Mathematics

Ann has 8 apples she give 2 to Jack how much apes does he have left?

Mathematics


Project description
Instructions
Use the table below each of your assigned problems to write out each step needed to solve the problem along with the calculations necessary to find the answer to your assigned problem.
• The “Calculations” column needs to show each step that you would need to write out if you were showing your work when doing this problem by hand or trying to teach the concept to a friend.
• For each step, you will also have to provide a thorough a description of your thought processes for the calculation in the “Explanations” column.
• The first row (or step) should always be to copy the entire problem into the “Calculations” column or write out the important information. You can use copy and paste.
• Make sure that your final answer is clearly stated.
• You do not have to use all of the rows provided. However, if you need more rows to write out all of the steps you took to complete the problem, add rows.
NOTE: This assignment requires that everyone must submit at least 2 problems. Therefore, each person in the group must complete Question #1; however, you can choose any of the 4 remaining problems as your second choice.
Week 3
W3.1
Convert the given measurement to the unit indicated. Round to the nearest hundredth.
37cm to in.
Calculations Explanations
1 1 in = 2.54cm Copy the problem or write out important information.
2
(Add rows as needed).
W3.2
Find the circumference of the circle.
A.) Express answers in terms of and then
B.) express the answer, rounding to the nearest tenth. Use the button on your scientific calculator.
Show each parts A and B clearly in your work. Highlight the solutions.
Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).
W3.3
Find the area of the circle.
A.) Express answers in terms of and then
B.) express the answer, rounding to the nearest tenth. Use the button on your scientific calculator.
Show each parts A and B clearly in your work. Highlight the solutions.

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Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).
W3.4
Use an algebraic equation to find the measure of each angle that is represented in terms of x.
Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).
W3.5
Convert 3.5 L to cm3.
Calculations Explanations
1 Copy the problem or write out important information.
2
(Add rows as needed).
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MATHEMATICS

MATHEMATICS

ALGEBRA
1
:
(a) Prove that that there is no linear transformation
F
:
R
3
!
R
3
such that ker(
F
) =
R
(
F
).
(b) Find a linear transformation
F
:
R
2
!
R
2
such that ker(
F
) =
R
(
F
). You must explicitly
show that your example has this property.
2
:
Let
F
:
R
3
!
R
2
be the linear transformation
F
(
x;y;z
) = (
x;y
+
z
) and let
G
:
R
2
!
R
3
be
dened by
G
(1
;
0) = (0
;
1
;
2) and
G
(0
;
1) = (0
;
2
;
0).
(a) Find the standard matrix of the composition
G
F
.
(b) Find the kernel and range of
G
F
.
(c) Find the standard matrix of the composition
F
G
.
(d) Find the kernel and range of
F
G
.
3
:
Let
F
:
R
2
!
R
2
be (anticlockwise) rotation by
3
4
, let
G
:
R
2
!
R
2
be the orthogonal projection
onto the line
y
=
3
x
, and let
H
:
R
2
!
R
2
be a dilation by a factor of
p
8 (i.e. a dilation with
t
=
p
8). Find the standard matrix for each of the following linear transformations:
(a)
F
H
G
(b)
F
G
H
(c)
H
G
F
.
4
:
(a) Find the standard matrix
A
of the linear transformation
F
representing the cyclic permu-
tation
F
(
x
1
;x
2
;x
3
;x
4
) = (
x
4
;x
1
;x
2
;x
3
)
:
(b) What is the eect of the composition
F
F
? What is the standard matrix for
F
F
?
(c) Show that
A
3
=
A
1
. Why would you have expected this for the standard matrix of
F
?
(d) Is
F
invertible? Explain.
5
:
Let
F
:
R
l
!
R
m
and
G
:
R
m
!
R
n
be linear transformations.
(a) Show that ker(
F
)
ker(
G
F
).
(b) Show that
R
(
G
F
)
R
(
G
).
6
:
Classify the following conic sections by completing the square to put them into standard form
and sketch each one:
(a) 4
x
2
+
y
2
20
x
+ 24 = 0
(b)
x
2
+
y
2
2
x
+ 2
y
+ 2 = 0
(c)
y
2
+ 3
x
+ 6
y
+ 8 = 0
(d)
4
x
2
+ 9
y
2
4
x
6
y
+ 3 = 0

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