Coverage of the final exam

*************************

Hello Professor Taylor

I have a question regarding the final exam on May 5. Is it a cumulative exam? Or just the sections covered after Test 2? Can you please tell me what all sections to focus on?

Thank You,

###########

**************************

The final exam will be comprehensive, however the material covered since midterm#2 will receive more detailed emphasis.

webwork questions

***************
1) (section 8.2 #3) Hello,
I was trying to solve the problem, but I am having issues trying to reach
the quadratic formula form.
In the book, it outlines a way using theorem 1, but it does not explain how
to find it.
I've found -2 = a1 + a2 from C = a1(r1)^0 + a2(r1)^0, and -4 = a1 + a2 from
C = a1(r1)^0 + a2(r1)^0, but I am stuck on how to approach the problem
next.Thanks,

2) number 8.2 problem 4 is completely unsolveable with the r that webwork
claims is correct. please help me!

********************

1) Interestingly, problem 4, which is copied above describes pretty carefully how to do this, except that you would change the right hand side to 9r^{n-2} instead of -4r^{n-1}-4r^{n-2}.  Also, since -4 is the initial condition corresponding to n=1, so you would need the equation -4 = a_1r_1 + a_2r_2 instead of -4 = a1 + a2; it's important for you to understand this, because the final exam will be an unhappy experience otherwise!

2)  I'm a little confused by what you mean by "completely unsolvable", the problem basically takes you by the hand and leads you to the solution, which it looks like you've found.  Please clarify.

HW next week

Webwork section 9.1 due Monday April 28@8am

Bookwork section 9.1 and section 9.5 due Wednesday April 30 @8am

HW! This week!

Webwork section 8.2. Due Midnight on Friday

Bookwork Section 8.2. Due Friday April 25 @10:30am

Course Evaluations

This is your chance to grade your instructor:  you can access the Course Evaluation participant portal on MyASU through the 'Course Evaluations' link under under 'My Classes.'

webwork questions

********************
just got 2 of them. first is 6.3 problem 18:

How many 6-letter words that have the letter 'x' are possible? Letters may be repeated, and the words don't have to be meaningful. (Hint: First count the words without 'x' .)

this one I just don't know what to do and have 1 try left :S

2nd is 6.3 problem 7:

In how many ways can 4 different novels, 2 different mathematics books, and 1 biology book be arranged on a bookshelf if:

(a) The books can be arranged in any order? 

(b) The mathematics books must be together and the novels must be together? 

(c) The novels must be together but the other books can be arranged in any order?

for the 2nd one I got a.)7! b.)288 c.)144 I have 2 right but not the 3rd. forgot which is wrong but I got all the others done. 

********************

1) Well, first of all, you know that you can login as "Guest" and work this problem as many times as you like--this might help lower the stress about this question and help you think more clearly.

Second, you need to understand that the use of the word "word" here is different than the words that appear in the dictionary.  Here it just means any six character string from the given character set-it doesn't have to make sense in any language; e.g. zzzzzz is a perfectly fine word, as is yzchkk.

Now, supposing that only lower case characters are allowed, so that there are only 26 letters you have to worry about, you need to answer two questions: 1) how many six letter words are there with characters taken from the whole alphabet, and 2) how many six letter words are there without the character "x".  Then you need to keep in mind that that the words you want are all of those not in the second class.

2) as for part a), since the type of book doesn't matter, this is the basic ordered counting problem.  For Part b) you get to count the orders of each type of book, and then count the ordering of types. When you count the orders of books and types together, keep in mind that the two operations can be done independently.  Part c) is like part b) except that you count the mathematics books and the biology book as just one type. 

Webwork Question

*******************

I am a little confused on the WebWork problem which states

"A computer is printing out subsets of a 4 element set (possibly including
the empty set).

(a) At least how many sets must be printed to be sure of having at least 2
identical subsets on the list?

(b) At least how many identical subsets are printed if there are 49 subsets
on the list? "

what are you considering elements in the set? I am having a hard time
visualizing what the problem is asking for. If you could clarify this for
me I would be very grateful.

*******************

This problem is designed to confuse, especially for those who never had a firm grasp on the notion of the power set  P(S), which has elements that are subsets of S.  In your case, the subsets of a four element set like {a,b,c,d} are the elements of the power set P({a,b,c,d}).  A critical first step for you is to understand how many elements does this power set have?  Now how many of these elements chosen at random (with repetition allowed) do you need to write down, before you are *guaranteed* that you have written down at least one element (i.e. some subset of {a,b,c,d}) twice?  If you write down 49 subsets (49 elements of P({a,b,c,d}), what is the smallest number of elements that must be duplicates? (For instance if you got to pick the elements, you could choose all 49 the same and would have 49 duplicates--but this question is asking about a lower bound, not an upper bound)

homework due next week

We've gotten a bit behind on the homework, so I'm going to pace the webwork a little more closely;

Webwork section 6.1 and section 6.2 are now open due next Monday at 6pm.
Webwork section 6.3 and section 6.4 are now open due next Wednesday at 6pm

Book homework for chapter 6 is due Next Friday at the beginning of class.

The exam on monday...

will cover sections 3.2-6.2

A practice exam

The practice exam can be accessed through this link.