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by nona.m.nona
Fri Feb 27, 2015 4:04 pm
Forum: Discrete Math
Topic: Find two proofs for the identity
Replies: 4
Views: 96

Re: Find two proofs for the identity

Using a combinatorial argument, prove the following identity: \binom{2n}{2}\,=\,2\,\binom{n}{2}\,+\,n^2 To use a "combinatorial argument", one must consider sets of elements. On the left-hand side: Consider a set with 2n elements, and pick two elements at a time. This may be done in C(2n,...
by nona.m.nona
Sun Feb 15, 2015 3:05 am
Forum: Calculus
Topic: Finding the derivative of arctan
Replies: 1
Views: 97

Re: Finding the derivative of arctan

y=arctan sqrt[(1+x)/(1-x)] what i did: let u= sqrt[(1+x)/(1-x)] du=1/2 [(1-x)/(1+x)]^1/2 [{(1+x)(-1)-(1-x)}/(1+x)^2]dx I solved this problem many times, but I don't get the right answer.... Where did you take the derivative of the inverse tangent? What did you get for your answer? What is "the...
by nona.m.nona
Fri Jan 30, 2015 7:37 pm
Forum: Matrix (Linear) Algebra
Topic: is A C B^T = B C^T A^T ?
Replies: 1
Views: 275

Re: is A C B^T = B C^T A^T ?

I don't understand how A C B^T + B C^T A^T = 2 A C B^T This may be rearranged as: A C B T + B C T A T = A C B T + A B C T This results in: B C T A T = A B C T Two properties of transpositions are that the transpose of a transpose is the original matrix, and that the transposition of a product resul...
by nona.m.nona
Fri Jan 30, 2015 7:26 pm
Forum: Advanced Algebra ("pre-calculus")
Topic: Eigen Vaues and Eigen Vectors
Replies: 1
Views: 223

Re: Eigen Vaues and Eigen Vectors

The information at the link appears to be as follows: \left[ \begin{array} {rr} 50&-40\\-40&45 \end{array} \right] \,\left[ \begin{array} {cc} X_1\\X_2 \end{array} \right]\, =\, \lambda\,\left[\begin{array}{rr}2&0\\0&5 \end{array} \right] \,\left[ \begin{array} {cc} X_1\\X_2 \end{arr...
by nona.m.nona
Fri Jan 30, 2015 7:10 pm
Forum: Geometry
Topic: Line Geometry and Euclid proposition 4 and 8 in book I
Replies: 1
Views: 187

Re: Line Geometry and Euclid proposition 4 and 8 in book I

Is there a book which has axioms for geometry on a line? Possibly ("probably"?) not. However, some information is available, such as ( this ) online article. Most other resources appear to be quite advanced, usually treating one-dimensional "cases" of other topics, such as "...
by nona.m.nona
Wed Jan 28, 2015 1:03 pm
Forum: Calculus
Topic: Inverse Function for y = x^(m+1) + x
Replies: 2
Views: 251

Re: Inverse Function for y = x^(m+1) + x

wan nini wrote:I...need to find the inverse function.

y=xm+1+x

I can't think of any way to invert this. How did you arrive that this function? What was the original exercise? Thank you.
by nona.m.nona
Mon Dec 22, 2014 5:38 pm
Forum: Advanced Algebra ("pre-calculus")
Topic: Multi Variable Partial Fraction Problem
Replies: 2
Views: 374

Re: Multi Variable Partial Fraction Problem

The problem is to develop . . . . . \dfrac{(x\, -\, \alpha)(x\, -\, \beta)(x\, -\, \gamma)}{(x\, -\, a)(x\, -\, b)} into partial fractions. Someone challenged me to solve this and said that the answer is . . . . . x\, -\, (\alpha\, +\, \beta\, +\, \gamma\...
by nona.m.nona
Sun Dec 07, 2014 5:47 pm
Forum: Uncategorized
Topic: Calculation of point of no hope
Replies: 1
Views: 327

Re: Calculation of point of no hope

Is there a mathematical way to calculate a student's grade standing in real time so that they can know when they have reached the point of "no hope" in passing the course? I would like to provide a simple method for my students to know when they need to take action regarding my course bas...
by nona.m.nona
Sat Oct 04, 2014 3:25 am
Forum: Discrete Math
Topic: Counting
Replies: 1
Views: 418

Re: Counting

Let A be a set with n elements and B with m elements. How many functions are there from A to P(B)? A has n elements so A = n, B has m elements so B = m. P(B) = 2 m . Are there (2 m ) n functions from A to P(B)? What is the definition of "P(B)"? Mathematically, a set is not equal to its ca...
by nona.m.nona
Thu Oct 02, 2014 1:12 pm
Forum: Discrete Math
Topic: Functions And Encylopedia of Integer Sequences
Replies: 2
Views: 435

Re: Functions And Encylopedia of Integer Sequences

1. Where did the concept of a function first arise, and describe how this concept was first used. This is a question related to the history of mathematics. Resources (such as books ) may be consulted for this information, should it be available. (It is noted that many questions, such as "why u...

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