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April 18, 2014

Search: Math - determinants

Number of results: 213,811

Determinants
Why are finding determinants important? Aside from Cramer's rule when are determinants used?
Thursday, March 11, 2010 at 11:43am by Kevin

Determinants
Determinants appear often when you are interested in finding the inverse of an operator that is a square matrix. They also appear in tensor calculus, which is the mathematical form in which the General Theory of Relativity is written. In my 50 years as an applied physicist, I ...
Thursday, March 11, 2010 at 11:43am by drwls

maths
Assuming you know how to calculate a determinant, the answer is x = |24 -6| / |3 -6| = -18/-9 = 2 ....|-23 5|/ |-4 5| You can get y by substitution of x=2 in either equation, or from a separate ratio of determinants. If you are not familiar with the notation, nor why I chose ...
Wednesday, January 2, 2008 at 3:03am by drwls

health care
http://www.google.com/search?q=determinants+of+respiration&oq=determinants+of+respiration&aqs=chrome..69i57.1637j0j7&sourceid=chrome&espv=210&es_sm=119&ie=UTF-8
Sunday, March 30, 2014 at 5:52am by Writeacher

Math
http://www.intmath.com/matrices-determinants/4-multiplying-matrices.php Remember length of row of first must equal number of rows of second
Thursday, January 26, 2012 at 9:54am by Damon

Math - determinants
| x 5 2 | |-6 4 1 | = x(squared) + 22x - 1 | 3 1 x | Solve for x.
Thursday, November 4, 2010 at 11:42pm by Kye

Math
Do you mean using inverse matrix? Determinants? Elimination?
Friday, October 11, 2013 at 8:37pm by Steve

Math
are you certain of the first equation? I would use determinants to solve this.
Thursday, January 17, 2013 at 8:17am by bobpursley

Math
Solve using Determinants and Cramer's Rule? I was absent and missed the lecture on Cramer's rule and Determinants and have no idea how to start the homework.. The directions and problem are as follows: Using Cramer's Rule, set this problem up to find "a". Only evaluate the ...
Tuesday, November 30, 2010 at 4:50pm by Euphoria

Algebra II
1) when using cramer's rule to solve the system of equations containing 5x - y = 5 and -3x + y = -9 the denominator for the x and y variables looks like which of these determinants ? a) |5 5 | b) |5 -1 |-3 9| |-3 1| c) |5 -1| |-9 1| d) none of these 2) when using cramer's rule...
Friday, April 8, 2011 at 7:52am by anonymous

Math: determinants
As you can see from your own post, it is very difficult to type and show matirices and determinants in this format. Take a look at these sites, thy summarize most of the important properties very nicely. http://www.sosmath.com/matrix/determ0/determ0.html http://www.ping.be/~...
Sunday, December 2, 2007 at 11:45pm by Reiny

health care
what is determinants of respiration?
Sunday, March 30, 2014 at 5:52am by natkrt

Algebra
|A| = 5*5 - 1*1 = 24 If that isn't clear, review how to calculate determinants.
Monday, March 18, 2013 at 3:16am by Steve

Math
determine the number of solutions using determinants 3x-y=-6 2x=3y+2 I get: 3 -1 2 -3 D = -9-(-2)=-7 and 3 -6 2 2 D = 6-(-12)=18 solution set is (-7,18) when I plug them in to check, they don't come out right
Sunday, March 21, 2010 at 7:59pm by Paula

Math
If you will "plug in" x = 2 and y=3 to either equation, you will see that your solution is incorrect. Cramer's rule involves using the determinants of matrices. You do have the denominator determinant (26) correct. The numerator for y is wrong. It should be -78. y = -3
Tuesday, February 26, 2008 at 2:47pm by drwls

Algebra
Do you have Gaussian reduction on your calc? That is the easy way. Not having that option, I would use the method of determinants.
Friday, August 20, 2010 at 1:04pm by bobpursley

Math grade 12
write the partial fraction decomposition of the following rational expression ( hint: binomial expansion with Pascal triangle can be used to expand binomials. technology may be used to solve large systems using matrices or determinants) 4 ------------------------------------- ...
Sunday, January 1, 2012 at 8:40pm by Rass

Math grade 12
this better? write the partial fraction decomposition of the following rational expression ( hint: binomial expansion with Pascal triangle can be used to expand binomials. technology may be used to solve large systems using matrices or determinants) 4/x^3(x-3)(x+2)(x-1)^2(x^2+...
Sunday, January 1, 2012 at 8:40pm by Rass

health
Is it true that societal health determinants are predicated on policy?
Monday, September 23, 2013 at 11:01pm by Jimmy

math
I could help you solve those equations, but I do not understand the matrix part of your question. You could use determinants (a matrix calculation) to solve them, but that is not necessary. What are R1 and R2? Are your matrices supposed to be related to your set of equations?
Saturday, January 24, 2009 at 11:08pm by drwls

College Algebra
By what method are you using. If not your calculator on matricies, then Irecommend the method of determinants.
Saturday, December 11, 2010 at 2:28am by bobpursley

health
What are "societal health determinants"? Once you can name them, the answer should be clear.
Monday, September 23, 2013 at 11:01pm by Writeacher

Algebra
x = |11 1| |5 -1| ------ |1 1| |1 -1| = -16/-2 = 8 y = 11-x = 3 The | | /| | symbols represent the ratios of two 2x2 determinants
Friday, March 2, 2012 at 9:50am by drwls

health studies
How can I talk about social determinants of health and effective bureauracy to eliminate child labour?
Friday, February 25, 2011 at 8:51pm by 5678

physics
come on laura, it is an algebra II skill. How do yo solve for x here? 3x+4y=67 -x+5y=9 you can use substitution, elimantion of variables, or determinants. You know how to do this.
Saturday, December 3, 2011 at 7:52pm by bobpursley

algebra
what, you can't find the determinant? Those two zeros in the top row make it easy: |A| = (2.8)(4.4)-(4.3)(2.1) = 3.29 Better review your determinants if this technique is going to come up often.
Tuesday, April 2, 2013 at 11:31am by Steve

math-algebra
Since this is multiple choice, why not just try which of the three sets of numbers satisfy all equations? Obviously, answer A does not satisfy x+y+z=3 Alternatively, use standard methods of algebra two reduce the number of vaiables to one, or use determinants. I will be happy ...
Wednesday, September 26, 2007 at 1:17am by drwls

Solving system of linear equations
I don't know about rref. You can use a calculator to compute the inverse of a matrix, do Gaussian elimination, or use Cramer's rule which uses determinants of matrices...
Sunday, February 22, 2009 at 5:55pm by Count Iblis

Algebra 2
let a = no. adult tickets let s = no. senior tickets let c = no. child tickets c + s = 30 + 1/2 a s = 5 + 4c 5.5a + 4s + 1.5c = 14970 I'll leave the solution to you. Substitution, Gaussian elimination, determinants, whatever.
Wednesday, October 5, 2011 at 12:29am by Steve

algebra 2
i need answers to the pennfoster book matrices and determinants exam number :00703500. please make sure all the answers are correct. please and THANK YOU (:
Thursday, September 10, 2009 at 11:14pm by hellomynameis

Macroeconomics
Manipulation of the Cobb Douglas Equation gives us expression for output per working age person: growth rate of (Y/N)=[1/(1-alpha)*growth rate of TFP]+[(alpha/(1-alpha))*growth rate of (K/Y)]+ [growth rate of (L/N)] N is the working age population K is capital stock L is labor...
Friday, February 9, 2007 at 11:04am by joe

Foundations of Law
Hopefully you will find the answer here: http://www.google.com/search?q=biological+theories+of+crime+causation+assume+basic+determinants+of+beh+avior+are+based+upon+what+2+things&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a Sr a
Sunday, May 10, 2009 at 3:43pm by SraJMcGin

Algebra
I suggest you try them all and form your own opinion. With two or three unknowns, I prefer elimination as a method. It is quick and there is less opportunity to make mistakes. With four or more unknowns, I would use determinants.
Tuesday, March 4, 2008 at 4:31am by drwls

working with school aged children
Which of the following are the major determinants of physical growth and development? A. Heredity, parents, and school B. Intelligence, cleanliness, and aggression C. Nutrition, emotional well-being, and culture D. Food, TV, and technology I am thinking that it's C
Monday, May 16, 2011 at 11:57pm by Heather

Math: determinants
If det(A)=-7 A= | a b c | | d e f | | g h i | Find det(2A^-1), det((2A)^-1). Find | a g d | | b h e | | c i f |
Sunday, December 2, 2007 at 11:45pm by Amelie

Maths
just solved the system of equations. I used wolframalpha.com, but you can use elimination, determinants, substitution, or whatever you like to use for solving systems of equations. Algebra I stuff. Dust off those skills.
Tuesday, February 26, 2013 at 10:38am by Steve

Math
An even simpler method for 2x2 matrices is by determinants. As we have seen above, |A| = 7 we can calculate x and y directly by calculating the determinant of A after replacing the corresponding column of A by the B vector, and dividing by |A|. Thus x= |18 4| |19 5| divided by...
Wednesday, July 8, 2009 at 4:52pm by MathMate

Determinants of Interest Rates
If the rate of inflation is 5%, what nominal interest rate is necessary for you to earn a 3% real interest rate on your investment?
Wednesday, October 20, 2010 at 2:17am by Anonymous

Foundations of Law
I am a little lost on this. I read my book that my professor told me to read, however, I still do not see the answer to this question Biological theories of crime causation assume that the basic determinants of behavior are based upon two things; what are they
Sunday, May 10, 2009 at 3:43pm by Criminal Admin Major

math
No. Eliminate variables one at a time, or use Kramer's method of determinants. Here is how to get rid of x. Add the first two equations. 3w + 3z = 9 or w + z = 3 Multiply the third equation by 2 and the fourth equation by 3, and add. 4w + 6x + 4y - 2z = -4 9w - 6x - 3y - 9z...
Friday, January 28, 2011 at 7:51pm by drwls

Math
So, follow Reiny's suggestion, using determinants You can verify your solution here: http://ncalculators.com/matrix/cramers-rule-calculator.htm
Thursday, January 17, 2013 at 8:17am by Steve

Biology
Good day! I actually just have one question and I have been looking at links and everything, but i still dont understand>>>>... "What abiotic factors seem to be the greatest determinants of terrestrial biome locations?"
Sunday, June 26, 2011 at 2:53pm by Sam

Determinants of Interest Rates
8%, if you ignore taxes. Tax rates on interest income depend upon income level, whether you are in the AMT category, and the type of fixed-income investment. Municipal bonds and money market funds that hold them are tax free in the USA.
Wednesday, October 20, 2010 at 2:17am by drwls

matrices
the determinant of your matrix is 6a - 12 to solve for a we must know what that is equal to. Are the choices you give possible answers for a? If so, you don't have enough information Are the choices you give the value of the determinants? Then you have 4 different questions ...
Thursday, March 13, 2008 at 10:07am by Reiny

economics
What are 5 deteminants of demand for JONES Soda Co? What are 4 determinants of supply for JONES Soda Co? Think about what influences supply and demand e.g., what are some factors that would shift the supply curve? the demand curve? And this will be your answer.
Sunday, March 11, 2007 at 11:21pm by Kayla

math
Have your reviewed the subject of how to solve systems of equations with determinants? You need to do that. There are plenty of tutorials online on that subject. You want to use Cramer's Rule. See http://www.maths.surrey.ac.uk/explore/emmaspages/option1.html It would require ...
Tuesday, February 24, 2009 at 10:09pm by drwls

maths
Cramer's rule is well explained here: http://www.purplemath.com/modules/cramers.htm You will need to calculate the determinants of four 3x3 matrices. I assume you know how to do that. If not, it's high time to learn how.
Thursday, July 28, 2011 at 9:18am by drwls

Linear Algebra 2 question
Hello, I have another question from my linear algebra class. I'm asked to find the area of a triangle using determinants, but they don't give me the vertices, only the sides. Where A,B,C and D are the vertices, u and v are 2 out of the 3 sides. Now they give me u=(-3,1) and v...
Sunday, August 26, 2012 at 8:10pm by Robert

economics case analysis
My thoughts are not in the vocabulary of economics -- but they may get you started. 1. Bob knew how much had to spend and what he wanted. Then he researched and realized he didn't have enough money (resources) to meet his wants. He increased his resources by working extra ...
Sunday, October 4, 2009 at 9:58pm by Ms. Sue

College Physics
You need to learn the method of taking the cross product of two vectors with determinants. That is what I did. For a brief summary see http://www.ucl.ac.uk/mathematics/geomath/level2/mat/mat121.html
Saturday, March 10, 2012 at 1:48am by drwls

DRWLS CAN YOU ANSWER
How do i solve inequalitites with three variables. I still can't figure it outplease help. x+y=1 y-z=-3 2x+3y+z=1 THE ANSWERS ARE3,-2,1 HOW DID THEY GET THAT ANSWER. This can be solved a number of ways. 1) subsitition 2) determinants 3) matricies. Substution: x= 1-y y= z+3 or ...
Sunday, October 22, 2006 at 8:55pm by Jasmine202005

cramers rule
Solve the following linear system for x using Cramer’s rule. Show work. x + 2y – 3z = -22 2x – 6y + 8z = 74 -x – 2y + 4z = 29 Cramer’s rule uses determinants to find the solution Set up a 3by3 matrix using the coefficients of the x,y and z, and find its determinant, calling it...
Wednesday, August 8, 2007 at 5:43pm by linda

(pls help) algebra
here are several ways to do this (as I'm sure your textbook will show - read it, and do web searches for alternate presentations). Substitution: (1) 4x+y-3z = 1 (2) 6x-y-4z = 7 (3) 10x+2y-6z = 5 From (1) we see that y = -4x+3z+1, so plug that into (2) and (3): 6x - (-4x+3z+1...
Monday, July 8, 2013 at 6:07am by Steve

FRENCH to SraJMcGin
http://www.jiskha.com/display.cgi?id=1244070552 http://www.jiskha.com/display.cgi?id=1244070552 E.G. I appreciate you being persistent on this question, which prompted me to do a little more research, and here is what I found. (see references 1 and 2) In summary, what your ...
Wednesday, June 3, 2009 at 11:19pm by MathMate

Algebra
<<Here are the three equations x=8, x=13, x=18 y=5.4, y=6.3, y=5.6 >> Those are not three equations. They are possibly the coordinates of three points, arranged in a confusing manner. (x,y) = (8,5.4), (13,6.3) and (5.5,5.6) With those points, and the Gauss-Jordan ...
Sunday, December 13, 2009 at 6:16am by drwls

Science
Newton's laws are empirical determinants of how gravity operates. Gravity operates regardless of the law. I think I responded to the second question previously. Since this is not my area of expertise, I searched Google under the key words ""Newton's Laws" "everyday life"" to ...
Wednesday, March 26, 2014 at 8:21pm by PsyDAG

statistics
An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year...
Thursday, March 15, 2012 at 10:56pm by ronald

statistics
An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year...
Monday, March 19, 2012 at 9:11pm by ronald

Math (matrices)
No one answered my matrix question. Let me rephrase: Let A, B, and 0 be 2x2 matrices. Assuming that A is invertible and 0 is all zeroes, what is the inverse of the matrix [A|0] [B|A] (that is a 4x4 matrix represented as 4 2x2 matrices) The answer is in the form: [A^-1|0 ] [C |...
Thursday, November 16, 2006 at 1:23pm by James

economics case analysis
Bob is really excited about next year at the university, which starts in two weeks. But his parents just dropped a bombshell: he is going to have to buy all of his own clothes for the fall semester. On no, he has never paid for his own clothes! And he really wants more od his ...
Sunday, October 4, 2009 at 9:58pm by Danielle

College Algebra-Study Material
I am going to take the CLEP (College Level Examination Program) College Algebra examine. I am trying to decide on what books I should use to prepare for this examine. The following is what is going to be covered in this examine: 25% Algebraic operations Factoring and expanding...
Friday, November 28, 2008 at 10:15am by G

math
Math stinks depending on how you feel about it. Last year, I became Math Wiz because I love Math. Your feeling about Math can change the way you think about Math if you think of it more. And also, thinking of it helps you be better at Math. Math may start easy but soon gets ...
Monday, October 9, 2006 at 10:23pm by Visitor

macroeconomics
1. What is the demand for money? What are the types of Money Demand? Explain further utilizing the determinants of Money Demand. How does the demand for money depend on the nominal interest rate? On the price level? On income? Explain in terms of the costs and benefits of ...
Tuesday, December 3, 2013 at 5:12pm by Latesha

Math
WHAT ABOUT NUMBA ONE? IM GONNA FAINT RIGHT NOW SO I DONT HAVE TO GO TO SCHOOL TOMORROW I HATE MATH I HATE MATH I HATE MATH I HATE MATH I HATE MATH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Tuesday, November 20, 2007 at 6:20pm by Veronica

math
all i can say is math stinx dont mess with math. without math, a lot of things wouldn't exist right now...
Monday, October 9, 2006 at 10:23pm by Anonymous

math math math math
math art wrighting spelling
Monday, January 10, 2011 at 5:04pm by emma

Math...For All Math Tutors
I would like to know how many of the people answering math questions here are current math teachers, were math teachers at one time, are current tutors working for a tutoring company or simply love math. What's your story? I would love to hear from all math tutors. Thanks, ...
Friday, February 15, 2008 at 10:29am by Guido

math
I just do not understand how to figure this out. Find the number of subsets of the given set. {math, English, history, science, art} Would I do something like this: 1. {} 2. Math 3. English 4. history 5. science 6. art 7. Math and English 8. math and history 9. math and ...
Wednesday, April 14, 2010 at 8:10pm by Bart

English Grammar
A: What time is your math/Math class? B: At eleven forty-five. Do we have to use 'math' or 'Math'? And is it a common noun or a proper noun?
Friday, April 18, 2008 at 10:52am by John

math
Directions are as follows: Use a tissue box to display Top - The math concept or idea the box provides information about Bottom - Students name and rsources used in research of the math concept Side 1 - A brief description, including facts about the math concept Side 2 - A ...
Sunday, February 12, 2012 at 1:54pm by Buddy

math math math math
a. what is the general term of the following series? 60/121-30/11+15-... +219 615/16 b. how many terms does the series have?
Monday, January 10, 2011 at 5:04pm by Anonymous

What Makes A Good Math Teacher?
I think a good math teacher is someone who can explain math topics at the level of students. A good math teacher is someone who does not try to impress students with his or her math skills (college math professors are famous for boasting). In your opinion, what makes a good ...
Friday, February 22, 2008 at 4:29pm by Guido

3rd grade Math
Actual question on homework."EXPLAIN HOW YOU CAN BREAK APART ARRAYS WHEN YOU MULTIPLY BY 3." (there is no array on the paper to use) I don't like this new math, what was wrong with the old math I learned, I am Accounting /Finance supervisor, but don't understand this math.
Thursday, January 21, 2010 at 11:18pm by Jennfer

Geometry
i dont like MATH! MATH MATH MATH!
Tuesday, January 8, 2008 at 8:50pm by makaiya

math math math math
- 15 x ² + 2x + 13 = 0
Monday, January 10, 2011 at 5:04pm by Anonymous

English Grammar
You use "math" when you're making a general reference to the class, whether it's Algebra I or Geometry or whatever. You use "Math" when it's part of the formal name of the course. "When I was a senior in high school, my math course was called Math IV."
Friday, April 18, 2008 at 10:52am by Writeacher

Math
All of my life I have gotten a C average in math. I have been trying to set a goal to make above a C in math. I don't know why I have trouble with math. Can someone help me?
Thursday, August 18, 2011 at 12:51am by Aquion

Microeconomics help please!
If someone colud help with these questions I would be very greatful, Ive been trying for awhile now and Im at my ropes end. 1)The perfectly competitive ice cream industry is assumed to be in long-run equilibrium. Suppose there is an increase in the market demand for ice cream...
Friday, July 15, 2005 at 1:25pm by crstudent

Math...For All Math Tutors
You may not have actual teaching experience but you are a professional nonetheless. I was an excellent math student back in my pre-college and college years but never taught math in my own classroom except as a substitute teacher. Sub teaching is more like baby-sitting than ...
Friday, February 15, 2008 at 10:29am by Guido

English
Revise the folloing sentences to create parallel constructions. (Question) Some students hate math; some students dislike math, and math is liked by other students. (my answer) Some students hate math, some dislike math, and some like math. every way I have tried it just doesn...
Wednesday, June 30, 2010 at 7:01am by Rita

math
That's right. I'm not a math teacher and my math skills don't go much beyond 7th grade. Please be patient. Math tutors may be on a little later this evening. I'll give you a hint, though. If you post what you know and think you know about your questions, you're more likely to ...
Sunday, March 20, 2011 at 4:48pm by Ms. Sue

math
There are any types of math problems- unfortunately we cannot help you unless you give us something to work with, like a difficult math problem. I do not really get math either sometimes, Elizabeth, but as Ms. Sue said, if you post a couple of confusing problems, we'll try to ...
Wednesday, September 26, 2012 at 5:33pm by Delilah

Math(thanks)
Thanks. I posted this question 4 times titled math, math repost, math repost, and this one. You must be thinking of the other question about writing the standard form of the equation of the circle but oh well.
Wednesday, April 22, 2009 at 10:07pm by Jon

Math
Is IB Math Studies the same as Pre-Calculus? I heard that IB Math Studies is for students who have a low background in math. Is that right?
Tuesday, August 20, 2013 at 2:02am by Anonymous

Math
For this go on to the website discovery education. Then go under students and click math. And then where it says step by step math in green, click on trigonmetry and calculus. I forgot what area of math this is but choose from one of the items. And jot it in the box search ...
Tuesday, November 22, 2011 at 10:40pm by Fizzylicous

math
Whether because of a poor elementary and middle school math curriculum or because of my own inaptitude, I barely passed third year high school math -- advanced algebra and solid geometry. I haven't taken any math since then(except a statistics for dummies in grad school). ...
Saturday, January 8, 2011 at 11:14pm by Ms. Sue

math
N(Math OR English) = N(Math) + N(English) - n(Math AND English) = 13 + 33 - 6 = 40 So 40 took either Math or English, then 6 took neither of these subjects You can also do this with Venn diagrams
Friday, May 21, 2010 at 4:29pm by Reiny

math - needs help
The School Subject is NOT 10th grade. Is it math? If so, state that for a math teacher to help you. Sra
Thursday, May 27, 2010 at 8:50am by SraJMcGin

Math
A math book is .78 centimeters thick. What is the width of 21 math books on a shelf?
Thursday, October 14, 2010 at 8:29pm by TJ

MATH
Hehehe!! My math skills stop at elementary math. I have no idea how to help you with this problem!
Sunday, December 4, 2011 at 10:36pm by Ms. Sue

math
Sorry, I'm not the best at math whatsoever, I've already posted like 5 math questions.
Tuesday, November 20, 2007 at 3:57pm by Ariana

Math
My friend if you don't care about your own math work, then no one else will, too. Math rules!
Thursday, February 14, 2008 at 12:33am by Guido

math math math .
The coefficient of the first term in the polynomial 2x^2y+3xy-1 is _?_
Friday, October 24, 2008 at 2:02pm by margiee (: !

Math
If you want a math tutor to help you, please type math in the school subject line.
Thursday, January 6, 2011 at 5:27pm by Ms. Sue

MATH
BTW, the Subject is not 3rd grade but Math, if you wish a Math teacher to read your post. Sra
Tuesday, January 19, 2010 at 2:43pm by SraJMcGin

math
forgot my math book at school, i need the questions saxon math grage 6 lesson 14
Monday, September 13, 2010 at 7:12pm by kolbi

math
Ms Sue when you said 25 in the overlapping section of math and english did mean math and history/
Monday, August 6, 2012 at 6:53pm by kyle

math
for every 20 math books a school buys, they they get 7 aditional books for free. The school needs 297 math books. What is the total number of math books the school must buy in order to receive 297 math books in all?
Wednesday, February 8, 2012 at 6:16pm by ali

math 098
I made 3 f's on my tests in math 098, do you think i need to withdraw and take math 090 instead. this is my first semester and i really want to do my best please help. math 098 is algebra math 090 is basic for college. the score were equations--52,distance problems---55, ...
Friday, July 6, 2012 at 7:09am by %%%Rena%%%

math
Will you help me with my math homework? what level of math? Please repost with the specific problems, so we can help. Thanks for asking.
Wednesday, February 21, 2007 at 10:17pm by morgan

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