content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Help: Case analysis
Solve the inequality $\frac{1}{x}<x<1$ by Case Analysis. What is 'Case Analysis' ??
Consider two cases: Case I. $x>0$ and then solve. Case II. $x<0$ annd then sove.
Have you noticed that on MA132 Foundations Exercises 1 there's a typo in Section A? 1 ii) doesn't make sense! Anyway, plato was right... | 4 | [
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0.0390625,
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Question on determinants
July 9th 2010, 05:37 PM
Doktor_Faustus
Question on determinants
Hi guys,
This may have been answered already.
Let A be an nxn matrix and c a non zero scalar. If matrix B is obtained from A by multiplying the elements of a row by c then det (B) = cdet (A).
Show that det (cA... | 5 | [
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0... | 6,801 | 6801 | |
Math Help
January 26th 2011, 11:04 AM #1
Junior Member
Joined
Sep 2009
Posts
39
Confused
number 8 is written as 3 components sum like that, where the first 2 cube amount(a^3+b^3.that means this sum is the lowest), plus 3rd component (C), multiplied by 9, is the lowest.
It is also known, that the fi... | 4 | [
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Plzz Help solving polynomial
March 22nd 2007, 03:32 PM #1
Newbie
Joined
Mar 2007
Posts
7
Plzz Help solving polynomial
I REALLY need help with these problems.. its factoring polynomial equations.. and i kinda understand how to do it BUT these problems are just way over my head would love some help plz her... | 4 | [
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... | 6,803 | 6803 | |
Length of C
March 24th 2008, 10:28 PM #1
Member
Joined
Sep 2007
Posts
94
Length of C
I'm not too bad on this section of the book but this question has got me stumped.
Let C be the curve of intersection of the parabolic cylinder x^2 = 2y and the surface 3z = xy. Find the exact length of C from the or... | 5 | [
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Infinite series : convergence.
July 11th 2008, 01:32 PM
arbolis
Infinite series : convergence.
$\sum_{n=1}^{+\infty} \frac{2^nn!}{n^n}$. I must show whether it converges or not. Using my intuition I think it converges. I tried to use the root test, the only test I think that works.
So I'm stuck when I must f... | 5 | [
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-0.0181... | 6,805 | 6805 | |
Order of this automorphism group
February 9th 2009, 10:55 AM #1
Newbie
Joined
Jan 2009
Posts
12
Order of this automorphism group
Assuming that a field F of order $p^n$ (p prime) contains an element whose minimal polynomial over $Z_{p}$ has degree n, show that the automorphism group of F has order at most... | 5 | [
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... | 6,806 | 6806 | |
Squre root of 1 I guess
November 11th 2009, 08:16 AM
bkbowser
Squre root of 1 I guess
I begin with $x^2+8x=-15$. Since they say to solve by completing the square, I ignore that it can be factored as is and add one to each side. Since $(1/2*8)^2=16$. And get $x^2+8x+16=1$ after
moving the -15 and adding one t... | 4 | [
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double a cubes volume
February 2nd 2009, 12:39 AM #1
Newbie
Joined
Dec 2008
Posts
9
double a cubes volume
I know that to double the volume of a cube multiply each dimension by the cubic root of 2 (about 1.26). I worked it out myself but cannot explain it to my fellow student teachers why it is. Any
h... | 4 | [
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Parametric Graphs and Trig. Identity
March 24th 2008, 03:25 PM #1
Member
Joined
Jan 2008
Posts
91
Parametric Graphs and Trig. Identity
Hey everyone,
I'm asked to graph $x = \cos(\sin(t)), \ \ y = \sin(\sin(t)), \ \ 0 \leq t \leq 2\pi$.
So I graphed it and everything. But now I need to find an e... | 4 | [
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... | 6,809 | 6809 | |
Proving a conjecture in differentiation
November 27th 2012, 04:56 AM
Tutu
Proving a conjecture in differentiation
How do I prove the conjecture that
d^(n)y
______ = k^(n) y
dx^(n)
The n are in the same position like 2 in the second derivative, d2y/dx2. And the n on the RHS is an exponent, but ... | 5 | [
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Math Help
I've got a very simple question yet it has been bugging me for ages, WHY/HOW does 0 permutations/arrangements =1 (0!=1)?
It's simply a matter of definition - and it is a useful definition at that. But if you wanted to be really clever, note that $n! = n(n - 1)!$ $(n - 1)! = \frac{n!}{n}$. By letting $n = 1$... | 4 | [
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easy, easy question
July 14th 2009, 06:06 AM #1
easy, easy question
Can somebody please help me out with this? I had the answer easily the first time, but now my mind is blank:
How many ways are there to seat 10 people, consisting of 5 couples, in a row of seats (10 seats wide) if all couples are to get adja... | 4 | [
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Number of Permutations with k-inversions and with a single clamped value
up vote 5 down vote favorite
2
This question is cross-posted from math.stackexchange because it might be too technical.
Let $S_n$ be the symmetric group. Recall that the number of inversions of a permutation $\sigma\in S_n$ is the number of orde... | 5 | [
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0.01611328125,
0.0269775390625,... | 6,813 | 6813 | |
Math Help
August 23rd 2008, 04:07 PM #1
Newbie
Joined
Aug 2008
Posts
16
differentiate
My maths assignment is due tomorrow, and i dont understand it. i know how to do it using the secant method, but we are not allowed to use it.
I NEED TO DIFFERENTIATE THIS PROBLEM!!!
tan(230/x)
if anyone ... | 5 | [
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Domain/Range, and Inverse
January 16th 2010, 11:06 PM #1
Junior Member
Joined
Sep 2009
From
Russia
Posts
47
Hey guys, I can't figure these out,
(refer to the posted graph)
a. Evaluate f^-1 (1).
b. If If g(x) = x^2 + 1, evaluate (f^-1 o g)(1) and (g o f )(1).
c. Graph y = 1 – f(x + 3)... | 4 | [
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Algebraic Fractions Questions
August 25th 2010, 11:44 PM #1
Algebraic Fractions Questions
Hello everyone.
I have two urgent maths questions related to simplifying and solving algebraic fractions. I will be very gratified if you could pinpoint my mistakes and correct them with clear explanations.
1. $\df... | 4 | [
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A nonlinear problem
September 2nd 2012, 10:01 AM
markel
A nonlinear problem
I have been trying to find a solution to the following problem.
x^(4/3) - x^(-2/3) + c = 0 where -1 < x > 1
I think if I could solve,
s^(-2) - s + c = 0,
I could use substitution to solve the first equation, but I hav... | 4 | [
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Gradient of dot product
February 7th 2013, 11:00 AM
aplrt
Gradient of dot product
Removed this post because I thought it was solved, having to add it again. What is the gradient of acos(u1*u2) (u1 and u2 are the unit vectors)? Apparently the gradient of u1*u2 is u2-(u1*u2)u1
and I know the derivative of acos... | 5 | [
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De Moivre's theorem
June 16th 2008, 11:29 PM
DefilerAlpha
De Moivre's theorem
Question: Use De Moivre's theorem to turn the functikons of the multiple angle into a polynomial in the sine or cosine of the angle theta as indicated.
(a) cos(6theta) in terms of cos(theta)
I have no idea at all where to beg... | 5 | [
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Topic: X/O Grid
Replies: 1 Last Post: Dec 23, 2012 1:17 P... | 4 | [
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... | 6,820 | 6820 | |
John Carmack's Unusual Fast Inverse Square Root (Quake III)
up vote 33 down vote favorite
32
John Carmack has a special function in the Quake III source code which calculates the inverse square root of a float, 4x faster than regular (float)(1.0/sqrt(x)), including a strange 0x5f3759df
constant. See the code below. Ca... | 4 | [
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0.0... | 6,821 | 6821 | |
Another factorising algebraic fraction
December 29th 2008, 05:00 PM #1
Newbie
Joined
Dec 2008
Posts
11
Another factorising algebraic fraction
Simplify:
(x^2 - y^2 - 2x - 2y) X (xy-3y^2)
(x^2 - 2xy - 3y^2) X (y-x+2)
Guide through it will be appreciated, thanks
$\frac{(x^2 - y^2 - 2x - 2y... | 4 | [
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... | 6,822 | 6822 | |
Math Forum: Teacher2Teacher - Q&A #18119
Teacher2Teacher Q&A #18119
Teachers' Lounge Discussion: "Bottoms up" as a method to factor trinomials
... | 4 | [
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0.09423828125,
... | 6,823 | 6823 | |
Double Induction for (1+t)^t > 1+nt
March 10th 2011, 12:16 PM #1
Newbie
Joined
Jan 2011
Posts
8
Double Induction for (1+t)^t > 1+nt
Hi, I have the following problem which I think I have solved correctly (it would be great if you could check it), but I don't know how to answer to "simple" questions about ... | 5 | [
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0.0000734329223632812... | 6,824 | 6824 | |
Existence of the Anti-Derivative.
January 6th 2006, 11:31 AM
ThePerfectHacker
Existence of the Anti-Derivative.
Given a function $f(x)$ defined on interval $[a,b]$. Prove that there must exist a function $F(x)$ with the property that $F'(x)=f(x)$$\forall x\in (a,b)$.
With this we can prove the second fundam... | 4 | [
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0.00909423828125,
... | 6,825 | 6825 | |
Working with external and internal direct sums
October 6th 2010, 11:20 AM #1
Member
Joined
Jan 2010
Posts
232
Working with external and internal direct sums
My information for this one is limited, so I'll need a hand.
Suppose $V$ and $W$ are vector spaces over a field $F$.
Now suppose $W_1$ and... | 4 | [
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-0.0... | 6,826 | 6826 | |
Volume of ellipsoid
Date: 05/22/97 at 22:51:42
From: Anonymous
Subject: Calculation of the volume of ellipse
Dear Dr. Math,
I have forgotten how to calculate the volume of an ellipse. I guess
the volume of ellipse with radius of a and b should be (2/3*pi*a^2*b)
where a is shorter radius and be is longer radius.
Wo... | 4 | [
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-0.00677490234375,
-0.060546875,
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0.00099945068359375,
0.1044921875,
-0.038818359375,
-0.0089111328125,
-0.007354736328125,
-0.01263427734375,
0.0024566650390625,
0.03955078125,
0.01409912109375,
-0.040... | 6,827 | 6827 | |
Proving vector space properties
November 25th 2010, 02:48 PM #1
Senior Member
Joined
Apr 2010
Posts
487
Proving vector space properties
The question:
Prove that the following properties are true for every vector space.
a) 2v = v + v
b) nv = v + ... + v, where there are n terms on the right
... | 4 | [
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0.0234375,
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0.01507568359375,
0.0488... | 6,828 | 6828 | |
Rearranging exponential equation
January 22nd 2013, 01:20 AM
mpylon
Rearranging exponential equation
Hi,
I've tried this on a Maths teacher friend of mine, who is currently stumped, so I hope it classes as 'advanced'. Essentially, I'm trying to rearrange the following equation:
x = y / [A - e^(By)]
... | 5 | [
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... | 6,829 | 6829 | |
Quadratic function (HELP)
March 27th 2013, 12:21 AM #1
Newbie
Joined
Mar 2013
From
Philippines
Posts
5
Could you please help me to answer this question
The Quadratic function which takes the value 41 at x=-2 and the value 20 at x = 5 and is minimized at x = 2 is
y = __x^2 - __x +__
the ... | 4 | [
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0.00958251953125... | 6,830 | 6830 | |
Find the best way to solve this question
June 21st 2009, 03:53 AM
simplependulum
Find the best way to solve this question
Find the equation of the circle which is tangent to the line $3x - y - 1 = 0 ~$ at $A(1,2)~$ and passes through the point $B(5,-2)$
I've got the best way to solve this problem , do you k... | 4 | [
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0.039794921875,
-0.12695312... | 6,831 | 6831 | |
How to calculate root mean std dev given 2 readings?
February 27th 2011, 09:18 AM #1
Member
Joined
Jul 2009
From
London
Posts
109
How to calculate root mean std dev given 2 readings?
Hello
I am at a loss as to how to work out a rsmd (for 52 weeks) given a rsmd for 20 and 32 weeks.
The quest... | 5 | [
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0.01324462890625,
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Every bijection has a two sided inverse
October 25th 2009, 07:05 PM #1
Every bijection has a two sided inverse
I believe I have the same professor G as mathgirl13 and the whole class is struggling.
I need to prove the converse of the above:
If f: X $\longrightarrow$ Y has a two-sided inverse, prove that... | 4 | [
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-0.0... | 6,833 | 6833 | |
Question on integration..finding the area?
April 18th 2010, 01:10 PM
rubbersoul923
Question on integration..finding the area?
y=x^3.
P = (3,27)
PQ is tangent to the curve at P
Picture of graph: http://i42.tinypic.com/fvl8gy.jpg
Find the area of the region enclosed between the curve, PQ and the x... | 5 | [
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0.0732421875,
0.09228515625,
-0.0732421875,
-0... | 6,834 | 6834 | |
Generalized quasi-perfect numbers
up vote 4 down vote favorite
1
A number $n \in \mathbb{N}$ is called quasi-perfect if $\sigma(n) = 2n+1$, where $\sigma$ is the sum of divisors function. It is known that if $n$ is quasi-perfect, then it must be the square of an
odd integer (an oddly beautiful Putnam problem from the ... | 4 | [
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... | 6,835 | 6835 | |
need help with 10 questions
May 6th 2007, 10:41 AM #16
question number 8 doesnt really make sense isnt it suppose to be polar coordinates? what i tried to do for xy=1 is uhmm x and y has to rather equal pi/4 or 5pi/4(cuz its int he 3rd quardnant)
from there i did tan(@)=1 @=pi/4 or 5pi/4 x=rcos x=1 therefore ... | 4 | [
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0.05859375,
0.040283203125,
-0.0673828125,
... | 6,836 | 6836 | |
Minimize Perimeter(S)/Area(S) for S inside the unit square.
up vote 9 down vote favorite
3
This is a very silly question.
For all regions S contained inside the unit square, what is the infimum of the quantity Perimeter(S)/Area(S)? This ratio being considered is not scale invariant, so it is only the constraint of be... | 5 | [
0.059326171875,
0.076171875,
0.0074462890625,
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0.1650390625,
0.02856445312... | 6,837 | 6837 | |
Proof that if A is a subset of P(A), P(A) is a subset of P(P(A))
May 20th 2011, 11:29 PM #1
Newbie
Joined
May 2011
From
Los Angeles
Posts
23
Proof that if A is a subset of P(A), P(A) is a subset of P(P(A))
3.3.4.pdf
Attached is a proof that $A \subseteq \wp{(A)} \rightarrow \wp{(A)} \subseteq \w... | 5 | [
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0.00... | 6,838 | 6838 | |
Evaluate efficiently
September 17th 2011, 08:08 PM
jzellt
Evaluate efficiently
This is a question from my numerical analysis class. I apologize in advance if I'm in the wrong thread...
Evaluate
p(x) = 1 - x^3/3! + x^6/6! - x^9/9! + x^12/12! - x^15/15!
as efficiently as possible. How many multiplicat... | 4 | [
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-0.037353515625,
0.0... | 6,839 | 6839 | |
Diagonalization of Matrix A
October 10th 2011, 07:51 AM #1
Newbie
Joined
Sep 2011
Posts
10
Diagonalization of Matrix A
Hi,
A is a 2 by 2 matrix:
a 1
ab b
i found the eigenvalues λ: 0 and a+b,
the corresponding (column)eigenvectors:
[1/√(1+a^2) -a/√(1+a^2)] & [1/b√(1+(1/b)^2) 1... | 5 | [
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0.0125122070312... | 6,840 | 6840 | |
Brilliant, Nick and geogebra
Hi;
This one is hard ( I am reminded that it is not for some ) but geogebra with a lot of work and some luck makes it easy:
Rhombus, ABCD, has sides of length 12. A circle with center A passes through C. Another circle with center B passes through D. The two circles are tangent to each o... | 4 | [
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-0.0864257... | 6,841 | 6841 | |
Closest Point on a 3D Quadratic Surface
February 8th 2010, 08:22 AM
davesymm
Closest Point on a 3D Quadratic Surface
Hi All, first post, hope I'm obeying all the rules :)
If I have a 3d quadratic surface defined by $ax^2+by^2+cz^2+d=0$ and a point in space defined by the position vector $p={px,py,pz}$ , how... | 5 | [
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0.01422119140625,
-0.02111816406... | 6,842 | 6842 | |
Sorting and Searching
We will now turn our attention to some of the most common problems that arise in computing, those of searching and sorting. In this section we will study searching. We will return to sorting later in
the chapter. Searching is the algorithmic process of finding a particular item in a collection of ... | 5 | [
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0.0255126953125,
... | 6,843 | 6843 | |
Negative root
July 30th 2012, 11:40 AM #1
Junior Member
Joined
Jul 2012
From
Who knows anymore
Posts
27
Negative root
Ok if I enter (-sqrt(3))^2) into my calculator I get the answer 3. Where does the - go?
I know this is basic but...
Re: Negative root
Re: Negative root
I did that. And it ... | 4 | [
-0.035400390625,
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... | 6,844 | 6844 | |
estimating error Taylor polynomials
July 25th 2011, 09:07 PM
CountingPenguins
estimating error Taylor polynomials
I have been asked to do the following:
Suppose that f is a function with the property that | $f^n(x)$| $\leq$3 for all n and for all x on [-1,1].
a. Estimate the error if the Taylor polynomia... | 5 | [
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-0.003997802734375,
... | 6,845 | 6845 | |
Math Help
November 3rd 2008, 08:53 AM #1
Junior Member
Joined
Oct 2008
Posts
29
Polar Form
Hey guys wondered if someone could help me out again, if you let Z=root 3 - i what is Z in polar form?
Then how do I find the real and imaginary parts of (z^7)/8?
$x= r cos(\theta)$ and $y= r sin(\theta)... | 4 | [
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0.006225... | 6,846 | 6846 | |
differential equations with constant coefficients
Lets use Variation of Parameters. I have always preferred that method, but that's me. From the auxiliary equation we get: $m^{2}-9m+20=(m-5)(m-4), \;\ m=5, \;\ m=4$ $y_{c}=C_{1}e^{4x}+C_{2}e^{5x}$
Now use the determinants to find W, W1, W2: $W=\begin{vmatrix}y_{1}&y_{2}... | 5 | [
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0.09765625,
-0.04052734375,
0.08203125,
-... | 6,847 | 6847 | |
Find the cost
September 11th 2012, 05:02 PM #1
Junior Member
Joined
Sep 2012
From
ny
Posts
32
Find the cost
A local photocopying store advertises as follows. " We charge 11 cents per copy for 350 copies or less, 7 cents per copy for each copy over 350 but less than 400 , and 4 cents per copy for each... | 4 | [
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0.01055908203125,
0.0308837890625... | 6,848 | 6848 | |
A hard to crack definite integral
December 22nd 2009, 07:43 AM #1
Newbie
Joined
Nov 2009
Posts
12
A hard to crack definite integral
Please help me solve the following integral
∞
∫ t^2 e^t Cost dt
0
I have been hinted that this integral can be solved using Laplace transform but I don't se... | 5 | [
-0.0712890625,
0.052978515625,
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-0.07373046875,
0.0038299560546875,
-0.0402832031... | 6,849 | 6849 | |
(a^2 -1) / (-a -1) yet another simple one
December 7th 2006, 11:38 AM
shenton
(a^2 -1) / (-a -1) yet another simple one
Simplify:
(a^2 - 1) / (-a - 1)
Answer key: 1 - a
This looks like another simple problem. But I tried AfterShock method of splitting the numerator and find nothing to cancel; I al... | 4 | [
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0.0341796875,
0.0003566741943359375,
-0.009704589843... | 6,850 | 6850 | |
working out if an investment is economic. (question inside)
August 6th 2007, 04:51 PM
kelly_m
working out if an investment is economic. (question inside)
if an investment returned $1000 every year for the first 4 years and returned $1200 yearly after that for 5 years. which after the return becamse $2000 forever... | 5 | [
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0.047119140625,
-0.07275390625,
-... | 6,851 | 6851 | |
Why is Proj of any graded ring isomorphic to Proj of a graded ring generated in degree one?
up vote 11 down vote favorite
3
I have seen it stated that Proj of any graded ring $A$, finitely generated as an $A_0$-algebra, is isomorphic to Proj of a graded ring $B$ such that $B_0 = A_0$ and $B$ is generated as a
$B_0$-al... | 4 | [
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... | 6,852 | 6852 | |
Conductor of monomial forms with trivial nebentypus
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Is it true that the conductor of a holomoprhic or a Maass cusp form with trivial nebentypus corresponding to a two-dimensio... | 5 | [
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-0.0230712890625,
-0.04541015625,
-0.0123291015625,
-0.068359375,... | 6,853 | 6853 | |
urvature
Context
$\infty$-Chern-Weil theory
Ingredients
Connection
Curvature
Theorems
Differential cohomology
Ingredients
Connections on bundles
Higher abelian differential cohomology
Higher nonabelian differential cohomology
Fiber integration
Application to gauge theory
Contents
Idea
The formal notion ... | 4 | [
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-0.01055908203125,
0.0208... | 6,854 | 6854 | |
Exponential Q.
April 20th 2011, 11:45 AM #1
Junior Member
Joined
Mar 2011
Posts
34
Exponential Q.
y =-2f(2x+4) + 0
y =-2f[2(x+2)] + 0
So for the coordinates (x, y) x is x/2 -2
My Q. is, how did the x become x/2 -2 ???
Last edited by reallylongnickname; April 20th 2011 at 12:06 PM.
S... | 4 | [
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0.02099609375,
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-0.112792... | 6,855 | 6855 | |
the area of a triangle in a rectangle
Hi all! Not sure if it's the right part of the forum, but: Rectangle PQRS with Triangle PTV T between Q and R, V between R and S PQ=10m, PS=12m , TR=xm, VS=xm Show that the area of PTV, A square
metres of PTV is given by A(x)=60-6x+1/2x^2
Hello, Eenhoorn! Quote: Rectangle $PQRS$ w... | 4 | [
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0.0179443... | 6,856 | 6856 | |
Saving at the same rate
February 3rd 2010, 03:59 PM
ffezz
Saving at the same rate
Hello, i cant seem to wrap my head around this question
You want to invest 100 dollars every two weeks at 7 percent compounded monthly for the next 40 years. how much money will you have at the end of 40 years?
its driving... | 4 | [
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0.0654296875,
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-0.0... | 6,857 | 6857 | |
I need help in proving " If m and n are each sum of two squares, then their p....
February 5th 2013, 09:13 PM #1
Newbie
Joined
May 2008
Posts
11
I need help in proving " If m and n are each sum of two squares, then their p....
I need to prove " If m and n are each sum of two squares, then their product m... | 4 | [
0.0145263671875,
0.0849609375,
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0.061767578125,
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0.040771484375,
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... | 6,858 | 6858 | |
Nilakantha
Nilakantha Somayaji
Born: 14 June 1444 in Trkkantiyur (near Tirur), Kerala, India
... | 4 | [
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0.06787109375,
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-0.029052734375,
... | 6,859 | 6859 | |
Optimization using Lagrange multipliers
January 18th 2013, 04:12 PM #1
Newbie
Joined
Jan 2013
From
Hell
Posts
15
Thanks
2
Optimization using Lagrange multipliers
Hello. I am trying to teach myself the Lagrangean method for purposes of constrained optimization, and I've had a couple of shots at a ... | 5 | [
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-0.0... | 6,860 | 6860 | |
[SciPy-user] Question about scipy.optimize
Gísli Óttarsson gislio@gmail....
Fri Nov 21 06:10:41 CST 2008
Hello all.
I am a relatively new user of python and scipy and I have been trying
out scipy's optimization facilities. I am using scipy version 0.6.0,
as distributed with Ubuntu 8.04.
My exploration has centered... | 5 | [
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0.021240234375,
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0.06982421875,
-0.052490234375,
-0.... | 6,861 | 6861 | |
Find a point on a circle
August 27th 2009, 05:12 PM #1
Newbie
Joined
Aug 2009
Posts
2
Find a point on a circle
Refer to the picture below, my problem/questions will follow
I have two points, one is the center of the circle and one is a point on the circumference of the circle.
What I need to ... | 4 | [
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0.083984375,
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0.0179443359375,
-0.04541015625,
0.0170898... | 6,862 | 6862 | |
Convergent in Continued fraction
May 7th 2008, 07:04 PM #1
Junior Member
Joined
Mar 2008
Posts
33
Convergent in Continued fraction
If $\frac{p_k}{q_k}$ is the $k$th convergent of $[a_0;a_1, ... ,a_n]$ and $a_0 >0$, show
$\frac{q_k}{q_{k-1}} = [a_k:a_{k-1}, ... , a_2, a_1]$.
I think i have to us... | 5 | [
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0.0791015625,
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0.072265625,
-0.006591796875,
-0.0... | 6,863 | 6863 | |
solving trigonometric equation
September 6th 2008, 12:05 PM #1
Junior Member
Joined
Nov 2006
Posts
41
solving trigonometric equation
solve tanx+secx=2cosx
(sinx/cosx)+ (1/cosx)=2cosx
(sinx+1)/cosx =2cosx
multiplying both sides by cosx
sinx + 1 =2cos^2x
sinx+1 = 2(1-sin^2x)
2sin^2x... | 4 | [
-0.038330078125,
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0.06689453125,
0.07470703125,
-0.00014495849609375,
-0.0303955078125,
-0.006286621... | 6,864 | 6864 | |
Math Help
$\int \frac{\sin^2(x)}{\cos(x)} dx$ $= \int \frac{\sin^2(x)}{\cos^2(x)} \cos(x) dx$ $= \int \frac{\sin^2(x)}{1 - \sin^2(x)} \cos(x) dx$ $= \int \frac{u^2}{1 - u^2} du$ (where $u = \sin(x)$). $= \int
\frac{u^2 - 1+1}{1 - u^2} du$ $= \int \left( \frac{u^2 - 1}{1 - u^2} + \frac{1}{1 - u^2} \right) du$ $= \int (... | 5 | [
-0.02197265625,
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-0.06201171875,
0.0016326904296875,
-0.0625,
-0.0908203125,
0.0649414062... | 6,865 | 6865 | |
GMAT Tip: What Geometry Questions Really Measure
This tip on improving your GMAT score was provided by Brian Galvin at Veritas Prep.
When was the last time you used the Pythagorean Theorem in your job? Unless you’re a math teacher or a pyramid architect, the answer is quite likely “never.” So why does the GMAT test ge... | 4 | [
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0.0615234375,
0.064453125,
0.018310546875,
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0.00762939453125,
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0.05126953125,
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-0.0458984375,
0.0107421875,
-0.026977539... | 6,866 | 6866 | |
Divisors again
November 20th 2010, 09:18 AM #1
Newbie
Joined
Nov 2010
Posts
12
Divisors again
We have:
z = (2^(mn) - 1)/[(2^m - 1)(2^n - 1)], where (2^m - 1) and (2^n - 1) are prime numbers.
Prove that (2^m - 1) and (2^n - 1) are not the only prime factors of z.
I tried to solve it writing z... | 5 | [
0.00830078125,
-0.00946044921875,
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0.049560546875,
0.130859375,
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0.047119140625,
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0.055419921875,
0.0277099609375,
0.09326171875,
0.0164794921875,
0.00273132324218... | 6,867 | 6867 | |
Fourier Transform
ImageShack - Hosting :: questionyw0.jpg I was asked to find the fourier transform of x(n). Could someone explain whats happening in this answer? Thanks
I presume the problem is in simplifying $X(\omega)$? $X(\omega) = \sum_{n = -4}^{\infty} \left ( \frac{1}{4} \right )^ne^{-j \omega n}$ Define $m = n... | 5 | [
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0.060546875,
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0.07080078125,
-0.03662109375,
-0.011840820... | 6,868 | 6868 | |
determine the current flowing thru an element
January 6th 2011, 11:00 AM
bigwave
determine the current flowing thru an element
determine the current flowing thru an element is the charge flow is given by:
(a) $q(t) = (3t+8) mC$
assume the way to do this is just
$<br /> i= \frac{dq}{qt}=\frac{d}{dt... | 5 | [
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0.0712890625,
-0.07275390625,
0.031... | 6,869 | 6869 | |
Quadratic Equations
June 15th 2009, 06:59 AM #1
Junior Member
Joined
May 2009
Posts
68
Quadratic Equations
I need help answering this using Quadratic Equations. Please, also explain in detail what you did, so I KNOW how to do it for next time.
The time required for a train to make a 175 km trip is 1... | 4 | [
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-0.0378417968... | 6,870 | 6870 | |
Find the Limit
October 4th 2009, 07:48 PM #1
Junior Member
Joined
Sep 2009
Posts
32
Find the Limit
Hey all, sorry for bugging you again but I have another question...
I've been doing them right so far, so I'm confused as to why this one's supposedly wrong.
The question is: Evaluate the limit fo... | 4 | [
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-0.063476562... | 6,871 | 6871 | |
A parametrization of Heronian triangles
up vote 8 down vote favorite
1
Let $a,b,c$ be integers which are the sides of a triangle with integral area, a so called Heronian triangle. This website attributes to Gauss the result that there must then exist integers $m,n,p,q$
such that
$a = mn(p^2+q^2)$
$b = (mp)^2+(nq)^2$... | 5 | [
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0.0021820068359375,
-0.02... | 6,872 | 6872 | |
bearing problems...please help as soon as possible...
November 8th 2007, 05:51 PM #1
Member
Joined
Aug 2007
Posts
182
bearing problems...please help as soon as possible...
I have no idea how to work these problems...there are four of them...I have the answer for each of them (for the back of the book)...... | 4 | [
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-0.048339... | 6,873 | 6873 | |
Exponential Graph help? (Word Problem) 2
March 6th 2009, 11:20 AM #1
Junior Member
Joined
Feb 2009
From
Fiery pits of confusion
Posts
36
Exponential Graph help? (Word Problem) 2
A shipping company owns a fleet of heavy trucks if the purchase price of each truck is $245,000 nad its value depreciates b... | 4 | [
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-0.0947265... | 6,874 | 6874 | |
Math Help
November 3rd 2008, 03:34 PM #1
Junior Member
Joined
Nov 2007
Posts
32
isomorphism
Let y be an integer, which is not a square of another integer.
How do I prove that Q[sqrt(y)] = {a + bsqrt(y) : a,b in Q} is isomorphic to Q[x]/(x^2 - y) where Q is the set of rational numbers?
Thanks f... | 5 | [
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0.078125,
0.0184326171875,
-0.0... | 6,875 | 6875 | |
word problem
March 15th 2009, 01:14 PM
math1645
word problem
the speed of light is 1.863 x 10^5 miles per second.
assume 1 year is 365 days. write an expression to convert speed of light from miles per second to miles per year
make a table that shows the distance light travels in 1, 10, 100, 1000, 1000... | 4 | [
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0.00311279296875,
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0.078125,
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0.05517578125,
-0.016845703125,
-0.00... | 6,876 | 6876 | |
Number of perturbations of the Jordan form
up vote 3 down vote favorite
4
I am looking for information about the number of Jordan forms that can be obtained from a given Jordan form of a small perturbation.
For example, if a Jordan form consists of a single cell 2x2 $$J=\begin{pmatrix} \lambda_0 &1\\\ 0&\lambda_0\end... | 4 | [
0.01043701171875,
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0.00176239013671875,
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0.048095703125,
0.021484375,
0.011962890625,
-0.04345703125,
-0.0208740234375,
0.00933837890625,
-0.0303955078125... | 6,877 | 6877 | |
Angle of elevation problem
July 12th 2012, 03:52 AM #1
Newbie
Joined
Jul 2010
Posts
18
Angle of elevation problem
The angle of elevation at the top of a building at point A (on level ground) is 62 degrees. At a point 120m away from A, the angle of elevation is found to be 35 degrees. Find the height of t... | 4 | [
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-0.0244140625,
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0.050537109375,
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0.04345703125,
0.058837890625,
0.04736328125,
-0.09326171875,
0.005157470703125,
0.... | 6,878 | 6878 | |
Substitution Rule Integral Questions
July 15th 2008, 10:40 PM
SportfreundeKeaneKent
Substitution Rule Integral Questions
I have a few questions I'm unsure about, the first one is a indefinite integral:
1.) Find: antiderivative sqrt(1+lnx)*lnx*1/x dx
I got 2u^(5/2)/5 - 2u^(3/2)/3 for this one where u=1+... | 5 | [
0.025634765625,
-0.04638671875,
0.140625,
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0.0289306640625,
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0.06201171875,
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0.033203125,
-0.064453125,
0.0174560546875,
0.0079345703125,
-0.05078125,
-0.089... | 6,879 | 6879 | |
Fixed fields for Galois groups
April 6th 2006, 06:43 AM #1
Junior Member
Joined
Mar 2006
Posts
43
Fixed fields for Galois groups
I need some help with a Galois problem.
I need to find the splitting field for
$x^7 - 1$ over Q, then find its Galois group, then the subgroups of the Galois group, an... | 5 | [
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-0.0035858154296875,
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0.054443359375,
-0.1484375,
-0... | 6,880 | 6880 | |
Cow word problem
May 25th 2008, 11:54 AM
annie3993
Cow word problem
A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which
gives more milk in a day, a black or brown co... | 4 | [
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0.0390625,
-0.010009765625,
-0.0115... | 6,881 | 6881 | |
Groups, subgroups and indexes
January 19th 2011, 09:41 PM #1
Junior Member
Joined
Oct 2010
From
Zulu-5
Posts
60
Groups, subgroups and indexes
Here is a problem I think I have a solution for, I am just not 100% sure on one of the detail
Let $G$ be a group that does not have a subgroup of index 2.... | 5 | [
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Lead-Lag Frequency Response
One of the most common representations of dynamic coupling between two variables x and y is the "lead-lag" transfer function, which is based on the ordinary first-order differential equation
where a[0], a[1], b[0], and b[1] are constants. This coupling is symmetrical, so there is no implic... | 4 | [
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Abelian Groups
Associated Topics || Dr. Math Home || Search Dr. Math
Abelian Groups
Date: 05/15/2000 at 20:17:12
... | 4 | [
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Ring ElectronRight hand rule
Ring electrons
john.erich.ebner@gmail.com
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"Weighted" sum of divisor function
August 18th 2013, 04:21 PM #1
Newbie
Joined
Aug 2012
From
Florence
Posts
2
"Weighted" sum of divisor function
Hi, I am trying to solve a problem about the divisor function. Let us call d(n) the classical divisor function, i.e. d(n) is the number of divisors of the i... | 4 | [
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Normal random variable question
I really do not understand this question. Could anyone point me in the right direction? Thanks
Here is a start: (a) The cdf of Y is: $\displaystyle G(y) = \Pr(Y \leq y) = \Pr(aX + b \leq y) = \Pr\left(X \leq \frac{y - b}{a}\right)$ (assuming a > 0) $\displaystyle = \int_{-\infty}^{\frac... | 5 | [
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Finding the second derivative of a function
November 13th 2009, 06:34 PM
Archduke01
Finding the second derivative of a function
$y = (x^3 - 2x)^4$
$y' = 4(x^3 - 2x)^3 (3x^2 - 2)$
$y'' = ?$
I'm having difficulty proceeding from there to get the second derivative. The answer is $12(x^3 - 2x)^2 (11x^... | 5 | [
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Solving system of ODE's
November 29th 2009, 04:45 PM
robotENGR
Solving system of ODE's
I have a 2 seperate systems i am trying to solve but don't seem to know any technique that will solve this problem (the other is similar in nature to this one)
Problem:
$\frac{dC_{0}}{dt} = -\frac{3}{8} C_{0}^3 -\fra... | 5 | [
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Zack wishes to accumulate...
September 9th 2009, 10:49 AM #1
Junior Member
Joined
Sep 2009
Posts
36
Zack wishes to accumulate...
Zack wishes to accumulate $50,000 in a fund at the end of 20 years. If he deposits $100 + x in the fund at the end of every 3 months for the first 10 years and $100 in the fund... | 5 | [
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Some more factorial word problems
August 8th 2009, 08:54 PM #1
Newbie
Joined
Jul 2009
Posts
6
Some more factorial word problems
I find these a bit more complicated from the problem in my previous post. I can't seem to apply that logic to these problems.
1. How many 3-digit positive integers are odd ... | 4 | [
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college physics
Posted by Adam on Friday, May 14, 2010 at 2:58pm.
A space shuttle is in a circular orbit at a height of 250km, where the acceleration of Earth’s gravity is 93% of its surface value. What is the period of its orbit?
• college physics - tchrwill, Sunday, May 16, 2010 at 10:02am
The period of a bo... | 5 | [
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The Universal Properties of Map, Fold, and Filter
A lot of people who like functional programming often give the reason that the functional style is simply more elegant than the imperative style. When compelled or inspired to explain (as I did in my
old post, How I Learned to Love Functional Programming), they often p... | 4 | [
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factoring help
September 25th 2013, 06:27 PM
Jonroberts74
factoring help
I am working on being better at factor but I could use some help.
this (6-3x)^4 + x[4(6-3x)^3(-3)] factors to (6-3x)^3[(6-3x)-12x] to 3(6-3x)^3(2-5x)
looking for some help on how this is done. thank you.
September 25th 2013, 06:5... | 4 | [
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Cayley-Hamilton Theorem
Date: 04/19/99 at 13:03:32
From: Sarah Mastura
Subject: The Cayley-Hamilton Theorem - a proof
I was wondering if you could possibly send me a proof of the Cayley-
Hamilton Theorem, or if not point me in the right sort of direction
of one. The proof in my notes is quite incomplete and I can't,... | 5 | [
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Find the radius of convergence and the interval of conv...
July 18th 2013, 06:33 PM #1
Newbie
Joined
Jul 2013
From
California
Posts
1
Find the radius of convergence and the interval of conv...
convergence, also indicating the type of convergence, either absolutely or conditionally.
Σ [n=2 to n=i... | 5 | [
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[SOLVED] factorial manipulation
December 17th 2008, 03:48 PM #1
Newbie
Joined
Dec 2008
Posts
4
[SOLVED] factorial manipulation
hi,
I'm trying to do a proof by induction showing that (2x+1)!/(2^x (x)!) = ((2x+1)(2x-1)!)/(2^(x-1) (x-1)!) , but i don't quite remember factorial manipulation. I can recall... | 5 | [
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Proving if a function is odd or even
January 6th 2011, 11:35 AM #1
Junior Member
Joined
Nov 2010
Posts
58
Proving if a function is odd or even
A function f is even if: f(-x) = f(x)
A function f is off if: f(-x) = -f(x)
a) Suppose that f and g are both odd. Prove that y = f(x)g(x) is even.
b)... | 4 | [
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Polar coords and differentiation
October 26th 2008, 01:12 PM #1
Newbie
Joined
Oct 2008
Posts
1
Polar coords and differentiation
Hey guys, got a polar coordinates question Im stuck on.
A particle is moving with constant velocity $\vec{v} = u\hat{i}$ along the line $y = 2$. Describe $\vec{v}$ in polar... | 5 | [
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