content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Geometric Proof of Area of Triangle Formula
Date: 04/30/2008 at 01:01:17
From: Gerry
Subject: Proof of Area of Triangle Formula
I'm trying to prove the formula that the area of a triangle with co-
ordinates (0,0),(x1,y1) and (x2,y2) is 1/2(x1y2 - x2y1) without using
determinants. Am sure I recall an elegant way to d... | 4 | [
-0.0098876953125,
-0.01416015625,
0.02685546875,
-0.05224609375,
0.060791015625,
-0.09326171875,
-0.0732421875,
0.045166015625,
-0.072265625,
-0.0106201171875,
-0.0169677734375,
-0.0203857421875,
0.03125,
0.09619140625,
0.0634765625,
0.1337890625,
-0.042236328125,
0.004241943359375... | 38,000 | 38000 | |
integration
need a little help with this problem: $\int_{0}^{\pi/2} \dfrac{\sin\theta}{1+\cos^{2}\theta} d\theta$
The evaluation at the limits is simple once you find the anti-derivative. Thus, I will find the anti-derivative and let you do the evaluation. We have, $\int \frac{\sin x}{1+\cos^2 x} dx$ Let $u=\cos
x$ th... | 5 | [
-0.0113525390625,
0.038818359375,
0.09765625,
0.059814453125,
0.05029296875,
-0.0306396484375,
-0.024169921875,
0.0133056640625,
-0.06640625,
0.004852294921875,
0.051513671875,
-0.07568359375,
-0.0361328125,
-0.0118408203125,
-0.109375,
-0.0194091796875,
0.08935546875,
0.0169677734... | 38,001 | 38001 | |
Comparing Numbers in Different Bases
Date: 07/28/99 at 00:40:19
From: Agnes Morrison
Subject: Bases other than 10
If I am given a number in base 4 and asked whether it is bigger or
smaller than another number in another base, should I always convert
both to base 10 to compare, or is there an easier way?
Thank you.
... | 4 | [
0.06396484375,
0.04833984375,
-0.03125,
-0.072265625,
-0.022216796875,
-0.00018596649169921875,
-0.11865234375,
0.09033203125,
-0.033447265625,
0.0036163330078125,
-0.046875,
-0.0235595703125,
-0.00347900390625,
0.0294189453125,
0.000644683837890625,
0.0277099609375,
0.01165771484375... | 38,002 | 38002 | |
log and natural log
February 13th 2010, 11:27 AM #1
Newbie
Joined
Jan 2010
Posts
9
log and natural log
i have no idea if im doing this correct
400 = (1 - e^-.2t
ln400 = -.2tln(500(1- e)
.2t = ln(500(1 - e)
ln(400)
im stuck here, any help would be great
im trying to solve for T ... | 4 | [
-0.055908203125,
0.06982421875,
0.09716796875,
-0.034423828125,
0.023681640625,
-0.13671875,
0.019287109375,
0.1025390625,
0.0255126953125,
0.0791015625,
0.08203125,
-0.10498046875,
0.051513671875,
0.06689453125,
-0.031982421875,
0.0223388671875,
-0.0634765625,
-0.053466796875,
-... | 38,003 | 38003 | |
Homework Help
Posted by j on Tuesday, August 14, 2007 at 2:20am.
solve the system by addition:
-5x-9y = -5
x+5y=-15
I've tried this one over and over, but I can't seem to get the right answer. I don't even really know where to start. each time i try to do it, i go about it a little differently and i'm completely
lo... | 4 | [
-0.14453125,
0.006622314453125,
0.05908203125,
-0.03955078125,
0.09033203125,
-0.004364013671875,
0.0250244140625,
-0.0108642578125,
-0.040771484375,
0.005462646484375,
0.08935546875,
0.04296875,
0.1015625,
0.0076904296875,
-0.014404296875,
0.0830078125,
-0.0274658203125,
-0.003936... | 38,004 | 38004 | |
quick question on product rule and equality rule for logs
October 19th 2011, 11:29 AM
RYdis
quick question on product rule and equality rule for logs
so I have an equation:
ln (2x+1) + ln(x-2) -2lnx = 0
so to be able to use product rule I added the 2lnx and cancelled out for equality rule
ln(2x+1)... | 4 | [
-0.051025390625,
-0.0240478515625,
0.11181640625,
0.00096893310546875,
0.033935546875,
-0.00142669677734375,
0.03466796875,
0.00008916854858398438,
0.0137939453125,
0.04931640625,
0.10009765625,
-0.068359375,
0.039306640625,
0.01611328125,
0.0296630859375,
0.04443359375,
-0.141601562... | 38,005 | 38005 | |
Spivak's Calculus Question
July 11th 2011, 07:35 AM #1
Member
Joined
Mar 2010
Posts
78
Spivak's Calculus Question
Prove that if $|x - x_0| < e/2$ and $|y - y_0| < e/2$, then
$|(x + y) - (x_0 + y_0)| < e$,
$|(x - y) - (x_0 - y_0)| < e$.
I'm not looking for a complete solution, just a hint as... | 4 | [
-0.034912109375,
0.035400390625,
0.04736328125,
-0.04345703125,
0.0098876953125,
0.0181884765625,
0.02978515625,
0.05224609375,
-0.10791015625,
-0.0157470703125,
0.0157470703125,
0.013671875,
-0.02880859375,
0.0003681182861328125,
0.05908203125,
0.1064453125,
0.0244140625,
-0.00476... | 38,006 | 38006 | |
finding surface area and volume
May 20th 2009, 08:08 PM #1
Newbie
Joined
Mar 2009
Posts
14
finding surface area and volume
hI,
i am looking for some help!
I need to figure out the surface area of a 2cm cube, with dimensions length, width and height all 2cm. My answer is 0.0012 m squared... Is thi... | 4 | [
0.07421875,
0.023193359375,
-0.0128173828125,
-0.01031494140625,
-0.044677734375,
-0.0263671875,
-0.0137939453125,
0.1328125,
-0.038330078125,
-0.052978515625,
-0.050048828125,
-0.0206298828125,
-0.0089111328125,
0.0595703125,
-0.0035400390625,
0.01165771484375,
0.00848388671875,
0... | 38,007 | 38007 | |
Automorphism
August 11th 2010, 10:25 PM #1
Member
Joined
Dec 2009
Posts
224
Automorphism
Let $G = Aut(\mathbb{Z}_{315})$ and let $n$ be the order of the largest cyclic subgroup of G. What is $n$? And what would be the number of distinct cyclic subgroups of order $n$ in $G$?
You should start by think... | 5 | [
-0.046142578125,
0.0322265625,
-0.021728515625,
-0.087890625,
-0.01031494140625,
-0.032958984375,
0.06201171875,
-0.03515625,
-0.054443359375,
-0.05908203125,
0.007781982421875,
-0.0169677734375,
0.016845703125,
-0.07568359375,
-0.091796875,
0.016357421875,
-0.037353515625,
-0.0490... | 38,008 | 38008 | |
Partial Fraction Quadratic Factor Integration
May 16th 2008, 06:33 PM #1
Newbie
Joined
May 2008
Posts
11
Partial Fraction Quadratic Factor Integration
I think I understand the basic idea behind partial fractions but I am stuck on a couple of problems with quadratic factors. I think if I saw one done I co... | 5 | [
0.0155029296875,
-0.004791259765625,
0.059326171875,
0.00970458984375,
0.033203125,
0.05712890625,
-0.10400390625,
-0.01483154296875,
-0.06884765625,
-0.01202392578125,
0.0673828125,
0.01239013671875,
-0.0247802734375,
0.031005859375,
0.0185546875,
0.0220947265625,
0.08642578125,
0... | 38,009 | 38009 | |
Tricky Circles
April 29th 2005, 01:45 PM
Dylan
Tricky Circles
Hi Guys. I'm hoping there is someone out there who ca help me with question 4 of this problem.
The rest I have managed to solve, however any advice that anyone may have would be greatly appreciated.
Thanks in advance
Dylan Eave
April 29... | 5 | [
-0.06689453125,
0.03564453125,
-0.06884765625,
-0.0228271484375,
0.0196533203125,
-0.03271484375,
0.05029296875,
0.059326171875,
-0.0198974609375,
-0.04541015625,
-0.0118408203125,
-0.036865234375,
0.02392578125,
0.0576171875,
0.0263671875,
-0.00830078125,
-0.0947265625,
-0.0184326... | 38,010 | 38010 | |
Hecke operators acting as correspondences?
up vote 11 down vote favorite
6
This question is inspired by Relation between Hecke Operator and Hecke Algebra
I remember having heard of yet another way of looking at Hecke operators acting on the spaces of modular forms for classical congruence subgroups of $SL_2(\mathbf{Z... | 4 | [
-0.09814453125,
-0.00927734375,
-0.020751953125,
0.03173828125,
-0.0267333984375,
0.0296630859375,
-0.0186767578125,
0.017822265625,
-0.0235595703125,
-0.10888671875,
0.08544921875,
-0.005462646484375,
-0.009521484375,
-0.056396484375,
-0.0306396484375,
0.01611328125,
-0.064453125,
... | 38,011 | 38011 | |
Euler's totient function
Talk2
872pages on
this wiki
Euler's totient function, first found by Leonhard Euler, is a function that yields the number of totatives of an integer greater than 1. It is related to number theory. Note that a totative is a
relative prime less than or equal to a number. For instance, 15 i... | 5 | [
-0.0284423828125,
-0.06982421875,
0.01129150390625,
-0.02587890625,
0.05078125,
0.01092529296875,
0.0888671875,
0.12890625,
0.036865234375,
0.0089111328125,
-0.0213623046875,
0.056396484375,
0.051513671875,
0.0279541015625,
-0.068359375,
-0.04345703125,
0.0047607421875,
-0.06445312... | 38,012 | 38012 | |
Stuck on strange conditional probability question
March 7th 2011, 12:18 AM
angypangy
Stuck on strange conditional probability question
Hi
I have studied conditional probability and can do most of the questions. But this one has me stumped.
A school is divided into 2 parts: Upper school, 400 boys and 20... | 4 | [
0.04150390625,
0.0211181640625,
0.07861328125,
-0.053466796875,
0.00897216796875,
-0.0498046875,
0.04150390625,
0.0625,
-0.0301513671875,
0.0849609375,
0.0859375,
-0.0218505859375,
0.0791015625,
-0.0120849609375,
0.07373046875,
0.0810546875,
0.0267333984375,
-0.068359375,
-0.0668... | 38,013 | 38013 | |
Are these empirical discoveries about the Serre Swinnerton-Dyer ring of prime level modular power series actual theorems?
up vote 5 down vote favorite
In this question Joel Bellaiche constructed an algebra, M, of modular forms for gamma_0 (N) in finite characteristic (which he called p, but I'll call ell) and asked to... | 4 | [
-0.1376953125,
-0.04248046875,
0.007293701171875,
0.07470703125,
0.06396484375,
0.01422119140625,
0.03369140625,
0.05126953125,
-0.02978515625,
-0.07666015625,
0.032470703125,
0.0274658203125,
-0.01312255859375,
-0.0810546875,
-0.0264892578125,
-0.005126953125,
-0.045166015625,
-0.... | 38,014 | 38014 | |
Solving a 6x6 System of Equations
Date: 03/24/98 at 13:55:48
From: Jason Goodspeed
Subject: 6x6 equations
Could you please look at the following equation - is there a Cramer's
rule for a 6x6 equation?
a + b - 2c + d + 3e - f = 4
2a - b + c + 2d + e - 3f = 20
a + 3b - 3c - d + 2e + f = ... | 5 | [
-0.095703125,
-0.01031494140625,
-0.0244140625,
-0.07373046875,
0.0654296875,
0.1396484375,
-0.043701171875,
0.004608154296875,
-0.06982421875,
0.107421875,
0.059814453125,
-0.09228515625,
-0.00099945068359375,
-0.0322265625,
-0.0198974609375,
0.00823974609375,
-0.09033203125,
-0.0... | 38,015 | 38015 | |
A question about bisecting plane convex sets
up vote 2 down vote favorite
Suppose that S is a compact convex subset of the Euclidean plane E whose interior is non-empty. If p is a point of E such that every straight line in E which passes through p bisects the area of S,
is S necessarily centro-symmetric with respect ... | 5 | [
-0.0172119140625,
0.050537109375,
-0.005859375,
-0.06396484375,
0.049072265625,
0.00445556640625,
0.12255859375,
0.059326171875,
0.046875,
0.0250244140625,
0.0115966796875,
0.010986328125,
-0.02734375,
-0.019287109375,
0.0322265625,
-0.05908203125,
0.00081634521484375,
-0.046142578... | 38,016 | 38016 | |
Solving systems of linear equations by elimination (word problem)
September 19th 2008, 12:51 AM #1
Junior Member
Joined
Feb 2008
From
NWT, Canada
Posts
51
Fred flew from Point A to Point B at an average speed of 500km/h, and from Point B to Point C at an average speed of 600km/h. The total time in the... | 4 | [
0.0274658203125,
0.0264892578125,
-0.05419921875,
-0.03564453125,
0.0203857421875,
0.0128173828125,
-0.009765625,
0.01397705078125,
-0.08935546875,
0.048095703125,
0.059814453125,
-0.04052734375,
0.00341796875,
-0.004638671875,
0.0027008056640625,
0.11572265625,
-0.057373046875,
-0... | 38,017 | 38017 | |
Picard group of a very ample divisor in a smooth variety of dimension >3
up vote 1 down vote favorite
2
Let $X$ be a smooth complex projective variety, $\dim(X)>3$ and $D$ be a very ample possibly reducible divisor on $X$. Is it true that $\textrm{Pic}(X)\cong \textrm{Pic}(D)$? If not, what would be a
reasonable condi... | 5 | [
-0.054443359375,
-0.0201416015625,
0.0030975341796875,
-0.0267333984375,
0.111328125,
-0.0498046875,
0.055908203125,
0.03515625,
-0.04248046875,
-0.014892578125,
0.1298828125,
-0.02734375,
-0.002960205078125,
0.042236328125,
0.06591796875,
0.010986328125,
-0.01513671875,
-0.0087280... | 38,018 | 38018 | |
Solving Equations to Find Profit
Date: 8/10/96 at 4:22:5
From: Anonymous
Subject: Solving Two Equations to Find the Profit of...
You bought A and B for 40,000 Won. You sold A for a 0.3 percent
profit, and sold B at a 0.2 percent discount. You profited 5000 Won.
What was A's original price?
*Won-Korean money measure... | 4 | [
-0.035888671875,
0.1083984375,
-0.0390625,
-0.03076171875,
-0.0654296875,
0.00003409385681152344,
0.017578125,
0.06005859375,
0.035888671875,
0.06640625,
0.0159912109375,
-0.06396484375,
0.0673828125,
0.034423828125,
0.044921875,
0.1298828125,
-0.08203125,
0.036865234375,
-0.1308... | 38,019 | 38019 | |
Max Noether's AF+BG theorem
up vote 1 down vote favorite
I'm looking for an example of the following situation, related to Max Noether's AF+BG Theorem (see Bill Fulton's book on algebraic curves, page 61, at http://www.math.lsa.umich.edu/~wfulton/
CurveBook.pdf).
Fulton motivates the AF+BG Theorem by saying that if $... | 5 | [
-0.08935546875,
-0.05810546875,
-0.004180908203125,
0.01092529296875,
-0.08056640625,
0.050048828125,
0.01361083984375,
-0.005218505859375,
-0.07470703125,
0.004302978515625,
-0.02197265625,
0.03271484375,
0.02783203125,
-0.0108642578125,
0.00970458984375,
0.12890625,
-0.06982421875,... | 38,020 | 38020 | |
Compact Sets.
December 10th 2011, 07:34 PM #1
Junior Member
Joined
Nov 2011
Posts
45
Compact Sets.
Let $(X,d_{x})$ be a continuous function. Suppose that $K\subset X$ is compact and that $A\subset\ \mathbb{R}^k$ is compact.
Prove that $f(K)\bigcap A\ =\ \emptyset$ implies dist $(f(K),A)>0$
It's ... | 4 | [
-0.007354736328125,
0.09130859375,
-0.052001953125,
-0.0106201171875,
-0.00482177734375,
0.0615234375,
0.0927734375,
-0.01336669921875,
0.028564453125,
0.076171875,
0.043701171875,
0.0260009765625,
0.01416015625,
0.027099609375,
0.04638671875,
-0.035888671875,
0.0033111572265625,
-... | 38,021 | 38021 | |
vwap13
How to reduce the risk of executing VWAP orders?
- New approach to modeling intraday volume
Jedrzej Bialkowski*, Serge Darolles **, GaΓ«lle Le Fol***
November 27, 2006
... | 4 | [
-0.0064697265625,
0.06591796875,
0.0299072265625,
0.0233154296875,
-0.04833984375,
0.0167236328125,
-0.046630859375,
0.041259765625,
0.032470703125,
0.0029144287109375,
-0.01611328125,
0.0140380859375,
-0.03564453125,
0.038330078125,
0.0108642578125,
-0.06787109375,
0.01141357421875,... | 38,022 | 38022 | |
calculating angle
hello having position of 3 point i want to calculate the angle between them
If in 2D only, plot the 3 points on the same rectangular axes, so that you'd know how to get the angle between the two rays. For simplicity, put the corner of the angle on the origin (0,0). Use the
slopes of the rays. The slo... | 4 | [
-0.078125,
-0.059814453125,
-0.11572265625,
-0.0810546875,
-0.0177001953125,
0.002960205078125,
0.0147705078125,
0.041015625,
0.033203125,
0.01092529296875,
0.0927734375,
-0.0732421875,
0.0011138916015625,
0.0439453125,
0.0595703125,
0.10595703125,
-0.08740234375,
0.03564453125,
... | 38,023 | 38023 | |
Help my life is in game
August 18th 2010, 06:19 AM #1
Newbie
Joined
Aug 2010
Posts
2
Help my life is in game
I need help with this (i know its easy but i dont know how to resolve this problem )
cosalfa = 5/13 sin alfa is - , cos alfa is + , tg alfa is - and ctg alfa is -
I need to find a) sin(60... | 4 | [
-0.061279296875,
0.11572265625,
-0.0751953125,
-0.06005859375,
-0.05224609375,
0.07421875,
-0.00604248046875,
0.0693359375,
-0.02734375,
0.01287841796875,
0.06591796875,
-0.059814453125,
0.0306396484375,
-0.00433349609375,
0.05712890625,
0.0111083984375,
-0.09765625,
-0.03002929687... | 38,024 | 38024 | |
Generating Random Numbers In Order
Suppose we wish to generate n independent random numbers, uniformly
distributed between 0 and 1, and sort them into increasing order.
To avoid the sorting process, can we simply generate the random
numbers in order of size?
For a geometrical approach to this problem, consider first ... | 4 | [
-0.028076171875,
-0.042236328125,
0.006134033203125,
-0.06689453125,
-0.0087890625,
-0.050048828125,
-0.0098876953125,
-0.0771484375,
0.01904296875,
-0.0286865234375,
-0.052490234375,
0.06689453125,
0.1328125,
0.00653076171875,
-0.021240234375,
-0.0303955078125,
0.050537109375,
-0.... | 38,025 | 38025 | |
Math Forum: Ask Dr. Math FAQ: Fractions, Decimals, Percentages
A. Integers
Integers have no digits to the right of the decimal point. Examples of integers are 628, 3232542364357, and -54.
In the number 628,
8 stands for 8 ones
2 stands for 2 tens
6 stands for 6 hundreds
So 628 r... | 4 | [
-0.0191650390625,
0.051513671875,
-0.04736328125,
-0.024658203125,
-0.01446533203125,
0.0517578125,
0.0751953125,
0.1728515625,
0.0181884765625,
0.00019550323486328125,
-0.06005859375,
-0.0252685546875,
0.0908203125,
0.036376953125,
-0.035400390625,
-0.06787109375,
-0.08935546875,
... | 38,026 | 38026 | |
Numerical Simulation and Experiments of Barite Sag in Horizontal Annulus
Yahya Hashemian^1, Stefan Miska^1, , Mengjiao Yu^1, Evren Ozbayoglu^1, Nicholas Takach^1
^1Petroleum Enginerring Department, University of Tulsa, Tulsa, USA
Abstract
Under certain drilling conditions, the weighting material particles such as b... | 4 | [
-0.033203125,
-0.033203125,
-0.0167236328125,
0.06884765625,
-0.04736328125,
0.01080322265625,
-0.01708984375,
0.091796875,
-0.000823974609375,
-0.06298828125,
-0.123046875,
-0.00933837890625,
0.016845703125,
-0.007720947265625,
-0.0458984375,
-0.035888671875,
-0.0244140625,
0.0668... | 38,027 | 38027 | |
help on this pls
June 12th 2006, 03:43 AM #1
Newbie
Joined
Jun 2006
Posts
17
help on this pls
Actually i am just double checking my answer to see if i am doing it right. so anyone kindly help me out on these question. i just need the answer but working is prefered if you care to type it
out
1. F... | 4 | [
-0.061767578125,
0.07373046875,
-0.029052734375,
-0.0091552734375,
-0.006591796875,
0.04541015625,
-0.017822265625,
0.0203857421875,
0.023193359375,
0.0159912109375,
0.1162109375,
-0.08349609375,
-0.032958984375,
0.055908203125,
0.04638671875,
0.01458740234375,
-0.06689453125,
-0.0... | 38,028 | 38028 | |
This problem is ridiculous
If, ab/(a+b) = 2 ac/(a+c)=5 bc/(b+c)=4 then find a+b+c. I'd really appreciate a step by step solution.
Hi there, We would solve for one variable and after that replace it in the original equation in order to have only one variable equation: You can solve for a or for b, I will show you the e... | 4 | [
-0.0888671875,
0.0257568359375,
0.0299072265625,
0.034423828125,
-0.01324462890625,
0.04345703125,
-0.115234375,
-0.005584716796875,
-0.0238037109375,
0.020263671875,
0.01806640625,
-0.08203125,
-0.006591796875,
0.0341796875,
-0.0012359619140625,
0.09375,
-0.05029296875,
0.03515625... | 38,029 | 38029 | |
Adding Rational Expressions
June 25th 2013, 10:36 AM #1
Newbie
Joined
Nov 2012
From
United States
Posts
18
Adding Rational Expressions
Problem: $\frac{x - 8}{x^2 - 4} + \frac{3}{x^2-2x}$
Answer: $\frac{x-3}{x(x+2)}, xot=2$
What I ended up with: $\frac{x^2-5x+6}{x(x^2 - 4)}$
Any help on... | 4 | [
-0.0235595703125,
0.045166015625,
0.0419921875,
0.060302734375,
0.0267333984375,
0.09521484375,
-0.044677734375,
0.00830078125,
0.0030975341796875,
-0.0076904296875,
0.05859375,
-0.09033203125,
0.027099609375,
0.07080078125,
-0.01202392578125,
0.1025390625,
-0.0240478515625,
0.0198... | 38,030 | 38030 | |
How Do Cube Roots Work?
Date: 11/04/2003 at 13:01:17
From: Gina
Subject: i don't understand cubed square roots?
I do not understand how to do a square root problem when it is asking
you to do something with a cubed root. For example:
______
\3 / 216 = ?
\/
I don't understand what I am supposed to do with the ... | 4 | [
-0.038330078125,
-0.00092315673828125,
-0.048095703125,
0.03271484375,
-0.1005859375,
-0.04345703125,
-0.0234375,
0.05517578125,
0.06982421875,
-0.02880859375,
0.018310546875,
0.0400390625,
0.0107421875,
0.00156402587890625,
0.049072265625,
0.03466796875,
-0.095703125,
0.0310058593... | 38,031 | 38031 | |
Deriving MGF of Gaussian distribution
December 30th 2008, 03:06 PM #1
Deriving MGF of Gaussian distribution
Hi there,
I'm revising at the moment for a stats exam in about a week's time and I'm having trouble deriving the MGF of the Normal distribution.
I know that i should get:
$<br /> \exp\left(\mu ... | 5 | [
0.003936767578125,
-0.01312255859375,
0.04443359375,
-0.0022125244140625,
0.007110595703125,
-0.057373046875,
-0.0098876953125,
0.055419921875,
-0.0111083984375,
0.035400390625,
0.03955078125,
-0.006134033203125,
0.0419921875,
-0.037109375,
-0.00830078125,
0.0189208984375,
0.05957031... | 38,032 | 38032 | |
Integral by parts
March 9th 2013, 02:30 PM #1
Member
Joined
Dec 2012
From
NY
Posts
105
Thanks
1
Integral by parts
Integral from 9 to 16 lny/sqrt(y)
Here's my work and on the parts bolded I asked for help from someone else but Im not sure WHY he did those steps:
β« ln(y)β
y^(βΒ½) dy =
2... | 5 | [
-0.0390625,
-0.048095703125,
0.10205078125,
0.01116943359375,
0.1435546875,
-0.00811767578125,
-0.07763671875,
0.0218505859375,
-0.0294189453125,
0.0166015625,
0.033203125,
0.0107421875,
-0.0703125,
0.037841796875,
-0.00433349609375,
0.0703125,
-0.080078125,
-0.022216796875,
-0.1... | 38,033 | 38033 | |
Determine Signed Areas in a Problem
The solution to a definite integral gives you the signed area of a region. In some cases, signed area is what you want, but in some problems youβre looking for unsigned area.
The signed area above the x-axis is positive, but the signed area below the x-axis is negative. In contrast... | 5 | [
0.10546875,
0.048583984375,
-0.0361328125,
-0.0693359375,
-0.00103759765625,
-0.1455078125,
0.00067901611328125,
0.06640625,
-0.00811767578125,
-0.028564453125,
0.0015106201171875,
-0.004150390625,
0.0498046875,
0.07470703125,
0.031982421875,
-0.029296875,
-0.013671875,
-0.05175781... | 38,034 | 38034 | |
Contrapositive
July 1st 2008, 10:38 AM
sjenkins
Contrapositive
Can someone please tell me what the contrapositive to this statement is: the square of an even number is an even number.
I thought it was if a number is not even, then its square is not even.
July 1st 2008, 10:50 AM
Moo
Quote:
mmmm
... | 4 | [
-0.033935546875,
0.055908203125,
0.10693359375,
0.08935546875,
-0.03515625,
0.10888671875,
0.029052734375,
0.03857421875,
0.0830078125,
0.0274658203125,
0.041259765625,
0.052978515625,
0.03515625,
-0.014404296875,
0.018310546875,
-0.03955078125,
0.032958984375,
-0.052734375,
0.07... | 38,035 | 38035 | |
race and time problem...pls help
January 22nd 2013, 08:03 PM
hisajesh
race and time problem...pls help
In a 1000m race, if A gives B a 40 m start, A wins by 19 seconds, but if A gives B 30 seconds start, B wins by 40 m. Find the time each takes to run a 1000 m?
My attempt:
1. A gives B a 40 m start, A w... | 4 | [
-0.005096435546875,
0.0203857421875,
-0.08642578125,
-0.107421875,
-0.0537109375,
0.050537109375,
-0.07421875,
0.017578125,
-0.04638671875,
0.044921875,
0.0234375,
-0.01507568359375,
0.04443359375,
0.03515625,
0.04248046875,
0.1201171875,
0.00555419921875,
-0.03271484375,
-0.0157... | 38,036 | 38036 | |
Finding equation of tangent lines:
October 14th 2011, 11:12 PM #1
Newbie
Joined
Feb 2011
Posts
15
Finding equation of tangent lines:
Hello,
So I am having problems with trying to find the equations of tangent lines when the point the lines pass through is not on the original function.
ex:
f(... | 4 | [
0.00133514404296875,
-0.0419921875,
0.01275634765625,
-0.0026397705078125,
-0.0189208984375,
0.054931640625,
0.0322265625,
0.08642578125,
0.0216064453125,
0.01141357421875,
0.0888671875,
-0.05615234375,
0.0654296875,
-0.0184326171875,
-0.00823974609375,
0.17578125,
-0.036376953125,
... | 38,037 | 38037 | |
A couple more System of Equation problems that are stumping me!
February 18th 2009, 06:34 PM
Hapa
A couple more System of Equation problems that are stumping me!
This one I have tried 3 times, and still can not come up with a answer.
A manufacturing plant is going to use two different stamping machines to c... | 4 | [
-0.00131988525390625,
0.01043701171875,
0.01165771484375,
0.01043701171875,
-0.09228515625,
-0.099609375,
-0.1015625,
0.01361083984375,
-0.10205078125,
0.0020751953125,
0.01953125,
0.06298828125,
0.044189453125,
-0.025634765625,
-0.038818359375,
0.029052734375,
-0.004302978515625,
... | 38,038 | 38038 | |
Prove that the determinants are equal
b+c-a a a a b c b c+a-b b = b c a c c a+b-c c a b
The brute force approach: Calculate $\left| \begin{array}{ccc}<br /> b + c - a & a & a \\<br /> b & c + a - b & b \\<br /> c & c & a + b - c \end{array} \right|$. Calculate $\left| \begin{array}{ccc}
<br /> a & b & c \\<br /> b & c... | 4 | [
-0.02587890625,
-0.0311279296875,
0.019287109375,
-0.10888671875,
-0.08154296875,
-0.0380859375,
-0.041748046875,
-0.0830078125,
-0.09228515625,
-0.0264892578125,
-0.049560546875,
-0.0537109375,
0.049560546875,
0.012451171875,
-0.053466796875,
0.0311279296875,
0.0045166015625,
0.04... | 38,039 | 38039 | |
Inductive Proof, is this way valid?
October 8th 2009, 10:43 AM #1
Newbie
Joined
Oct 2009
Posts
20
Inductive Proof, is this way valid?
Have to prove 2^n >= n^2 for n>=4
I.H.: Works when I plug in four. Show that 2^(n+1) >= (n+1)^2 or show that 2^n * 2 >= (n+1)^2
Since we know 2^n >= n^2 then 2^n... | 5 | [
-0.0498046875,
0.0732421875,
0.051025390625,
0.06982421875,
0.0279541015625,
-0.024658203125,
-0.0830078125,
0.034423828125,
0.02880859375,
-0.0419921875,
-0.08837890625,
0.01904296875,
0.0252685546875,
0.026611328125,
-0.03857421875,
0.08251953125,
-0.0145263671875,
0.06787109375,... | 38,040 | 38040 | |
The Commutator
Subsections
4.5 The Commutator
As the previous section discussed, the standard deviation is a measure of the uncertainty of a property of a quantum system. The larger the standard deviation, the farther typical measurements stray
from the expected average value. Quantum mechanics often requires a min... | 5 | [
0.09375,
0.0019683837890625,
0.0037689208984375,
-0.0274658203125,
-0.09423828125,
-0.0274658203125,
-0.00250244140625,
0.03173828125,
0.1044921875,
-0.03662109375,
0.02197265625,
-0.02001953125,
0.033203125,
-0.0284423828125,
0.01263427734375,
-0.040771484375,
0.00286865234375,
0.... | 38,041 | 38041 | |
Not sure what I should do...
September 20th 2009, 06:14 PM #1
Member
Joined
Jan 2008
Posts
118
Not sure what I should do...
A racehorse is running a 10-furlong race. (1 furlong = 220 yards)
As the horse passes each furlong marker (F), its time is recorded.
F| 0 1 2 3 4 5 6 7 8 9 10
T| 0 20 3... | 4 | [
0.03515625,
0.01904296875,
0.0380859375,
-0.0206298828125,
-0.018798828125,
0.0269775390625,
-0.045654296875,
0.1005859375,
-0.02880859375,
-0.02001953125,
0.036376953125,
-0.064453125,
0.01953125,
0.03515625,
-0.080078125,
0.003662109375,
-0.03857421875,
0.049560546875,
-0.09130... | 38,042 | 38042 | |
absolute values are SCArY!!!
August 26th 2009, 05:46 PM
jazzyredsox5
absolute values are SCArY!!!
i understand that an absolute value is the distance on a number line from zero, and that abs(y)=8 would be 8, -8, but when it gets to like abs(c/4)=9, i know you have to make two equations, c/4=9
and c/4=-9, bec... | 4 | [
-0.06591796875,
0.01092529296875,
-0.0079345703125,
-0.00482177734375,
0.021728515625,
0.06689453125,
-0.059814453125,
0.10498046875,
0.0240478515625,
-0.039306640625,
0.041259765625,
-0.00872802734375,
0.056884765625,
0.036865234375,
-0.07470703125,
0.072265625,
0.042236328125,
-0... | 38,043 | 38043 | |
Isotopy classes on the disk and mapping tori
up vote 8 down vote favorite
2
Is the following true?
"The conjugacy classes of two homeomorphisms of the n-times punctured disk have isotopic representatives iff the associated mapping tori are homeomorphic."
By conjugacy class of a homeomorphism is meant the homeomorphi... | 4 | [
-0.00860595703125,
-0.037353515625,
-0.0028076171875,
-0.07958984375,
-0.06689453125,
-0.0291748046875,
0.03759765625,
-0.060302734375,
0.0279541015625,
-0.04052734375,
0.04443359375,
0.046875,
-0.0174560546875,
-0.037841796875,
-0.0283203125,
-0.0703125,
-0.08837890625,
0.00927734... | 38,044 | 38044 | |
Derivative exists
December 5th 2008, 10:58 AM #1
Junior Member
Joined
Sep 2008
Posts
42
Derivative exists
I have two functions. f: U->R is C^1 and f(0)=0. g: U->R defined with the piecewise function
g(x)= {f(x)/x if x not equal to 0; and lim (h->0) of f(h)/h if x=0}
I need to show that g(0) exi... | 5 | [
-0.0291748046875,
0.02978515625,
-0.0025177001953125,
0.0322265625,
0.052001953125,
0.00885009765625,
-0.010009765625,
-0.01953125,
-0.038330078125,
-0.045166015625,
0.008544921875,
-0.043701171875,
0.01007080078125,
0.049072265625,
-0.0107421875,
-0.021484375,
-0.0177001953125,
-0... | 38,045 | 38045 | |
trouble understanding a theorem on finite fields.
July 13th 2011, 02:21 AM
abhishekkgp
trouble understanding a theorem on finite fields.
THEOREM: Let $E$ be a field of $p^n$ elements contained in an algebraic closure $\bar{\mathbb{Z}_p}$ of $\mathbb{Z}_p$. The elements of $E$ are precisely the zeros in $\bar{\ma... | 5 | [
-0.02001953125,
0.08642578125,
0.0302734375,
0.02392578125,
0.06884765625,
-0.0693359375,
0.10546875,
0.0238037109375,
0.0091552734375,
-0.0859375,
-0.0250244140625,
0.02978515625,
-0.031005859375,
-0.059814453125,
0.00141143798828125,
0.03662109375,
-0.10009765625,
-0.01318359375,... | 38,046 | 38046 | |
`Naturally occuring' $K(\pi, n)$ spaces, for $n \geq 2$.
up vote 28 down vote favorite
13
[edited!] Given a group $\pi$ and an integer $n>1$, what are examples of Eilenberg-Maclane spaces $K(\pi, n)$ that can be constructed as "known" manifolds? (or if not a manifold, say some space
people had a pre-existing ... | 4 | [
-0.0869140625,
-0.009765625,
0.013427734375,
0.068359375,
-0.11865234375,
0.06884765625,
0.01104736328125,
-0.0634765625,
0.041259765625,
-0.0289306640625,
0.03173828125,
-0.05810546875,
0.0027313232421875,
0.012939453125,
0.00732421875,
-0.028076171875,
-0.0257568359375,
0.0551757... | 38,047 | 38047 | |
LOGIC-KNOWLEDGE-TAKEN-FOR-GRANTED-Q1-ANSWER
the inductive step of the rev-rev proof -- Answer to Question 1
Major Section: INTRODUCTION-TO-THE-THEOREM-PROVER
The correct answer to Question 1 in logic-knowledge-taken-for-granted is Choice (iv).
The Induction Step of the inductive proof of
(implies (true-listp z)
... | 4 | [
-0.1259765625,
0.08642578125,
0.0693359375,
0.0673828125,
0.033935546875,
0.04150390625,
0.041015625,
0.03271484375,
0.035400390625,
0.1376953125,
0.02783203125,
0.0010986328125,
0.0693359375,
0.034423828125,
-0.00537109375,
0.048095703125,
-0.017578125,
0.036376953125,
0.0319824... | 38,048 | 38048 | |
number of visits in a non homogeneous Markov chain
June 4th 2010, 01:50 PM #1
Newbie
Joined
Jun 2010
Posts
3
number of visits in a non homogeneous Markov chain
Hi
I have a stochastic process $\{X_t, t \geq 1\}$ representing a non homogeneous Markov chain. The transition matrix between $X_1$ and $X_2$... | 5 | [
-0.03662109375,
0.0166015625,
0.0274658203125,
0.005584716796875,
-0.007568359375,
-0.0230712890625,
0.059326171875,
-0.011474609375,
0.09912109375,
0.0732421875,
0.01556396484375,
-0.026611328125,
0.054931640625,
-0.01214599609375,
0.03466796875,
0.05224609375,
0.011474609375,
-0.... | 38,049 | 38049 | |
characters of S_n from A_n
December 15th 2009, 03:14 PM #1
Newbie
Joined
Dec 2009
Posts
6
characters of S_n from A_n
Using Frobenius Reciprocity, derive the character table of S_n from that of A_n when
(a) n = 3
(b) n = 4
(c) n = 5
This is for n=5.
The character table for S_5 is
... | 4 | [
-0.0517578125,
0.01190185546875,
-0.037841796875,
-0.06591796875,
-0.052001953125,
0.10400390625,
-0.0267333984375,
-0.0478515625,
-0.0517578125,
-0.039794921875,
0.058349609375,
-0.00909423828125,
-0.01263427734375,
-0.0546875,
-0.1572265625,
0.01190185546875,
-0.0005950927734375,
... | 38,050 | 38050 | |
Convergence of Schwartz kernels implies convergence of operators
up vote 6 down vote favorite
2
Let $K$ be a smoothing operator on $\mathbb{R}^n$, i.e., it defines a map on all Sobolev spaces $K\colon H^r(\mathbb{R}^n) \to H^s(\mathbb{R}^n)$ for all $r, s \in \mathbb{R}$. Now (a variation of)
the Schwartz kernel theor... | 4 | [
-0.0211181640625,
-0.06396484375,
-0.0322265625,
-0.064453125,
0.0478515625,
0.0634765625,
0.07373046875,
-0.04345703125,
-0.0296630859375,
-0.017333984375,
0.0238037109375,
0.0908203125,
-0.0086669921875,
-0.046875,
0.017578125,
-0.0625,
-0.0120849609375,
0.07568359375,
-0.00180... | 38,051 | 38051 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
Teacher2Teacher
Teacher Exchange
Workshops
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Volume of a Geodesic Dome
Replies: 4 Last Post: Fe... | 5 | [
-0.014404296875,
0.0576171875,
0.0213623046875,
-0.01220703125,
-0.0654296875,
-0.09716796875,
0.03857421875,
0.0152587890625,
0.07080078125,
0.04150390625,
-0.1171875,
-0.004364013671875,
0.04931640625,
0.05224609375,
-0.007080078125,
-0.08740234375,
-0.0830078125,
-0.012084960937... | 38,052 | 38052 | |
Decomposition into irreducible of induced representations
up vote 3 down vote favorite
1
If we consider an induced representation $Ind_{H}^{G}1_{H}$ of finite groups, where $1_{H}$ is the trivial caracter of $H$, how we decompose this representation into irreducible ? There is a
decomposition $Ind_{H}^{G}1_{H}=V\oplus... | 4 | [
-0.034912109375,
-0.006103515625,
0.004425048828125,
0.10498046875,
0.07373046875,
0.0673828125,
0.0223388671875,
-0.03857421875,
0.037109375,
-0.0390625,
-0.033935546875,
-0.044921875,
-0.01007080078125,
0.04296875,
-0.057373046875,
-0.0341796875,
-0.0218505859375,
0.033935546875,... | 38,053 | 38053 | |
Abelian subfactors, a relevant concept?
up vote 1 down vote favorite
3
Through the questions below, this post asks whether the concept of abelian subfactor is relevant.
Remark : here abelian qualifies an inclusion of II$_1$ factors $(N \subset M)$, $N$ is not an abelian algebra.
First some useful reminders about ... | 5 | [
-0.11474609375,
-0.038330078125,
0.006561279296875,
0.02490234375,
0.022705078125,
0.01019287109375,
-0.021728515625,
-0.0155029296875,
-0.07080078125,
-0.04541015625,
-0.00848388671875,
-0.03759765625,
0.06103515625,
0.01092529296875,
0.07373046875,
0.1298828125,
0.0191650390625,
... | 38,054 | 38054 | |
Binomial problem
July 16th 2013, 11:29 PM #1
Senior Member
Joined
Oct 2009
Posts
295
Thanks
9
Binomial problem
A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% ch... | 5 | [
0.09228515625,
0.0712890625,
-0.033935546875,
-0.0177001953125,
-0.0260009765625,
-0.006103515625,
0.0859375,
0.0703125,
-0.03662109375,
0.0537109375,
0.0277099609375,
-0.057373046875,
0.045166015625,
0.03662109375,
0.0380859375,
0.024658203125,
0.029296875,
-0.04296875,
-0.07910... | 38,055 | 38055 | |
Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just from the program?
up vote 23 down vote favorite
6
Question. Given a Turing-machine program $e$, which is guaranteed to run in polynomial time, can we computably find such a polynomial?
In other words, is there a computable functi... | 5 | [
-0.0478515625,
0.056884765625,
-0.05224609375,
0.014404296875,
0.0390625,
0.0162353515625,
-0.035888671875,
0.0234375,
-0.02685546875,
-0.0064697265625,
-0.0927734375,
0.054443359375,
0.005889892578125,
0.0361328125,
0.05810546875,
-0.03173828125,
0.00762939453125,
-0.022216796875,... | 38,056 | 38056 | |
Integral, log and Inverse
April 20th 2008, 03:24 PM #1
Newbie
Joined
Apr 2008
Posts
12
1. $\int_1^2 \frac{x-4}{x^2} dx$ *ANSWERED*
2. $log_a(2^a) = \frac{a}{4}$, then $a =$ * ANSWERED*
3.Inverse of $y=2x^3+3x^2+7x+4$ *ANSWERED*
(i know how to do inverse, but this polynomial is throwing me of... | 5 | [
0.06787109375,
-0.00531005859375,
0.031982421875,
0.000629425048828125,
0.0478515625,
-0.0703125,
0.0244140625,
0.05029296875,
0.0537109375,
0.08642578125,
0.03173828125,
-0.006317138671875,
-0.015869140625,
0.0230712890625,
-0.0024261474609375,
0.087890625,
-0.07080078125,
0.05004... | 38,057 | 38057 | |
Number of relations?
April 28th 2009, 08:06 AM #1
Newbie
Joined
Jan 2009
Posts
21
Number of relations?
Consider the set F={1,2,3,4}. How many symmetric relations are R are there on F such that 1R2?
My professor says the answer is 2^9 but I have no idea why.
Thanks!
Do you understand that t... | 4 | [
0.004669189453125,
-0.035400390625,
-0.041259765625,
-0.008544921875,
-0.01129150390625,
0.068359375,
-0.038330078125,
0.025634765625,
0.0057373046875,
0.00885009765625,
-0.0267333984375,
-0.01251220703125,
-0.00167083740234375,
0.060546875,
0.00168609619140625,
0.040771484375,
0.010... | 38,058 | 38058 | |
Combinatorics QUESTION
October 21st 2012, 02:18 PM #1
Member
Joined
Feb 2011
Posts
75
Combinatorics QUESTION
Let $A = {a_1, a_2, . . . , a_k}$ be an alphabet, and let n_i denote the number of appearances of
letter a_i in a word. How many words of length n in the alphabet A are there for which
$k ... | 4 | [
-0.050537109375,
-0.06689453125,
0.0033416748046875,
-0.007354736328125,
-0.07177734375,
0.058837890625,
0.08056640625,
-0.0079345703125,
-0.005279541015625,
0.041015625,
0.0771484375,
-0.021240234375,
0.058349609375,
-0.032958984375,
-0.053955078125,
0.041015625,
-0.0036773681640625... | 38,059 | 38059 | |
SPCS 8
Posted by: matheuscmss | March 1, 2012
SPCS 8
In SPCS6 and SPCS7, we studied a version of Avila-Viana symplicity criterion in the context of locally constant cocycles with values on
$\displaystyle G=GL(d,\mathbb{R}), Sp(d,\mathbb{R}), U_{\mathbb{C}}(p,q) \textrm{ or } U_... | 4 | [
-0.1220703125,
-0.022216796875,
0.006744384765625,
-0.0206298828125,
-0.0128173828125,
0.0263671875,
0.0034332275390625,
-0.00213623046875,
0.047607421875,
-0.09814453125,
0.1298828125,
-0.061767578125,
-0.07421875,
0.041748046875,
0.0419921875,
-0.0150146484375,
-0.055419921875,
-... | 38,060 | 38060 | |
Mass Triple Integrals
March 28th 2010, 09:03 AM #1
Member
Joined
Sep 2008
Posts
117
Mass Triple Integrals
Find the mass of the solid region bounded by the planes
x+z=1
x-z = -1
y=0
and the surface
y=sqrt(z)
The density of the solid is (x,y,z)=2y+5
My analytic geometry skills... | 4 | [
0.0244140625,
-0.046142578125,
-0.00738525390625,
-0.0654296875,
0.00142669677734375,
-0.0869140625,
0.0478515625,
-0.00457763671875,
-0.09716796875,
0.0211181640625,
-0.0986328125,
0.03515625,
-0.009033203125,
0.08837890625,
-0.0244140625,
0.0145263671875,
-0.039306640625,
-0.1035... | 38,061 | 38061 | |
Fast root finding for strictly decreasing function
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
What is a fast algorithm to find the root of a strictly decreasing function? If the root is not exact I want to find a roo... | 5 | [
-0.046875,
-0.0030975341796875,
0.01300048828125,
0.00592041015625,
-0.006439208984375,
-0.1240234375,
-0.061767578125,
0.06298828125,
0.056396484375,
0.038330078125,
-0.0146484375,
0.04833984375,
0.061767578125,
0.01153564453125,
-0.042724609375,
-0.040283203125,
-0.0201416015625,
... | 38,062 | 38062 | |
Group Cohomology of Symmetric Powers
up vote 3 down vote favorite
1
Let $G$ be a finite group and $V$ be an integral representation of $G$, i.e. a free abelian group of finite rank with $G$-action. Now consider the symmetric power $Sym(V)$ of $V$ over $\mathbb{Z}$,
which has again a $G$-action by the functoriality of ... | 5 | [
-0.060791015625,
0.0262451171875,
0.01275634765625,
0.00341796875,
0.013671875,
0.02880859375,
-0.03125,
-0.06494140625,
-0.0302734375,
0.006317138671875,
0.03857421875,
-0.022705078125,
-0.038330078125,
0.0023651123046875,
0.055908203125,
0.06201171875,
-0.0302734375,
0.1005859375... | 38,063 | 38063 | |
Given Derivative Thru a Point
December 8th 2007, 03:37 PM
Super Mallow
Given Derivative Thru a Point
Another question..
f'(x)=1/XSQRED + 2X and goes through (-1,1).
I need to find a function that has that derivative and passes through that point
December 8th 2007, 03:41 PM
Jhevon
December 8th 2007, 0... | 4 | [
-0.037841796875,
-0.02490234375,
0.08203125,
0.1025390625,
0.0263671875,
0.01263427734375,
-0.0113525390625,
0.076171875,
0.003692626953125,
0.00885009765625,
0.09521484375,
-0.07958984375,
0.0546875,
0.0062255859375,
-0.09033203125,
-0.007568359375,
0.013671875,
-0.041015625,
0.... | 38,064 | 38064 | |
Question on bigraded modules
up vote 2 down vote favorite
1
Let $R$ be a polynomial ring $k[x_1,...,x_n]$, let $f_1,...f_s$ be some non-zero polynomial sin $R$ of degree $p_1,...,p_s$ respectively.Define $S$ by $k[X_1,...,X_n, T_1,...T_s]$ with bigrading
defined by $degX_i=(1,0)$ and $degT_j=(p_j,1)$. For a bigraded $... | 5 | [
-0.08544921875,
0.056884765625,
-0.048583984375,
0.01422119140625,
0.0062255859375,
0.06640625,
0.042724609375,
0.0087890625,
-0.005523681640625,
-0.058349609375,
0.00982666015625,
0.03271484375,
-0.01397705078125,
-0.01287841796875,
0.031982421875,
0.0164794921875,
0.006866455078125... | 38,065 | 38065 | |
Need help proving that $\sum\limits_{j=0}^{k-1}(-1)^{j+1}(k-j)^{2k-2} \binom{2k+1}{j} \ge 0$
up vote 17 down vote favorite
9
Hello.
I have been trying very hard to show that $\sum\limits_{j=0}^{k-1}(-1)^{j+1}(k-j)^{2k-2} \binom{2k+1}{j} \ge 0$ and could not quite get anywhere. This inequality has been verified by com... | 5 | [
0.052734375,
0.033935546875,
0.055419921875,
0.000774383544921875,
0.00701904296875,
0.00653076171875,
0.033203125,
0.064453125,
-0.028076171875,
0.0771484375,
-0.08056640625,
-0.05615234375,
0.060546875,
-0.042236328125,
-0.041748046875,
0.03662109375,
0.033447265625,
-0.000385284... | 38,066 | 38066 | |
Simplifying Expressions
Date: 11/24/97 at 02:23:53
From: Jacques Thurman
Subject: Regarding Simplifying Expressions
Hello Dr. Math,
My name is Lisa Pagan and I am in 9th Grade. I am stuck on lots of
problems but I really need your help on this one particular problem:
2x - ( 3 - x ) = x - 7
Date: 11/24/97 at 1... | 4 | [
-0.07373046875,
0.0615234375,
0.0869140625,
0.03369140625,
-0.0216064453125,
0.002197265625,
0.003204345703125,
0.01708984375,
-0.05029296875,
0.044189453125,
-0.0019989013671875,
-0.10888671875,
0.017822265625,
0.032470703125,
0.049072265625,
-0.031494140625,
-0.051025390625,
0.06... | 38,067 | 38067 | |
Tensor Product of Galois Extensions of Rings
March 27th 2011, 01:20 PM #1
Member
Joined
Nov 2010
Posts
193
Tensor Product of Galois Extensions of Rings
I was hoping that someone familiar with a bit of commutative algebra could help me see why this is true.
Suppose that $R,S$ are commutative rings wi... | 4 | [
-0.0244140625,
-0.03515625,
-0.01092529296875,
-0.00927734375,
0.0849609375,
0.055908203125,
0.09130859375,
0.052734375,
-0.041259765625,
-0.017822265625,
0.004608154296875,
0.05029296875,
0.044189453125,
-0.00019168853759765625,
-0.00775146484375,
0.05517578125,
0.0244140625,
0.06... | 38,068 | 38068 | |
Is $\mathcal{B}^{\mathbb{Z}}(l^\infty(\mathbb{Z}))$ a commutative algebra?
up vote 9 down vote favorite
2
Consider $l^\infty(\mathbb{Z})$ the Banach space of bounded complex valued functions on the abelian group $\mathbb{Z}$ with the supremum norm. It has a natural action by $\mathbb{Z}$ given by $(zf)
(g):=f(z^{-1}g)... | 4 | [
-0.044189453125,
-0.042724609375,
-0.0279541015625,
0.036376953125,
-0.035888671875,
0.08349609375,
0.042724609375,
-0.0262451171875,
-0.054931640625,
-0.036376953125,
0.0052490234375,
0.02685546875,
0.045654296875,
-0.044677734375,
0.02880859375,
0.0966796875,
-0.0244140625,
0.032... | 38,069 | 38069 | |
xn + ym is a Cauchy sequence
October 7th 2010, 05:35 PM
kathrynmath
xn + ym is a Cauchy sequence
Let xn and yn be Cauchy sequences.
Give a direct arguement that xn+yn is a Cauchy sequence that does not use the Cauchy Criterion or the Algebraic Limit Theorem.
given epsilon>0 there exists an N in the... | 4 | [
-0.080078125,
-0.03271484375,
0.026611328125,
-0.0146484375,
-0.001556396484375,
0.07470703125,
0.0439453125,
0.00732421875,
-0.0888671875,
-0.06494140625,
0.1162109375,
0.028564453125,
-0.0147705078125,
-0.017822265625,
-0.03125,
0.08935546875,
0.016845703125,
-0.006927490234375,
... | 38,070 | 38070 | |
Math Help
September 20th 2012, 04:13 PM #1
Member
Joined
Aug 2012
From
north carolina
Posts
107
limit help
if lim[x->a][f(x) + g(x)] = 2, and lim[x->a][f(x) - g(x)] = 1, find lim[x->a][f(x)g(x)]
please explain how the answer is 3/4!!!!
Re: limit help
$\lim_{x \to a} \left[f(x)+g(x)]^2 = ... | 4 | [
0.000946044921875,
-0.049560546875,
0.0203857421875,
0.038330078125,
-0.036865234375,
0.07275390625,
0.034423828125,
-0.047607421875,
-0.0146484375,
-0.0174560546875,
0.00494384765625,
-0.0030517578125,
0.044677734375,
-0.059814453125,
-0.021484375,
0.0103759765625,
0.0076904296875,
... | 38,071 | 38071 | |
trigo inverse
Is this your equation? $\displaystyle 2\tan^{-1}{(\sin{x})} = \tan^{-1}{(2\sec{x})}$ for $\displaystyle 0^{\circ} < x < 90^{\circ}$...
Hello, prasum! $\text{Solve for }x\!:\;2\tan^{\text{-}1}(\sin x) \;=\; \tan^{\text{-}1}(2\sec x),\;\text{ for }0^o < x < 90^o$ Let: . $\begin{Bmatrix}\alpha &=& \tan^{\te... | 4 | [
-0.0145263671875,
0.00347900390625,
0.0087890625,
0.041015625,
-0.0211181640625,
-0.08203125,
0.0078125,
0.026123046875,
-0.04541015625,
-0.003753662109375,
0.123046875,
-0.05126953125,
-0.050048828125,
0.00811767578125,
0.06494140625,
0.05126953125,
0.01953125,
-0.0172119140625,
... | 38,072 | 38072 | |
Prove rational numbers form a group (associativity - done most of it)
May 29th 2009, 02:59 AM
RAz
Prove rational numbers form a group (associativity - done most of it)
Q: Prove that the set of rational numbers form a group under the operation * where a * b = 2a + 3b + 4ab
I have to prove (a * b) * c = a * (... | 4 | [
-0.06787109375,
0.01904296875,
-0.00811767578125,
-0.00133514404296875,
-0.0859375,
0.06591796875,
0.01019287109375,
-0.033935546875,
-0.0284423828125,
-0.08935546875,
-0.034423828125,
-0.037353515625,
0.00628662109375,
0.0213623046875,
-0.001983642578125,
0.042236328125,
-0.02783203... | 38,073 | 38073 | |
If N is Odd
Date: 12/05/97 at 00:44:14
From: waldo
Subject: Number theory
My question pertains to number theory. I have no idea where to start
or which process to use. If you could get me started on the right path
then I think I might be able to finish it.
The problem is this: Prove that if n is odd, then 8 divides... | 4 | [
-0.036865234375,
0.0859375,
0.08984375,
0.0654296875,
0.056884765625,
0.04833984375,
0.031005859375,
0.0771484375,
0.01287841796875,
-0.099609375,
-0.060791015625,
0.0279541015625,
0.016357421875,
0.05224609375,
-0.08544921875,
-0.07666015625,
0.01422119140625,
0.0140380859375,
-... | 38,074 | 38074 | |
Centroid of plane areas
March 3rd 2011, 06:40 PM
jasonlewiz
Centroid of plane areas
Can someone show me the solution of this problem? Thanks..
a.Find the centroid of the area bounded by the curve y=x^2 and the line y=2x+3.
b.Find the centroid of the area bounded by the curve y=2x+1, x+y=7 and x=8.
Mar... | 4 | [
-0.0093994140625,
-0.032958984375,
-0.00921630859375,
-0.04833984375,
0.00799560546875,
0.0294189453125,
-0.04296875,
0.11181640625,
-0.0201416015625,
0.0771484375,
-0.07666015625,
0.007293701171875,
-0.0380859375,
0.048583984375,
-0.01202392578125,
-0.00714111328125,
-0.1220703125,
... | 38,075 | 38075 | |
Genus 2 curves vs Abelian surfaces
up vote 5 down vote favorite
In the Satake compactification of abelian surfaces we have the following degeneration of a family of abelian surfaces in $\mathbf{H}_2$
$lim_{t \to \infty}\begin{pmatrix} it & b \\\ b & \tau\end{pmatrix} = \tau.$
Since we have that $M_2$ is an open of $... | 4 | [
-0.1259765625,
-0.056640625,
-0.022216796875,
0.023681640625,
-0.0096435546875,
-0.0179443359375,
-0.061279296875,
0.0517578125,
0.00168609619140625,
-0.076171875,
0.10595703125,
-0.06494140625,
-0.02978515625,
-0.0228271484375,
0.031005859375,
0.06640625,
-0.14453125,
-0.026367187... | 38,076 | 38076 | |
electric dipole moment
Enter a value into either text box and select units using the drop-down boxes.
What is the Electric Dipole Moment?
In physics, for any given system of charges, the electric dipole moment is a measure of the separation of positive and negative charges within that system. This effectively amount... | 4 | [
-0.037841796875,
0.0191650390625,
0.0184326171875,
0.00604248046875,
0.03955078125,
0.05419921875,
0.1298828125,
0.10400390625,
0.11328125,
0.018310546875,
0.05224609375,
0.0201416015625,
0.0286865234375,
0.03662109375,
0.03173828125,
-0.04736328125,
-0.057373046875,
-0.07470703125... | 38,077 | 38077 | |
killing limits, please
January 30th 2009, 11:07 AM #1
Newbie
Joined
Jan 2009
From
Croatia
Posts
2
Please, I need step by step solution of this two limits. I'd be so greatful for help. please don't mind my stupidity of not knowing L'Hospital rule...
So, this's killing me:
1. lim (x/x-1 - 1/ln x... | 5 | [
-0.0262451171875,
-0.08935546875,
-0.038818359375,
-0.02880859375,
0.0289306640625,
-0.04931640625,
0.057861328125,
-0.0159912109375,
0.02734375,
0.051513671875,
0.07470703125,
-0.06396484375,
0.033203125,
-0.0225830078125,
0.0142822265625,
0.02880859375,
-0.04931640625,
-0.0336914... | 38,078 | 38078 | |
first and second differences
The first part of the question A) ; given the following graph and the values of h and h, h=2,k=3 Determine its equations (there is a picture of a parabola with given points A(0,2); out of this i got
its equation to be y=-5(x-2)squared+3 The second part(b) says to calculate the first and sec... | 4 | [
-0.07861328125,
0.05126953125,
-0.0084228515625,
-0.07861328125,
0.0198974609375,
-0.01068115234375,
-0.01495361328125,
0.017822265625,
-0.01177978515625,
0.01513671875,
0.1015625,
-0.002044677734375,
0.06689453125,
0.01153564453125,
-0.0064697265625,
0.017578125,
-0.041259765625,
... | 38,079 | 38079 | |
Half-Life of a Radioactive Substance
Associated Topics || Dr. Math Home || Search Dr. Math
Half-Life of a Radioactive Substance
... | 4 | [
-0.0634765625,
0.0498046875,
0.068359375,
0.0291748046875,
0.021240234375,
-0.047607421875,
0.005615234375,
0.10546875,
-0.06591796875,
0.07421875,
-0.0002536773681640625,
-0.046142578125,
-0.00640869140625,
0.002716064453125,
-0.02197265625,
0.01348876953125,
-0.03955078125,
-0.05... | 38,080 | 38080 | |
Adjunction up to distributor
up vote 3 down vote favorite
2
Suppose we have functors $F : C \to D_1$ and $G : D_2 \to C$, together with a distributor (profunctor) $D : D_1^{\rm op} \times D_2 \to {\rm Set}$. We could define "$G$ is right adjoint to $F$ up to
$D$" as the existence of a natural isomorphism $C(c, Gd) \co... | 4 | [
-0.04736328125,
-0.08447265625,
0.003173828125,
-0.0240478515625,
-0.05615234375,
0.031005859375,
-0.03125,
0.027099609375,
-0.01104736328125,
0.029541015625,
-0.00141143798828125,
-0.041748046875,
-0.051025390625,
0.033447265625,
0.06494140625,
0.0054931640625,
0.07568359375,
0.12... | 38,081 | 38081 | |
Help on Easy Slope Problems
May 13th 2009, 07:58 PM
lastlion
Help on Easy Slope Problems
Hello, this is my first post. I am trying to learn some easy algebra and was hoping to get some help.
I have some problems, and answers, but no idea how to arrive at the answers.
Please explain:
1) Find the sl... | 4 | [
-0.027587890625,
0.01708984375,
-0.023193359375,
0.00017642974853515625,
-0.068359375,
0.119140625,
0.0235595703125,
-0.048583984375,
0.072265625,
0.05712890625,
0.06689453125,
0.00396728515625,
0.0284423828125,
0.060302734375,
0.04150390625,
0.1337890625,
-0.11572265625,
0.0281982... | 38,082 | 38082 | |
Number of Possible Telephone Numbers
Date: 7/15/96 at 21:23:43
From: Anonymous
Subject: Number of Possible Telephone Numbers
How many phone numbers can be made under the following conditions:
(First digit cannot be 0 or 1 because you'll get the operator or long
distance.)
a) The first two digits are 3 followed by 6
... | 4 | [
-0.07177734375,
0.0272216796875,
0.06689453125,
-0.06591796875,
-0.1064453125,
0.07177734375,
0.02978515625,
0.06298828125,
-0.004852294921875,
0.028564453125,
-0.025634765625,
0.012451171875,
0.0400390625,
0.006683349609375,
-0.0498046875,
-0.044677734375,
-0.076171875,
-0.0568847... | 38,083 | 38083 | |
Where Do We Stand on Meshfree Approximation Schemes?
Where Do We Stand on Meshfree Approximation Schemes?
In a previous posting, Timon provided a nice overview of meshfree methodsβ starting from SPH and leading up to some of the key developments over the past decade (diffuse element method, element-free
Galerkin, rep... | 4 | [
-0.07373046875,
0.052490234375,
0.09228515625,
0.00921630859375,
0.107421875,
-0.0184326171875,
-0.0869140625,
0.0927734375,
0.0189208984375,
0.0400390625,
0.01043701171875,
0.01025390625,
-0.00518798828125,
-0.06787109375,
0.0267333984375,
-0.0771484375,
0.0771484375,
-0.023071289... | 38,084 | 38084 | |
Nakagami distribution
Nakagami
Probability density function
Cumulative distribution function
Parameters $m\ or\ \mu >= 0.5$shape (real)
$\Omega\ or\ \omega > 0$ spread (real)
Support $x > 0\!$
pdf $\frac{2m^m}{\Gamma(m)\Omega^m} x^{2m-1} \exp\... | 4 | [
0.033447265625,
-0.06005859375,
0.002593994140625,
0.0137939453125,
-0.05810546875,
-0.087890625,
-0.0162353515625,
0.10302734375,
-0.02685546875,
0.01275634765625,
0.1357421875,
-0.035400390625,
0.09716796875,
-0.037353515625,
0.0235595703125,
0.037353515625,
0.0322265625,
-0.0505... | 38,085 | 38085 | |
What structure supports division to a unique quotient and remainder?
up vote 1 down vote favorite
This has been bugging me for a while.
According to https://en.wikipedia.org/wiki/Euclidean_division, if I divide integer $a$ by integer $b$, I get unique $t$, $r$ such that $a = t b + r$, $0 \le r < b$.
Furthermore, for... | 4 | [
-0.107421875,
-0.0194091796875,
-0.158203125,
-0.041259765625,
-0.0164794921875,
-0.0537109375,
0.00872802734375,
-0.029296875,
0.052978515625,
-0.083984375,
-0.0294189453125,
0.00592041015625,
0.06884765625,
0.09716796875,
0.0184326171875,
-0.0390625,
0.0255126953125,
0.0299072265... | 38,086 | 38086 | |
Line Integral and Electric Potential
February 17th 2008, 05:28 PM #1
Member
Joined
Jan 2008
Posts
91
Line Integral and Electric Potential
Hey I've been having a lot of trouble with a question involving the calculating the potential difference between two points.
So I have the following equations for... | 5 | [
0.0242919921875,
0.047607421875,
-0.017822265625,
-0.10888671875,
0.040771484375,
0.01123046875,
-0.034912109375,
0.042724609375,
-0.053466796875,
0.0179443359375,
0.01177978515625,
0.016357421875,
-0.0830078125,
0.0244140625,
0.050537109375,
-0.0035247802734375,
-0.07861328125,
-0... | 38,087 | 38087 | |
Urgent Help Please
December 9th 2008, 02:29 PM #1
Newbie
Joined
Dec 2008
Posts
13
Urgent Help Please
I really need help with this question, I have to present the answer and how to do it in front of my class tomorrow. If someone can please help me with as much detail as possible I would really
appreci... | 4 | [
-0.0286865234375,
0.06494140625,
-0.0517578125,
-0.1083984375,
-0.0732421875,
0.0703125,
0.051025390625,
0.008544921875,
-0.040283203125,
0.006195068359375,
0.056884765625,
-0.0732421875,
0.08154296875,
0.01287841796875,
0.0634765625,
-0.01348876953125,
-0.0235595703125,
0.01586914... | 38,088 | 38088 | |
Galley or Scratch Method of Division
Date: 12/08/2002 at 14:59:04
From: Julie
Subject: Division in the 1400s
In the 1400's what was the method for performing division?
Date: 12/08/2002 at 23:00:04
From: Doctor Peterson
Subject: Re: Division in the 1400s
Hi, Julie.
According to D. E. Smith's History of Mathematics... | 4 | [
-0.07568359375,
0.02392578125,
-0.034912109375,
-0.0308837890625,
-0.09228515625,
-0.0693359375,
-0.049072265625,
0.03662109375,
-0.0478515625,
0.07861328125,
0.003631591796875,
0.0169677734375,
0.0186767578125,
0.072265625,
-0.0771484375,
-0.1357421875,
-0.0157470703125,
-0.005859... | 38,089 | 38089 | |
Progress On The Jacobian Conjecture
January 29, 2014
More on the crypto approach to the Jacobian Conjecture
Arno van Essen is one of the world experts on the Jacobian conjecture (JC)βwe have discussed his work before here. He has made many contributions to it, with my favorite being: To Believe Or Not To
Believe: T... | 5 | [
-0.1669921875,
0.01031494140625,
0.07958984375,
-0.0111083984375,
0.050048828125,
0.0286865234375,
0.056396484375,
0.0130615234375,
-0.040771484375,
0.08935546875,
-0.027099609375,
0.1005859375,
0.0115966796875,
0.005859375,
0.054931640625,
0.0238037109375,
-0.050537109375,
0.08544... | 38,090 | 38090 | |
Math Forum Discussions
Re: correlation function
Posted: Nov 18, 2012 5:16 PM
> I get different results but have no idea why.
Hi. If I'm not mistaken, you are loosing data with the default settings of Fourier.
As a personal technique, since I never remember these, I use these variables.
{
fftDefault={0,1},
fftData={-... | 5 | [
-0.041259765625,
-0.0712890625,
0.060791015625,
0.06494140625,
-0.0654296875,
0.061767578125,
-0.028076171875,
0.0361328125,
0.032958984375,
0.0016632080078125,
-0.01300048828125,
-0.050537109375,
0.0042724609375,
0.01068115234375,
-0.01287841796875,
-0.0751953125,
-0.032958984375,
... | 38,091 | 38091 | |
calculating expectation using conditional probability
September 20th 2009, 11:33 AM #1
Newbie
Joined
Sep 2009
Posts
1
calculating expectation using conditional probability
Hello,
I am trying to calculate a simple expectation of the form E[h(X)], where X is the random variable, h is a function of X. ... | 4 | [
0.03173828125,
-0.029052734375,
0.046142578125,
-0.0927734375,
0.06787109375,
-0.04345703125,
0.09033203125,
-0.0203857421875,
-0.10009765625,
-0.0400390625,
-0.0238037109375,
0.06640625,
0.06640625,
0.08154296875,
0.007110595703125,
0.056396484375,
-0.02880859375,
0.01611328125,
... | 38,092 | 38092 | |
Functions of a Complex Variable
Date: 10/05/2002 at 11:28:34
From: Jay
Subject: Functions of a complex variable
Show that w=f(z*), where z*=x-iy and f is a differentiable function,
is not an analytic function of z.
Date: 11/11/2002 at 11:43:14
From: Doctor Nitrogen
Subject: Re: Functions of a complex variable
Hi, ... | 5 | [
-0.1142578125,
0.035400390625,
0.02734375,
0.1259765625,
0.00970458984375,
-0.0157470703125,
0.041748046875,
-0.0203857421875,
-0.051513671875,
0.0279541015625,
0.048583984375,
-0.01300048828125,
-0.0306396484375,
0.052978515625,
0.009033203125,
-0.04541015625,
-0.058349609375,
-0.... | 38,093 | 38093 | |
Solve d^2y/dx^2 + 4y = 0?
October 1st 2009, 11:04 AM
ZaZu
Solve d^2y/dx^2 + 4y = 0?
Hi there,
$(d^2y)/(dx^2) + 4y = 0$ is obviously the second derivative.
What I know is that if its $dy/dx$ I must separate the dy and only the y to one side , and the x's and any number attached to the y along with dx to ... | 4 | [
0.0020599365234375,
0.0006256103515625,
0.0830078125,
0.050537109375,
0.0186767578125,
-0.03564453125,
-0.0277099609375,
0.007293701171875,
0.057861328125,
-0.0341796875,
0.10888671875,
0.04150390625,
-0.0184326171875,
0.07958984375,
0.028564453125,
0.0498046875,
-0.033203125,
0.02... | 38,094 | 38094 | |
Variable of two populations
July 27th 2008, 07:24 PM
sjenkins
Variable of two populations
Can someone help me understand how to get started on this problem?
A variable of two populations has a mean of 40 and a standard deviation of 12 for one of the populations and a mean of 40 and a standard deviation of 6... | 4 | [
0.11669921875,
0.06982421875,
0.042724609375,
-0.0235595703125,
0.00799560546875,
0.06591796875,
-0.06298828125,
0.0859375,
-0.057861328125,
-0.00531005859375,
0.043701171875,
0.01123046875,
0.0036773681640625,
0.031494140625,
0.035888671875,
-0.052490234375,
-0.05615234375,
0.0190... | 38,095 | 38095 | |
Interactive Multigrid Image Warping
βββ¬ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β β Interactive Multigrid Image Warping β
... | 4 | [
-0.035400390625,
0.0137939453125,
-0.0400390625,
0.00102996826171875,
0.0458984375,
-0.060546875,
-0.06494140625,
0.0159912109375,
-0.005889892578125,
-0.0250244140625,
0.02734375,
-0.068359375,
-0.020263671875,
0.0322265625,
-0.0634765625,
-0.010986328125,
-0.0947265625,
0.0617675... | 38,096 | 38096 | |
Decomposition of positive definite matrices.
up vote 11 down vote favorite
1
It is known that a $n^2 \times n^2$ positive semidefinite matrix $A$ cannot always be written as a finite sum $$ A=\sum_{j} B_j \otimes C_j $$ with $B_j$ and $C_j$ positive semidefinite matrices (of
size $n \times n$). For example, it can be ... | 5 | [
0.001922607421875,
-0.049560546875,
-0.07763671875,
-0.01123046875,
-0.0634765625,
0.00299072265625,
-0.0172119140625,
-0.1142578125,
-0.0091552734375,
-0.0223388671875,
-0.04833984375,
0.005950927734375,
0.00982666015625,
0.01141357421875,
-0.0537109375,
0.062255859375,
0.0659179687... | 38,097 | 38097 | |
Simplify a Geometric Series
Date: 05/06/2003 at 16:51:02
From: sharath
Subject: Formula needed
Can you please tell me the formula for
x^n + x^(n - 1) + x^(n - 2) + ... + x^(n - n)
I don't know how to condense this formula. I came to it while trying
to find out the 'inflation' effect on each year's savings.
Than... | 4 | [
-0.007293701171875,
0.058349609375,
0.0189208984375,
0.09814453125,
0.0120849609375,
-0.0234375,
-0.037353515625,
-0.00555419921875,
0.0341796875,
-0.0081787109375,
-0.0458984375,
-0.0439453125,
0.06298828125,
0.0032196044921875,
-0.00058746337890625,
0.04248046875,
-0.054931640625,
... | 38,098 | 38098 | |
First Post... Desperately need help before exam.
July 22nd 2013, 03:36 PM #1
Newbie
Joined
Jul 2013
From
Anchorage
Posts
3
First Post... Desperately need help before exam.
Hi Everyone, I firstly want to apologize for the long post, but I have a Linear Algebra Exam on Wednesday, and We received a rev... | 5 | [
-0.07275390625,
0.01519775390625,
0.017578125,
0.06884765625,
0.05517578125,
0.0732421875,
0.0859375,
-0.0162353515625,
-0.01348876953125,
-0.07421875,
-0.016845703125,
0.0084228515625,
-0.01318359375,
-0.041748046875,
-0.057861328125,
0.068359375,
-0.040771484375,
-0.0634765625,
... | 38,099 | 38099 |