Calculus
In-Class Assignment #5
(3.1+3.2)
Name_KEY_
Complete all of the following problems. Show work when appropriate.
1) When f is defined by f ( x ) = x , find a so
that f ( a) is three times the value of f (2) .
f ( x ) = x1 / 2
1
f ( x) = x -1 / 2
2
Classwork Activity #1
Given the following system of linear equations:
cfw_
Write the augmented matrix for this system.
Use elementary row operations to reduce
the matrix TO THE POINT WHERE
YOU CAN DETERMINE IF THE
MATRIX REPRESENTS A
CONSISTENT OR INCONSI
B rown U niversity School o f Engineering
ENGN0030: I ntroduction t o Engineering
Homework 3 Solutions
Due: Thursday October 6
By 10:20 in Lecture o r
By 4:00pm delivered t o Stephanie Gesualdi on
1 . (Prob. 5.27) The airplane's weight is W
7 th
f l
Solutions to Homework
Section 1.4 #1, 5, 7, 9, 13, 19, 23
1. Undefined the number of columns of A must equal the number of entries of x.
5.
7.
9. Vector Equation:
Matrix Equation:
13. The vector u is in the plane spanned by the columns of A if and only if
Solutions to Homework
Section 1.3 #1, 3, 7, 9, 11, 13, 17, 19, 23
1.
3.
7.
9.
11. To be handed in.
13. To be handed in.
17. Answers will vary. Any weights on v1 and v2 are allowed. Here are some example answers:
19. To be handed in.
23. Will be discussed
Solutions to Homework
Section 1.2 #1, 3, 7, 11, 13, 17, 19, 21
1. Study Guide:
To check whether a matrix is in echelon form, ask these questions:
(i).
Is every nonzero row above the all-zero rows (if any)?
Matrix (c) fails this test, so it is NOT in echel
Solutions to Homework
Section 1.1 #1, 7, 13, 17, 19-22, 23, 25
1.
7.
Since the system is inconsistent, the solution set is empty.
Inconsistent System!
13.
17. Row reduce the augmented matrix of the corresponding system:
The third equation in the system is
PHY* 222
Project-Problems
Physics 222 Projects
Statements of the Problems
Form a group with two to three members and choose one of the following projects. The goals
of these projects are (i) to understand and explain the role of circuit elements such as r
MANCHESTER COMMUNITY COLLEGE
Physics 222, Calculus-Based Physics II
Answers to Final Exam Practice-Problems
Key: CW Clockwise . CCW Counterclockwise.
T
y
qE
x
mg
Figure 1:
1. a) Refer to Figure 1.
b) 0.779 C.
c) Positive.
2. Refer to the textbook.
3. a) 8
State
Alaska
Regional Location
Northwest
California
Southwest
Colorado
Southwest
Florida
South
Iowa
Midwest
Missouri
Midwest
New York
Northeast
North Carolina
South
North Dakota
Midwest
Pennsylvania
Northeast
Rhode Island
Northeast
Texas
Southwest
Virgini
Prob 16.22
Pg 503
diameter, feet, d =
velocity, ft/sec, v =
thickness of insulation, feet, t =
density, lbm/ft3 rho, (given) =
oil flow, w lbm/hr
Pumping Power, P =
Heat Loss, Btu/hr, Q =
Pumping cost, Cp =
Cost of Insulation, dollars, Ci =
of Energy Lost
Classwork Activity Sections 1.3 & 1.4
1. Given the following vectors:
Determine if
[
]
[
]
is a linear combination of
That is, can we find weights
,
,
[
]
[
]
.
such that
[
]
[
]
[
]
[
]
Solving this vector equation can be done using an augmented matrix: