2022W1_MATH_100C_ALL_2022W1
.pdf
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School
University of British Columbia *
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Course
math 100
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
10
Uploaded by HighnessBravery13778
Lea Grandin
2022W1
MATH
100C
ALL
2022W1
Assignment Webwork-Assignment-9 due 11/24/2022 at 11:59pm PST
Problem 1.
(1 point)
Each row of the spreadsheet below contains the position of a parti-
cle at a given time. The times are stored in column B, and the cor-
responding positions in column A. Column C should contain the
average rate of change between two consecutive rows. To com-
pute these rates of change, you will write a formula in cell C1 and
copy it to cells C2, C3, C4, and C5.
Assume all cells not shown below are blank
position
time
average rate of change
A
B
C
1
0
0
?
2
0
1
↓
3
4
3
↓
4
5
4
↓
5
6
7
↓
6
8
8
a) What formula should you write in C1?
•
(
A
2-
A
1)/(
B
2-
B
1)
•
=(A2-A1)/(B2-B1)
•
=(B2-B1)/(A2-A1)
•
=(
A
2-
A
1)/(
B
2-
B
1)
•
(B2-B1)/(A2-A1)
•
(
B
2-
B
1)/(
A
2-
A
1)
•
(A2-A1)/(B2-B1)
•
=(
B
2-
B
1)/(
A
2-
A
1)
b) Suppose you copy the formula from C1 to cell C6. What num-
ber will be displayed when you press the enter key?
Answer(s) submitted:
•
•
(incorrect)
1
Problem 2.
(1 point)
In the spreadsheet pictured, an arrow indicates the contents of a
cell are copied down its column.
In the spreadsheet below, column A holds different values of
h
,
and column B computes
f
(
0
+
h
)
-
f
(
0
)
h
for the function
f
(
x
) =
|
x
|
.
(Writing
=abs(A1)
in a spreadsheet will compute the absolute
value of the number in cell A1.)
A
B
1
1
=abs(A1)/A1
2
=-A1/10
↓
3
↓
↓
4
↓
↓
5
↓
↓
6
↓
↓
a) What number shows up in cell A5?
b)
f
0
(
0
)
does not exist. Select below the best explanation of a way
you could suspect that from the spreadsheet.
•
The numbers in column B have different signs
•
The values in column B are not converging to one number
•
The numbers in column B have the same absolute value
•
The values in column A are converging to 0
•
The values in column A are not converging to 0
Answer(s) submitted:
•
•
(incorrect)
Problem 3.
(1 point)
Is each of the following functions a solution to the differential
equation
y
00
+
3
y
0
-
10
y
=
0?
?
1.
y
=
-
8
e
3
x
?
2.
y
=
4
e
-
4
x
?
3.
y
=
7
e
2
x
Answer(s) submitted:
•
•
•
(incorrect)
Problem 4.
(1 point)
Find all values of
r
so that the function
y
=
x
r
solves the differen-
tial equation
x
2
y
00
+
2
xy
0
-
12
y
=
0
.
Hint: Plug
y
=
x
r
into the equation and find values of
r
that satisfy
the resulting equation.
r
=
If there are more than one answer, use commas to separate the
answers.
Answer(s) submitted:
•
(incorrect)
Problem 5.
(1 point)
Verify that every member of the family of functions
y
=
ln
x
+
C
x
is a solution of the differential equation
x
2
y
0
+
xy
=
1
.
Answer the
following questions.
1.
Find a solution of the differential equation that satisfies the
initial condition
y
(
3
) =
10
.
Answer:
y
=
2.
Find a solution of the differential equation that satisfies the
initial condition
y
(
10
) =
3
.
Answer:
y
=
Answer(s) submitted:
•
•
(incorrect)
Problem 6.
(1 point)
Let
y
00
-
49
y
=
0.
Find all values of
r
such that
y
=
ke
rx
satisfies the differential
equation.
If there is more than one correct answer, enter your
answers as a comma separated list.
r
=
help (numbers)
Answer(s) submitted:
•
(incorrect)
2
Problem 7.
(1 point)
This problem is an example of a
differential equation
: an equation
that relates a function to one or more of its derivatives. You can
solve this problem by doing some educated guessing. (”educated”
means ”remember what we did in the past.”)
Suppose
f
is the function that satisfies
f
0
(
x
) =
-
f
2
(
x
)
for all
x
in its domain, and
f
(
1
) =
1
.
Then
f
(
x
) =
.
Hint: try some of your familiar functions: parabolas, hyperbolas,
exponential, trig, power functions.
Answer(s) submitted:
•
(incorrect)
Problem 8.
(1 point)
Check by differentiation that
y
=
3cos3
t
+
5sin3
t
is a solution to
y
00
+
9
y
=
0 by finding the terms in the sum:
y
00
=
9
y
=
So
y
00
+
9
y
=
Answer(s) submitted:
•
•
•
(incorrect)
Problem 9.
(1 point)
For each of the following differential equations, determine if the
proposed function is a solution.
a)
Let
C
and
k
be constants.
Given the differential equation
f
0
(
t
) =
k f
(
t
)
, the function
f
(
t
) =
Ce
kt
is
?
b) Given the differential equation
dy
dt
=
2
y
t
, the function
y
(
t
) =
3
t
2
is
?
c)
Given the differential equation
dy
dx
=
-
3
y
,
the function
y
=
2
e
-
3
x
is
?
d) Given the differential equation
f
0
(
t
) =
1
-
f
(
t
)
, the function
f
(
t
) =
-
e
-
t
is
?
Answer(s) submitted:
•
•
•
•
(incorrect)
Problem 10.
(1 point)
In the figure below, which of the following is a solution to the
differential equation
dy
dt
=
0
.
5
y
with initial value
y
(
0
) =
3? [?/I/II/III/IV]
Note: pay attention to axis labels.
Answer(s) submitted:
•
(incorrect)
3
Problem 11.
(1 point)
Consider the slope field shown.
(a) For the solution that satisfies
y
(
0
) =
0, sketch the
solution curve and estimate the following:
y
(
1
)
≈
and
y
(
-
1
)
≈
(b) For the solution that satisfies
y
(
0
) =
1, sketch the
solution curve and estimate the following:
y
(
1
)
≈
and
y
(
-
1
)
≈
(c) For the solution that satisfies
y
(
0
) =
-
1, sketch the
solution curve and estimate the following:
y
(
1
)
≈
and
y
(
-
1
)
≈
Answer(s) submitted:
•
•
•
•
•
•
(incorrect)
Problem 12.
(1 point)
Consider the slope field shown.
(a) For the solution that satisfies
y
(
0
) =
0, sketch the
solution curve and estimate the following:
y
(
1
)
≈
and
y
(
-
1
)
≈
(b) For the solution that satisfies
y
(
0
) =
1, sketch the
solution curve and estimate the following:
y
(
0
.
5
)
≈
and
y
(
-
1
)
≈
(c) For the solution that satisfies
y
(
0
) =
-
1, sketch the
solution curve and estimate the following:
y
(
1
)
≈
and
y
(
-
1
)
≈
Answer(s) submitted:
•
•
•
•
•
•
(incorrect)
4
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