Hennepin Technical College
ATTN: Business Office
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Phone: 952-995-1300
2017 Spring Account Activity
October 04, 2017
Elijah Gar
7.7: Determinants
y
l2=a2+c2
1
For 2 2: (assume a = 0)
A=
a b
c d
a
b
0 d bc/a
a(d bc/a) = ad bc = 0
Def.: The determinant of A is
def
det(A) = ad bc
Geometric Interpretation:
|det(A)| is the area of
4.7: Forced Harmonic Motion
Periodically forced mass-spring system: mx +x +kx = F0 cos t
2
or x + dx + 0 x = A cos t
where d = /m, 0 = k/m, A = F0/m
(A) Undamped Case
2
x + 0 x = A cos t
(1) Beats. As
7.5 Span of a Set of Vectors
Def.: Given vectors x1, . . . , xk Nullspaces:
in Rn , the set of all their linear Ex.: Consider Ax = 0 for
1
3 2
combinations is called their
0
A = 0 1
span, and is den
7.6 Square Matrices
A: square matrix (n n)
Def.: A is nonsingular if for
any b, Ax = b has a solution
Thm.: The following properties are equivalent:
A is nonsingular
REF (A) has no free variables
R
8.2-3: Geometric Interpretation and Qualitative Analysis
Autonomous system:
x = f (x),
x = [x1, . . . , xn]T
Example: Lotka-Volterras
predator-prey equations
R = (a bF )R
F = (c + dR)F
For any t: x(t)
Name:
Second midterm practice exam, Math 340
Each problem is worth 10 points. One problem with the lowest score will be
dropped. Good luck!
Problem
1
2
3
4
5
6
7
8
Total/Total - lowest
Score
1. (10 pt
Name:
Sections 1.5 & 1.6 : Math 115
Answer the following
Section 1.5
1. Solve for x if
|2x 3| = 9.
2. Solve for w if
w2 = 3(w + 6)
3. Solve for x if
1 1
1
= +
y
x z
Section 1.6 - How to succeed with w
Untitled
MA115 : Section 2.2
Warm-up Problem Find the equation of the line
Functions
1. To graph piecewise functions, simply think of the function as two different functions and graph each one over IT
Untitled
MA115 : Section 2.1 & Variation
Warm-up Problem A spoonful of cream is taken from a pitcher of
cream and put into a cup of coee. The coee is stirred. Then a spoonful
of this mixture is put in
MA115 : Section 2.2 : Average Rate of Change
Warm-up Problem Could this curve denotes temperature of a cup of
coee at a given time, where time is plotted along the x-axis?
1. The function f is increas
Name:
Sections 1.1 and 1.2 Exercises : Math 115
Answer the following
1. Find the indicated sets if
A = cfw_1, 2, 3, 4, 5, 6, 7, B = cfw_2, 4, 6, 8 and C = cfw_7, 8, 9, 10
(a) A B
(b) A B
(c) B C
(d) A
Untitled
Name:
Sections 1.5 & 1.6 : Math 115
Answer the following
Section 1.5
1. Solve for x if
|2x
3| = 9.
2. Solve for w if
w2 = 3(w + 6)
3. Solve for x if
1
1 1
= +
y
x z
Section 1.6 - How to succe
MA115 - 3.1-3.3
MA115 : Sections 3.1 & 3.2 & 3.3 Polynomials, Long Division &
Rational Zeros
1. Find a polynomial of degree 3 that has zeros 2, 1, 3
2.
1
is a rational function with NO zeros.
x
3. We
MA115 2.7
MA115 : Section 2.7 : Combining Functions
The most important way to combine functions is by composition of
functions.
You basically apply each function rule, one after the other.
For example
MA115 - 2.4
MA115 : Section 2.4 : Function Transformations and Max/Min
Sketch the transformations indicated in each caption. Scale the axes as
appropriate.
(a) 4 Vertical Shifts of f (x) = x6
(b) 4 Ho
Untitled
MA115 : Section 2.2
Warm-up Problem Find the equation of the line
Functions
1. To graph piecewise functions, simply think of the function as two different functions and graph each one over IT
MA104 Final Exam Practice
1. Solve the following triangle: A = 65 , B = 15 , C = 100
2. Solve the following triangle: A = 25 , b = 10, c = 0
3. Solve the following triangle: a = 8, b = 12, A = 40
4. S
MA 104 1/14/14
Chapter 1 - Review
Name_
To receive credit, you must show your work.
1. Evaluate WITHOUT a calculator.
a.
b.
(
(
)
)
( )
c.
d.
(
)
(
)
(
)(
e.
f.
[
(
[
]
)
]
( )
[
]
[
]
MA 104 1/14/14
MA 104 1/21/14
Chapter 2 Word Problems
Name_
1. Find a number such that one-half of the number is the same as 10 more thanone-fifth of the number.
[
[
]
[
[
]
]
]
[
]
2. Suppose that the width of a re