style=padding-top: 35px> and Calculate the average rate of change for the following function:   between   and  <div style=padding-top: 35px>
سؤال
Perform the following operations on the given matrices: Perform the following operations on the given matrices:      <div style=padding-top: 35px> Perform the following operations on the given matrices:      <div style=padding-top: 35px> Perform the following operations on the given matrices:      <div style=padding-top: 35px>
سؤال
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?
سؤال
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model <div style=padding-top: 35px> 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
سؤال
Find the derivative of Find the derivative of   .<div style=padding-top: 35px> .
سؤال
Find the derivative of Find the derivative of   .<div style=padding-top: 35px> .
سؤال
Evaluate: Evaluate:  <div style=padding-top: 35px>
سؤال
Find the derivative of Find the derivative of   .<div style=padding-top: 35px> .
سؤال
What kind of mathematical model contains derivatives of functions?

A)nonlinear equation
B)differential equation
C)exponential equation
D)logarithmic equation
سؤال
Boundary conditions provide information about what is happening physically at the boundaries of a problem.
سؤال
Evaluate: Evaluate:  <div style=padding-top: 35px>
سؤال
Many engineering problems are modeled using differential equations with a set of corresponding boundary and/or initial conditions.
سؤال
Initial conditions tell us about the initial conditions of a system (at time t = 0), before a disturbance or a change is introduced.
سؤال
Find the derivative of Find the derivative of   .<div style=padding-top: 35px> .
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Deck 18: Mathematics in Engineering
1
Find an equation of the line through (1,-3) with a slope of Find an equation of the line through (1,-3) with a slope of   . .
2
In general, engineering problems are mathematical models of physical situations.
True
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.
True
4
Hooke's Law describes the relationship between force F and deflection x in a spring according to the following equation: <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Logarithmic model .Which type of mathematical model is used in Hooke's Law?

A)Linear model
B)Nonlinear model
C)Exponential model
D)Logarithmic model
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5
What is the name of the following Greek alphabetic character? <strong>What is the name of the following Greek alphabetic character?  </strong> A)Omega B)Mu C)Gamma D)Lambda

A)Omega
B)Mu
C)Gamma
D)Lambda
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6
For nonlinear models (equations) the slope is constant.
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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.
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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
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9
What is the name of the following Greek alphabetic character? <strong>What is the name of the following Greek alphabetic character?  </strong> A)Omega B)Mu C)Gamma D)Lambda

A)Omega
B)Mu
C)Gamma
D)Lambda
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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.
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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.
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12
Find an equation of the line that passes through the points (-1,2) and (3,-4).
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13
Find an equation of the line through (5,2) that is perpendicular to the line Find an equation of the line through (5,2) that is perpendicular to the line   . .
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14
Find an equation of the line through (5,2) that is parallel to the line Find an equation of the line through (5,2) that is parallel to the line   . .
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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.
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16
What is the name of the following Greek alphabetic character? <strong>What is the name of the following Greek alphabetic character?  </strong> A)Epsilon B)Zeta C)Gamma D)Lambda

A)Epsilon
B)Zeta
C)Gamma
D)Lambda
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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
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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.
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19
Find the slope of the line that passes thru the points (2,1) and (8,5).
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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?
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21
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: <strong>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?</strong> A)0.002 m B)0.2 m C)2 m D)7.7 m 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
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22
The term rate of change always refers to how a physical quantity varies with time.
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23
Solve the following set of equations using matrices: Solve the following set of equations using matrices:
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24
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: <strong>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?</strong> A)1.1 m B)2.2 m C)28 m D)7.9 m 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
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25
Solve the following set of equations using the Gaussian method: Solve the following set of equations using the Gaussian method:
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26
Given the following matrix: Given the following matrix:   find   . find Given the following matrix:   find   . .
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27
Given the following matrix: Given the following matrix:   calculate the determinant of   . calculate the determinant of Given the following matrix:   calculate the determinant of   . .
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28
Calculate the average rate of change for the following functions: Calculate the average rate of change for the following functions:   between   and  between Calculate the average rate of change for the following functions:   between   and  and Calculate the average rate of change for the following functions:   between   and
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29
Calculate the average rate of change for the following function: Calculate the average rate of change for the following function:   between   and  between Calculate the average rate of change for the following function:   between   and  and Calculate the average rate of change for the following function:   between   and
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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
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31
Given the following matrix: Given the following matrix:   calculate the determinant of   . calculate the determinant of Given the following matrix:   calculate the determinant of   . .
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32
Perform the following operations on the given matrices: Perform the following operations on the given matrices:      Perform the following operations on the given matrices:      Perform the following operations on the given matrices:
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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.
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34
The position of an object subjected to constant acceleration can be described by the following function: <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model where <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model position (m) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model initial position (m) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model initial velocity (m/s) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model acceleration (m/s^2) <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model 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
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35
Perform the following operations on the given matrices: Perform the following operations on the given matrices:      Perform the following operations on the given matrices:      Perform the following operations on the given matrices:
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36
The rate of change refers to how a dependent variable changes with respect to an independent variable.
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37
Calculate the average rate of change for the following function: Calculate the average rate of change for the following function:   between   and  between Calculate the average rate of change for the following function:   between   and  and Calculate the average rate of change for the following function:   between   and
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38
Perform the following operations on the given matrices: Perform the following operations on the given matrices:      Perform the following operations on the given matrices:      Perform the following operations on the given matrices:
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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?
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40
The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: <strong>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?</strong> A)Linear model B)Nonlinear model C)Exponential model D)Trigonometric model 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
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41
Find the derivative of Find the derivative of   . .
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42
Find the derivative of Find the derivative of   . .
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43
Evaluate: Evaluate:
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44
Find the derivative of Find the derivative of   . .
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45
What kind of mathematical model contains derivatives of functions?

A)nonlinear equation
B)differential equation
C)exponential equation
D)logarithmic equation
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46
Boundary conditions provide information about what is happening physically at the boundaries of a problem.
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47
Evaluate: Evaluate:
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48
Many engineering problems are modeled using differential equations with a set of corresponding boundary and/or initial conditions.
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49
Initial conditions tell us about the initial conditions of a system (at time t = 0), before a disturbance or a change is introduced.
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50
Find the derivative of Find the derivative of   . .
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