Math 112 Section:
Instructors name:
Name:
Main Algebraic Solution:
Check Your Solution:
Make sure you check that the total amount of fencing is 1000 and that the area is maximized.
What are the dimensions that would maximize the area?
1. A farmer has 1000
Section 5.2
Math 112 Section:
Instructors name:
Name:
1. Consider the transformation of the natural exponential = +2 + 1. Describe the transformations in an appropriate order. Draw a
sketch and use it to determine the domain, range, and asymptote of = +2
Section 4.6
Math 112 Section:
1. Given the rational function () =
Instructors name:
3 2 2 8
2 4
Name:
, find the domain, intercepts, holes, and asymptotes. Sketch an accurate graph of the
rational function.
Make sure you check all of the features of the
Section 1.5
Math 112 Section:
Instructors name:
Name:
1. Suppose the base and height of a triangle sum to 24 cm, and the area of the triangle is 70 square cm. If the base is larger than the
height, what are the dimensions (base and height) of the triangle
Section 1.2
Math 112 Section:
Instructors name:
Name:
1. An airplane travels at a constant rate. Flying with the wind, it takes 3.3 hours to travel 1980 miles. Flying against the wind, the return
trip takes 5 hours. If there was no wind, how fast was the
Section 3.6
Math 112 Section:
Instructors name:
Name:
7
1. Given the function () = 2+3, find the inverse function 1 (). Determine the domain and range of () and 1 ().
Main Algebraic Solution:
Check Your Solution:
Section 3.6
Math 112 Section:
Instructors
Section 4.4
Math 112 Section:
Instructors name:
Name:
1. Completely factor () = 5 3 14 2 7 + 2 given that = 1 is a zero of ().
Main Algebraic Solution:
Check Your Solution:
Section 4.4
Math 112 Section:
Instructors name:
Name:
2. Determine the value of th
Section 3.4
Math 112 Section:
Instructors name:
Name:
3
1. Given () = 3 + 6, list the basic graph and describe the transformations in the appropriate order. Use the transformations to
create an accurate sketch of the function, labeling the coordinates of
Section 2.3
Math 112 Section:
Instructors name:
Name:
1. Suppose a line goes through the points (1, 7) and (2, 8). Write the equation of the line. Determine the intercepts of the line and
sketch the graph.
Make sure you check that both points are one the
MATH 322, SECTION 001
MATHEMATICAL ANALYSIS FOR ENGINEERS,
EXAM 2
Time: 50 minutes
Name:
Do not write in this area!
Page 1.
Page 4.
Page 2.
Page 5.
Page 3.
Page 6.
Total
Directions:
1. Turn off all cell phones and put them away (I will be keeping track of
Chapter 5
Section 5.2: Volumes
Notes
b
Golden rule: (if perpendicular to the x-axis/in terms of x)
A( x ) dx=V
a
d
(if perpendicular to the y-axis/in terms of y)
In terms of x
A( y) dy=V
c
in terms of y
Important formulas:
A(x) of square:
A(x) of equil
Chapter 5
Section 5.1: Area Between Curves as a Difference
Notes
b
Golden Rule:
[ f ( x )g ( x ) ] dx=Area under f ( x ) Area under g ( x )= Areabetween curves
a
b
=
f ( x ) dx
a
Vertical rectangles:
Horizontal rectangles:
b
g ( x ) dx
a
Chapter 5
Ex
Section 5.3 Volumes of Solids of Revolution (Disk, Washer, and Cylindrical Shell Method)
NOTES:
We can use the definite integral to find the volume of a solid that is obtained by revolving a plane region
about a horizontal or vertical line that does not p
Math 111 WA #1 (2.1, 2.2) Instructor:
Name_
Draw the following angles in standard position.
1. 135
3.
2.
7
3
2
4. 3
4
Convert each angle in degrees to radians. Leave answers in terms of .
5. 300
6. 225
Convert each angle in radians to degrees.
7.
5
8.
1
Review for Test #1
Complete the following without a calculator. Simplify fractions in terms of where
necessary. Be sure to include units, if necessary. Consult your instructor regarding
specific testing information: multiple choice, short answer, number o
Math 112 Spring 2015
Midterm 1 Review Problems
Page 1
1. Solve the equation.
2x 3
5
4 2x 5
7
The answer is:
(A)
(B)
(C)
(D)
(E)
Less than 5
Between 5 and 1
Between 1 and 3
Between 3 and 7
More than 7
2. Solve for x :
(A)
(B)
(C)
(D)
(E)
1
x 4
3
1
x 8 . Th
MATH 263
Written Homework #2
X
=12
5
So, X=60. We are able to choose any values as long as the median=17 & the mean= 12.
1) ? + ? +17+ ? + ?=
New data set: 1, 3, 17, 18, 21
2) Data set: 10, 20, 30, 40, 50, 200
Q1: 20
Q2: 35
Q3: 50
Mean: (11+20+30+40+50+20
MATH 263
Written Homework #1
1a)
Distribution of Life Expectancies from 181 Countries
49
50
40
37
30
Frequencies
26
20
13
10
12
11
15
14
3
0
Up To 45 45 To 50 50 To 55 55 To 60 60 To 65 65 To 70 70 To 75 75 To 80 80 To 85
Life Expectancy at Birth (years)
1 UNIT 2: Chap.4: Forces
AP B Physics
A. Newt 5 (PM
1. digce, No accgergtw fthe vector sum of all forces is zero, then an object will remain
WM. own-WW
at rest or move at constant velocity. Fnet = 0 or 2 F = 0.
(think of inertia as a lack of a net force
Section 1.4
Applied Combinatorics
Math 447/557
Chapter1
Marek Rychlik
Department of Mathematics, University of Arizona
January 4, 2014
Marek Rychlik
Applied CombinatoricsMath 447/557Chapter1
Section 1.4
Jordan Arcs and Jordan Curves
Definition (Jordan Arc
Section 2.1
Section 2.2
Applied Combinatorics
Math 447/557
Chapter2
Marek Rychlik
Department of Mathematics, University of Arizona
January 28, 2014
Marek Rychlik
Applied CombinatoricsMath 447/557Chapter2
Section 2.1
Section 2.2
Bridges of Konigsberg Puzzl
Final Exam
MATH 205, Fall 2014
Name:
Instructions: Please answer as many of the following questions as possible. Show
all of your work and give complete explanations when requested. Write your final
answer clearly. No calculators or cell phones are allowe
CHAPTER 1
ELEMENTS OF GRAPH
THEORY
1.1
GRAPH MODELS
The first four chapters of this book deal with graphs and their applications. A graph
G = (V, E) consists of a finite set V of vertices and a set E of edges joining different pairs of distinct vertices.
Section 1.1
Section 1.2
Section 1.3
Applied Combinatorics
Math 447/557
Chapter1
Marek Rychlik
Department of Mathematics, University of Arizona
January 4, 2014
Marek Rychlik
Applied CombinatoricsMath 447/557Chapter1
Section 1.1
Section 1.2
Section 1.3
Grap