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Math 105 Team Homework Notes - Fall 2009
General expectations and
guidelines for homework will be discussed by your instructor.
On all homeworks, it is acceptable to summarize problem statements,
as long as you have retained all
mathematically important information and
the general flavor of each problem.
See
the Team Homework page
for an example. It is in fact often better to restate
a problem than to copy it down verbatim, as
this site explains.
When graphing, please label the axes completely and correctly.
When writing, use complete sentences. To gain a better
sense of these expectations, take a look at
this tutorial. Please follow the advice.
Notes on particular homework problems
For the first few team homeworks, this page will contain
comments on some (but not all of) the problems. These comments are not meant
to include everything that you must pay attention to.
It is assumed that you will be able to apply the mathematical
advice given for the first few homeworks to
later homeworks.
Homework 1
- 1.1 #36 Assume that w is in miles.
Both parts of the problem address the same scenario.
- 1.2 #22 Be as accurate as possible. Your answer should
be accurate to within 1.5 years.
- 1.4 #40 (a),(d) Write your answer in slope-intercept form.
Homework 2
- 1.5 #32 (a) Write your answer in slope-intercept form.
(c) Your answer must be correct to the minute. As with all homework
problems, justify your answer and precisely describe your method
for obtaining your answer.
- 2.1 #34 (b) Justify how you know that you have obtained all times
when the object has a velocity of zero, and precisely describe your
method for obtaining your answer.
- 2.1#36 Read the question carefully! To check your understanding,
make sure that your interpretation leads you to conclude that
a person who makes $20,400/year in taxable income must pay roughly $1000 in taxes.
(c) Write your formula in the form L(x)=....
In general, when you are asked "to provide a formula" for something,
your answer should take the form "something= ... ".
(d) Address what your answer means in terms of the lawyers' incomes
in (a) and (d), and justify your answer. The term "tax liability" means "taxes that the person owes".
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2.1 #38 (b) Be very precise in your comparisons.
Homework 3
- 2.2 #36 Note that the chemist does not add or remove any tin,
she just works with the copper. You can assume that the chemist has
access to arbitrarily large amounts of copper.
(a) Your domain and range should reflect the description
of the problem's context.
(b) Your solution should contain an equation of the form
f(x)=....
(c) Justify your answer, and precisely describe the method
you used to obtain your answer.
- 2.3 #18 Read this question carefully. Check your
understanding by working through the examples the problem provides.
(a) In your answer, state the
price that yields the lowest possible refund, in addition
to justifying why the lowest possible refund is what you think it is.
(b) Assume and x and y are given in dollars. Your solution should contain
an equation of the form y=.....
Be sure that your domain is the one implied by the problem's context.
(c) Justify how you know you have gotten all possible answers.
-
2.5 #22 (a) It may help to express the length of
one of the salmon as a variable.
(b) If you use the words increasing, decreasing,
concave up, or concave down, reiterate their definition.
(d) Explain what this has to do with concavity and why, then
give an example to back up your assertion.
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2.Review #36(a) Remember to give units.
Homework 4
- 3.1 #34 (d) Your answer should be correct to 4 decimal places.
- 3.2 #31 Express the initial population
in exact terms as well as a rounded numerical answer.
- 3.2 #32 Put graphs on same set of axes, with appropriate domain
and range. Come up with a variable for the initial population,
and express your answers in terms of this variable. Answers
must be correct to 3 decimal places.
- 3.3 #44(a) After graphing, you should
analyse the graphs. Your analysis should address: Which graphs
are closest together when t is large?
Which ones are closest when t is small?
Which functions are largest when t
is large? Which functions are largest when t
is small? You must justify your answers by discussing properties
of the exponential function or by precisely describing what calculator
windows or menus you used.
(b) Put the graphs on the same set of axes.
(c) In your analysis, state which two models differ
the most in the long term, and which two models are closest
in the long term. Justify why, using properties of the exponential
function, or by precisely describing what calculator windows
or menus you used.
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3.Review #48 Answers must be
correct to at least four decimal places.
Homework 5
- 4.2 #46(a) State the units of N clearly.
(a) and (c) State the answer in exact terms as well as a numerical
answer rounded correctly to 2 decimal places.
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4.2 #56
State the answer in exact terms as well as a numerical
answer rounded correctly to 2 decimal places.
- 4.3 #38
State the answer in exact terms as well as a numerical
answer rounded correctly to 2 decimal places.
(c) State what variable T
is a function of. You may assume that
a=50 and
b=500. Describe whehter
the graph has an asymptote, and whether it crosses
the output axis with a positive, negative, or zero slope. Label
the intercepts.
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4.R 38
State the answers in exact terms as well as numerically,
rounded correctly to 2 decimal places.
(a) Your explanation of k
should relate k to 1.06
in financial terms.
(b) Your explanation of b
should relate k to 0.072
in financial terms.
Homework 6
- 5.4 #22(d) Write your answer as a fraction and
explain your reasoning as best you can. What is the pattern that you found in (a)-(c) that you have applied to (d)? Why does that pattern make sense,
in terms of stretches?
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5.R #40 Graph your answers for (a),(b),(c) on the same set of
axes. Label them clearly, so it is easy to tell which is which.
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5.R #34 Note that the function f(n)
is given in the Table 5.22, in the middle of second column
of the page. The function gives the total cost
for a carpenter to build n wooden
chairs.
(a) Phrase your answers in terms of chairs and costs. You do
not need to discuss graphs.
(b) The phrase "gross income" means how much total money
the carpenter charges his customers, including sales tax.
Homework 7
- 5.5 #34 You may assume that the distance and height are
both given by meters. For all parts of this question,
state your answers in exact form as well as numerically, correctly
rounded to 2 decimal digits.
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6.1 #30 In a sentence or two each, explain
the physical significance of the midline, amplitude, and period.
Justify your choice of midline, amplitude, and period.
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6.T #30 State your answers in exact terms as well
as numerically, rounded correctly to 2 decimal places.
Homework 8
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6.3#34, 6.T #28
Write your answers in exact terms as well as numerically,
rounded correctly to 2 decimal places.
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6.5 #44(c) Model the data with a sine curve. Justify your
choice of midline, period, and amplitude.
(e) State the estimate you obtained. Your answer should be within 3000 of the total actual population.
If you did not obtain this, you may need to adjust your reasoning
in a previous part of this problem.
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6.5 #46(a),(b) Your answers should be 3 or fewer sentences
and capture the relevant mathematical concepts. For part (b),
identify the day on which the peaks seem to occur,
and hypothesize briefly what might cause such such spikes in usage.
(c) Justify your choice of midline, period, and amplitude.
Homework 9
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8.2 #46 (f) The term "revenue" means "total money given to the company
by customers".
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8.2 #50 Assume the percentages are by volume. For example,
a 100 ml solution that is 40% alcohol would contain 40 ml of alcohol.
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8.R #54(a),(b),(c),(d) Give answers in exact form as well
as a decimal approximation accurate to at least 4 decimal places.
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8.2 #57 You are asked to compare the cost of building x
square feet against the cost of building 2x square feet.
Homework 10
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9.1 #32 (b) Your answer should explain why the relationship
holds in general, not just for one specific case.
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9.5 #32 You do not need to write your answer in exact
form. Please provide a decimal approximation that is accurate
to at least 4 digits.
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9.6 #38 In your solution, you should restate
the key properties of linear and exponential functions
that you use to support your answer.
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