Thursday

December 25, 2014

December 25, 2014

Total # Posts: 74

**Finite Math**

3! = 3*2*1 = 12 Starting at A, he can go to B or C or D (three choices). From there, the driver has two choices. Then will have only one route left. That sounds like an easy version of the standard traveling sales person problem.
*March 2, 2009*

**math**

Thanks guys. I wrote a simple computer program that verifies that S = 1/(1-x) holds when 0 < x < 1 (hence the series converges), but not when x > 1 (and the series diverges). That wasn't clear in the textbook. Thanks for the help.
*February 10, 2009*

**math**

I read from my textbook: If S is the infinite series 1 + x + x^2 + x^3 + ... Then Sx = x + x^2 + x^3 + x^4 + ... = S - 1 So, S = 1/(1-x) I follow what that logic, but it still doesn't make sense. The way I see it, if you plug any real number > 1 into x, S will be ...
*February 10, 2009*

**math**

Ah ha! That's exactly what that is. And I knew that a long time ago. Thanks! It doesn't show up on Wikipedia's greek alphabet page at all, but that's more than good enough! Thanks!
*January 16, 2009*

**math**

I'm reading a formula (lots of greek letters) and I see a symbol that looks like a backward six. That doesn't seem to be any greek letter... What is it?
*January 16, 2009*

**math**

Thanks for the great suggestion Count. I ordered the third edition of that book from Amazon. The TOC looks great. Thanks!
*April 25, 2008*

**math**

I've finished studying a full textbook on linear algebra and another on statistics. I've done most of the practice problems and I understand everything covered in these books very well. But I need to know more. Specifically, I'd like to understand more about: - ...
*April 25, 2008*

**C++ Programming**

That's code to walk through a linked list. I can't say the exact output because I can't see what the variable "list" is. Also, there are missing braces after the while statement. If the program is run without braces, and list is not null, the iteration ...
*April 18, 2008*

**math**

I'm trying to follow a research paper The paper shows an equation to minimize. That makes perfect sense. Then, the paper says: "The optimal solution to the least squares problem [above] is found by differentiation as a solution of a linear system of equations." I...
*April 18, 2008*

**Calculus**

That's what I needed. Thanks so much for the help!
*March 7, 2008*

**Calculus**

Integrate e^(-x^2/2) dx What branch of calculus is this? Is this differential equations?
*March 7, 2008*

**statistics**

Damon, that can't be right. As n approaches infinity, S^2 should approach sigma^2. Also, the wikipedia entry does use both sample size and population size in their formula which is one reason that I wanted to see it derived.
*February 21, 2008*

**statistics**

I meant "expected" value, not "estimated" value. Sorry about that.
*February 21, 2008*

**statistics**

sigma is the standard deviation of a population of size N S is the standard deviation of a sample of size n from within the population. What is the estimated value of S^2? If the population was infinitely large (size N = infinity), what would the estimated value of S^2 be?
*February 21, 2008*

**math**

Thanks so much for working that out. In hindsight, I did the problem right except that I made a mistake in calculating <v2,v2>
*January 18, 2008*

**math**

Find the least squares approximation of x over the interval [0,1] by a polynomial of the form a + b*e^x --------------------------------------------------------- The polynomial produces an output space with two linearly independent basis vectors: u1 = 1, u2 = e^x I believe ...
*January 18, 2008*

**math**

Thanks Count Iblis! I was mistakenly integrating with pi/2 instead of 2*pi and every time I redid the problem, I just remade the same mistake without noticing it. Your help pointed out the issue. Thanks so much!
*January 16, 2008*

**math**

A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos 2x + ... + cn * cos nx + d1 * sin x + d2 * sin 2x + ... + dn * sin nx The output vector space of such a function has the vector basis: { 1, cos x, cos 2x, ..., cos nx, sin x, sin 2x, ..., sin nx } Use ...
*January 16, 2008*

**calculus**

Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = sqrt(pi)/2 Solve for Definite Integral of e^(-ax^2) dx over [-infinity,infinity] I don't know how to approach the new "a" term. I can't use u-substitution, integration by parts, partial ...
*January 14, 2008*

**Calculus**

Thank you bobpursley. My surface area integral was bad. I was incorrectly assuming S = Int 2*pi*f(x) dx I read through proof. It is S = Int 2*pi*f(x)*sqrt(1+(dy/dx)^2) dx Thanks!
*January 13, 2008*

**Calculus**

Suppose that the region between the x-axis and the curve y=e^-x for x>=0 has been revolved around the x-axis. Find the surface area of the solid. I got 3*pi The book shows an answer of pi * [sqrt(2) + ln(1 + sqrt(2))] Where do I go wrong? For the sides of the surface, I ...
*January 13, 2008*

**Calculus**

That's probably close enough Damon. thanks!
*January 13, 2008*

**Calculus**

My book says to do the following problem via computer and via hand: Calculate the definite Integral of e^-x * cos x dx over (0, +infinity) My TI-89 calculator gets 1 (it gets the same thing when I replace infinity with 999). when I do this by hand, I get: 1/2. The formula e^-x...
*January 13, 2008*

**algebra**

If a is large and b is small: First rule: a = 12 + b Second rule: b + 2a = 39 Solve those two equations for a. The answer is choice "c"
*January 10, 2008*

**Calculus**

Suppose that ax^2 + bx + c is a quadratic polynomial and that the integration: Int 1/(ax^2 + bx + c) dx produces a function with neither a logarithmic or inverse tangent term. What does this tell you about the roots of the polynomial?
*January 10, 2008*

**Question**

Wow! Thanks for answering and thanks again for all the valuable homework help!
*January 7, 2008*

**Question**

Dear experts, What is your motivation to provide all this help? I'm extremely grateful for this service, but why do you help so much? Are you paid to do this? Are you teachers who like to assist in spare time? Trying to brush up on your own skills? Thanks!
*January 7, 2008*

**calculus**

Thanks Reiny + Iblis! This is from Wiley textbook "Calculus: Early Transcendentals Combined, 8th Edition", section 8.4. I think problem #41 (from memory). I typed it right. The answer you two wrote matches the book, however I couldn't figure out how to do it. ...
*January 6, 2008*

**calculus**

Integrate: dx/(2x^2 + 4x + 7)
*January 6, 2008*

**Calculus**

Calc length of arc of y=ln(x) from x=1 to x=2 ---- So far: Definite Integral over x=(1,2) of sqrt(1 + 1/x) dx 1/x = tan^2 t x = 1/tan^2 t sqrt(1+1/x) = sqrt(1+tan^2 t) = sec t dx = -2 * tan^-3 t * sec^2 t dt Integrate over x=(1,2): sec^3 t / tan^3 t dt Integrate over x=(1,2): ...
*January 2, 2008*

**math**

That doesn't look right. First, 36/5 = 7.2 (not 7.25) Secondly, you should do all multiplication first, then do subtraction. 9*4/5 - 4/5 7.2 - 0.8 = 6.4
*January 2, 2008*

**Math**

The max is 31/6 (no other value is greater) The minimum is -3 (no other value is less)
*January 1, 2008*

**calculus**

sorry. posted too quickly. got the answer. Via trig substitution answer comes to: ln|sqrt(x^2+4)/2| + c which is the same as the other answer
*December 31, 2007*

**calculus**

Integrate x/(x^2 + 4) dx via trig substitution and by u=x^2+4 substitution. Show that results are equal. Via trig substitution of x=2 *tan t, I get: 1/2 * tan^-1 (x/2) + c Via u = (x^2 + 4) substitution, I get: 1/2 * ln |x^2 + 4| + c How are these equal?
*December 31, 2007*

**calculus**

of course. That makes perfect sense. Thanks!
*December 31, 2007*

**calculus**

Ack! Actually, I just typed that up wrong. I didn't make that mistake on paper. My answer is still coming up wrong. Thanks for helping drwls. sqrt(x^2 - 9) = 3 * tan t dx = 3 * sec t * tan t * dt The rest is the same: Integral simplifies to: sec t dt Integrates to: ln|sec ...
*December 31, 2007*

**calculus**

Integrate: dx/sqrt(x^2-9) Answer: ln(x + sqrt(x^2 - 9)) + C I'm getting the wrong answer. Where am I going wrong: Substitute: x = 3 * sec t sqrt(x^2 - 9) = sqrt(3) * tan t dx = sqrt(3) * sec t * tan t Integral simplifies to: sec t dt Integrates to: ln|sec t + tan t| + C t...
*December 31, 2007*

**calculus**

thanks damon! I follow perfectly.
*December 31, 2007*

**calculus**

Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I start with the substitution x = sqrt(3)*tan t so: sqrt(x^2 + 3) = sqrt(3) * sec t dx = sqrt(3) * sec^2 t dt x^4 = 9 * tan^4 t The integral simplifies to: = dt/(tan^3 t * sin t) How do I solve that?
*December 31, 2007*

**math**

Nevermind. Found the solution: 1) Multiply by (csc x + cot x)/(csc x + cot x) 2) Substite u = csc x + cot x into integral 3) Comes out to -du/u 4) Integrates to -ln |u| + c 5) Equals -ln |csc x + cot x| + c
*December 17, 2007*

**math**

Integrate: csc x dx
*December 17, 2007*

**math**

Find the arc length of y = ln(cos x) over x = [0, pi/4]
*December 3, 2007*

**math**

How do I derive the secant reduction formula? Am I asking this question wrong? Integrate: (sec x)^n dx
*November 8, 2007*

**math**

How do I derive the secant reduction rule? Integral (sec x)^n dx = Integral (sec x)^(n-2) * (sec x)^2 dx = Integral ((tan x)^2 + 1)^(n/2-1) * (sec x)^2 dx Doing a substitution with: u = tax x du = (sec x)^2 dx = Integral (u^2 + 1)^(n/2-1) * du At this point I'm stuck. Any ...
*November 7, 2007*

**math**

integrate: (x^2 + 1)^k dx
*November 7, 2007*

**Calculus**

integrate: (x^2 + 1)^k dx
*November 6, 2007*

**calculus**

makes perfect sense. Thanks Count!
*November 5, 2007*

**calculus**

How do I derive the integration reduction formula for tangent? Integral of (tan x)^n dx = ... I can do the derivations for sin/cosine, but I'm getting stuck on tan. Thanks!
*November 5, 2007*

**math**

16a - 5b - (-6a - 15b) - (-4b) = 16a - 5b + 6a + 15b + 4b = 22a + 14b
*September 15, 2007*

**Beginning Alegbra**

(2b^3)^3 * 3(b^-4)^2 step #1) = 8b^9 * 3b^-8 step #2) = 24b Explanation: step 1: (2^3 is 8, b^3^3 = b^9, b^-4^2 = b^-8) step 2: Multiply the coefficients (8*3=24). Muliply the b terms: b^9 * b^-8 = b^1 = b
*September 15, 2007*

**math**

Thanks!
*September 15, 2007*

**math**

Integrate: (sin 2x)^3 dx I can see the answer, but how do I do this?
*September 15, 2007*

**math**

Thanks! Actually, the problem was printed in my textbook like that with the equation using the variable y, but with dx rather than dy. This seems to be a textbook error. I wasn't sure whether that was the case or whether I was doing something wrong.
*September 15, 2007*

**math**

Integrate: y/sqrt(2y+1) dx
*September 15, 2007*

**math**

Prove limit as x approaches +infinity of (1 + 1/x)^x = e
*September 8, 2007*

**Math**

The final answer is (x^2 + 5)(x^2 - 4) If you multiply that, you will get your original equation.
*September 4, 2007*

**Math**

(x^2 + 5)(x^2 - 4) If you set y = x^2 and look at the original as: y^2 + y - 20 It should factor easily to (y + 5)(y - 4) which equals: (x^2 + 5)(x^2 - 4)
*September 4, 2007*

**math**

limit (x -> 0): (cos x - 1) / x The answer is 0. I can see this with graphing calculator, but how do I solve algebraically?
*September 4, 2007*

**math**

Assuming there are 26 letters (no distinction among case) and 10 digits: A) 26 * 26 * 10 = 6760 B) 26 * 25 * 10 = 6500 C) 26 * 1 * 10 = 260
*September 4, 2007*

**linear algebra**

Prove that the trace is a similarity invariant. In other words, if two matrices are similar, then they must have the same trace. Got the answer from Wikipedia: tr(AB) = tr(BA) tr(ABC) = tr(CAB) tr(P^-1 * A * P) = tr(P^-1 * P * A) = tr(A)
*July 20, 2007*

**linear algebra**

if: A and B are matrices and A^2 is similar to B^2 Is A guaranteed to be similar to B? ------- Matrix similarity means that the matrices are identical if one of the matrices is converted to another basis. If matrices C and D are similar: C = P^-1 * D * P where P converts from ...
*July 20, 2007*

**Math: Linear Algebra**

Let T1: P1 -> P2 be the linear transformation defined by: T1(c0 + c1*x) = 2c0 - 3c1*x Using the standard bases, B = {1, x} and B' = {1, x, x^2}, what is the transformation matrix [T1]B',B T(c0 + c1*x) = 2c0 - 3c1*x ---> T(1) = 2 T(x) = -3x So, the matrix elements...
*June 9, 2007*

**math**

I'm having a little trouble understanding the difference between the codomain and the range of a function. I'm reading the Wikipedia article on Codomain (I can't post the URL), but it doesn't make sense. I understand what they are saying and it still doesn'...
*January 26, 2007*

**math**

Prove that if A is a symmetric n x n matrix, then A has a set of n orthonormal eigenvectors. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it doesn't prove what I'm ...
*January 19, 2007*

**math**

Prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A. http://ltcconline.net/greenl/courses/203/MatrixOnVectors/symmetricMatrices.htm I've read the entire page and while it's on the correct topic, it doesn't prove ...
*January 19, 2007*

**math**

Show that if x is a nonzero column vector in R^n, then the nxn matrix: A = I - 2/||x||^2 * xx^T is orthogonal. Notation key: ||x|| = norm of x x^T = transpose of x I = identity matrix. Let me try to convince a math student to use "physics" notations that many ...
*January 13, 2007*

**math**

If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column vectors of to be linearly dependent and then show...
*January 8, 2007*

**math**

There is one step in a proof that I don't understand. Could someone please explain? u = any vector in vector space S W = finite dimensional subspace of S with orthonormal basis of vectors {v1, v2, ..., vn} The theorem to prove is: u can be expressed exactly one way as u = ...
*January 5, 2007*

**math**

I'm having trouble understanding one step in a proof of the Cauchy-Schwarz inequality: u = a non-zero vector v = another vector a = <u,u> (so a > 0 by positivity axiom) b = 2<u,v> c = <v,v> (so c >= 0 by positivity axiom) t = any real number 0 <...
*January 4, 2007*

**math**

Factor: x^3 - 3/4x - 1/4 The answer is: (x - 1)(x + 1/2)^2 How do I learn to do that? I'd like to reread an appropriate chapter from an appropriate textbook and do practice problems. It takes experience and practiced eye. Algebra books have chapters on factoring; ask your ...
*January 2, 2007*

**math**

Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 - cos^2 t)= a^2 + b^2 - (a sin t - b cos t)^2...
*December 19, 2006*

**Trigonometry**

There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these standard trig formulas? What are they called...
*December 15, 2006*

**math**

Show that the formula for a line through two points (a1,b1) and (a2,b2) is: y=(b1-b2)/(a1-a2) * x + (a1*b2-a2*b1)/(a1-a2) The slope part looks right. Could someone explain how the y-intercept part makes sense? I would think that the y-intercept is: b1-slope*a1 or b2-slope*a2 ...
*December 6, 2006*

**Math: matrices**

If A and B are both square n x n matrices, If AB = I, prove BA = I Presumably you have to do this without using the usual properties of the inverse of matrices. But we do need to use that if there exists a matrix B such that A B = I then the equation A X = 0 has the unique ...
*December 4, 2006*

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