content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Maximum Area for Irrigation Channel
Date: 02/08/2002 at 23:35:06
From: Ingrid
Subject: Applied maximum and minimum problems in calculus
An irrigation channel made of concrete is to have a cross section in
the form of an isosceles trapezoid, three of whose sides are 4 feet
long. How should it be shaped to have a maxi... | 5 | [
0.09326171875,
-0.0294189453125,
0.05712890625,
-0.08984375,
-0.0703125,
-0.0859375,
-0.022216796875,
0.11669921875,
-0.0732421875,
-0.015625,
-0.0390625,
0.04541015625,
0.0419921875,
0.07080078125,
-0.00592041015625,
0.051513671875,
0.007598876953125,
0.00799560546875,
-0.107910... | 39,300 | 39300 | |
Linear transformation
September 17th 2009, 02:43 PM
Andres Perez
Linear transformation
Hi,
i have the following question:
If a function $T:\mathbb{R}^n\to \mathbb{R}^m$ satisfies:
$T(u+v)=T(u)+T(v)$ for all $u,v\in \mathbb{R}^n$
then
$T(\alpha u)=\alpha T(u)$ for all $\alpha\in \mathbb{R... | 4 | [
-0.0439453125,
0.0380859375,
-0.076171875,
-0.005157470703125,
0.0225830078125,
0.053466796875,
0.0299072265625,
-0.107421875,
-0.017578125,
0.016845703125,
0.078125,
0.01531982421875,
-0.056884765625,
0.05419921875,
-0.01312255859375,
-0.05029296875,
-0.04296875,
-0.0023193359375,... | 39,301 | 39301 | |
Absorption Laws
Associated Topics || Dr. Math Home || Search Dr. Math
Absorption Laws
Date: 04/10/2001 at 20:44:4... | 4 | [
0.0137939453125,
-0.003448486328125,
0.0120849609375,
0.0004253387451171875,
0.020751953125,
-0.0390625,
0.068359375,
-0.0830078125,
-0.08154296875,
0.03662109375,
0.0703125,
0.06298828125,
-0.0106201171875,
0.12109375,
0.05126953125,
0.0634765625,
-0.0576171875,
0.0118408203125,
... | 39,302 | 39302 | |
Short Calculus Word Problem
November 11th 2006, 08:52 PM #1
Affinity
Guest
A closed rectangular box is to be constructed with one side 1 meter long. The material for the top of the box cost $20 per square meter, and the material for the sides and bottom costs $10 per
square meter. Find the dimensions of the bo... | 5 | [
-0.029541015625,
0.042724609375,
-0.0050048828125,
-0.006103515625,
-0.0185546875,
-0.0291748046875,
-0.04345703125,
0.06884765625,
-0.08544921875,
0.09033203125,
-0.0732421875,
0.01214599609375,
0.060302734375,
0.0673828125,
-0.06884765625,
0.09375,
0.0152587890625,
0.022827148437... | 39,303 | 39303 | |
differential equation need Help
April 24th 2013, 08:44 AM
mastermin346
differential equation need Help
$dy/dx = -6xy$
$\int \frac{1}{y} dy = \int -6x dx$
$ln y = -3x^2 + c$
$y = e^{-3x^2 + c}$
is my answer Correct ?
April 24th 2013, 08:49 AM
BobP
Re: differential equation need Help
Yes, ... | 5 | [
-0.0830078125,
-0.050048828125,
0.00238037109375,
0.0198974609375,
0.0031280517578125,
0.03564453125,
-0.01031494140625,
0.0224609375,
-0.017822265625,
0.01104736328125,
0.119140625,
-0.09716796875,
-0.042724609375,
0.028564453125,
-0.00323486328125,
-0.0294189453125,
-0.1025390625,
... | 39,304 | 39304 | |
Solving Trig Identities??
January 13th 2009, 02:47 PM
shanzwhaat
Solving Trig Identities??
For my homework tonight, there is this one problem that is supposed to be easy but i can't figure it out.
Solve for exact solutions in the interval [0degrees, 360degrees)
[ means include, & ) means exclude
2si... | 4 | [
-0.04443359375,
0.1005859375,
0.0086669921875,
0.060791015625,
0.01611328125,
0.0108642578125,
-0.021728515625,
0.00092315673828125,
0.01141357421875,
-0.03857421875,
0.04833984375,
-0.1328125,
0.048095703125,
0.03271484375,
0.0908203125,
-0.0712890625,
-0.0277099609375,
-0.0009918... | 39,305 | 39305 | |
Statistics help!
November 28th 2007, 01:06 PM
monkeydoodie
Statistics help!
Question:
10 Honda Civic owners and 12 Toyota Corolla owners were randomly selected, and asked about their cars gas mileage. Yielded the following:
Honda - 28.5, 31.0, 29.6, 26.8, 36.2, 32.4, 30.8, 27.4, 26.6, 29.7.
Toyota ... | 4 | [
0.0264892578125,
0.033203125,
0.06298828125,
-0.0034027099609375,
-0.002166748046875,
0.00396728515625,
-0.03857421875,
0.125,
-0.0732421875,
0.007568359375,
0.055419921875,
-0.08251953125,
0.0390625,
-0.036376953125,
0.00457763671875,
-0.06298828125,
-0.01104736328125,
-0.00198364... | 39,306 | 39306 | |
Counting conjugacy classes in simple groups of Lie type
up vote 7 down vote favorite
2
Finite groups of Lie type include those obtained as rational points of a connected simple algebrraic group over a finite field $k = \mathbb{F}_q$ of characteristic $p$: these are split or
quasi-split. There are also several families... | 5 | [
-0.033935546875,
0.012451171875,
-0.0050048828125,
0.060791015625,
-0.10107421875,
0.033203125,
0.006927490234375,
0.018310546875,
0.0830078125,
-0.059814453125,
0.05029296875,
0.0189208984375,
-0.029052734375,
0.0206298828125,
-0.0732421875,
0.025390625,
-0.078125,
-0.04248046875,... | 39,307 | 39307 | |
Repetends and families
July 27th 2006, 11:16 PM
Bartimaeus
Repetends and families
List the families of repetends of fractions with the denominator 73. Give an example of a fraction which has each repetend.
Please include:
- The correct number of families
- Any six correct repetends
- The remaini... | 4 | [
-0.06201171875,
-0.0147705078125,
-0.08056640625,
0.010498046875,
-0.006134033203125,
-0.01220703125,
0.027587890625,
-0.0167236328125,
-0.01220703125,
0.028564453125,
0.0517578125,
-0.059814453125,
0.0576171875,
0.00439453125,
-0.04150390625,
-0.0576171875,
-0.06591796875,
0.03710... | 39,308 | 39308 | |
Find SURFACE AREA of a pyramid (hexagonal-base)?
December 4th 2007, 10:43 PM #1
Newbie
Joined
Nov 2007
Posts
7
How to find the surface area of a pyramid which has a regular hexagonal base of edge 6 cm and a height of 8 cm?
Surface area
The area of the base should be simple, so the problem is the six... | 4 | [
0.045654296875,
0.0269775390625,
0.01312255859375,
-0.0284423828125,
-0.035400390625,
0.03759765625,
-0.09375,
0.1376953125,
-0.06689453125,
-0.0045166015625,
-0.045654296875,
-0.04443359375,
-0.038818359375,
-0.01361083984375,
0.0115966796875,
0.06689453125,
-0.09521484375,
0.0144... | 39,309 | 39309 | |
Proving the IVP using the lemma...
November 21st 2009, 01:28 PM #1
Proving the IVP using the lemma...
Lemma: Let be a transitive relation on the interval . If each has a neighborhood such that whenever and , then .
First, I am not sure how exactly to prove the lemma, which is the first part of my pro... | 4 | [
-0.000827789306640625,
0.037353515625,
0.029541015625,
-0.0294189453125,
-0.03662109375,
0.10107421875,
0.08251953125,
-0.0673828125,
-0.046142578125,
-0.052490234375,
-0.057373046875,
-0.005279541015625,
0.10791015625,
0.044189453125,
0.0242919921875,
0.05859375,
0.0419921875,
-0.... | 39,310 | 39310 | |
Prove Inn(G) is isomorphic to G
April 12th 2011, 06:50 AM #1
Junior Member
Joined
Apr 2010
Posts
58
Prove Inn(G) is isomorphic to G
Show that for G = S3, Inn(G) G.
Here is what I have:
Construct φ: G à Inn(G) by φ(a) = ia a G.
(Prove φ is a homomorphism)
Pick a G
Then φ(ab) = iab
... | 5 | [
-0.08251953125,
0.00909423828125,
0.0732421875,
-0.0306396484375,
-0.107421875,
0.021240234375,
0.1396484375,
-0.0693359375,
-0.022705078125,
-0.038818359375,
0.041015625,
-0.06103515625,
0.04150390625,
-0.0223388671875,
0.00225830078125,
0.02783203125,
-0.007049560546875,
0.009948... | 39,311 | 39311 | |
Strict applications of deformation theory in which to dip one's toe
up vote 19 down vote favorite
8
I hesitate to ask a question like this, but I really have tried finding answers to this question on my own and seemed to come up short. I readily admit this is due to my ignorance of algebraic
geometry and not knowing w... | 4 | [
-0.1220703125,
0.01226806640625,
0.044677734375,
-0.005706787109375,
-0.0220947265625,
-0.0216064453125,
0.0732421875,
0.03759765625,
0.01031494140625,
0.01031494140625,
0.0101318359375,
-0.01025390625,
-0.0498046875,
0.0751953125,
0.01348876953125,
-0.0159912109375,
-0.056396484375,... | 39,312 | 39312 | |
Talk:Firework Star
From Minecraft Wiki
[edit] Crafting
So, uh... is the crafting square messed up, or do we just not know how to craft these things yet? Cobalt32 18:35, 7 December 2012 (UTC)
I personally do not know how to craft it, and I set the page up, if you do, I can put it in. Cultist O 18:36, 7 December ... | 4 | [
-0.04931640625,
0.03369140625,
-0.044921875,
0.07958984375,
0.01348876953125,
-0.046875,
-0.041748046875,
-0.04150390625,
-0.03564453125,
-0.008056640625,
-0.0126953125,
-0.0126953125,
0.0108642578125,
-0.09375,
-0.026123046875,
0.02490234375,
-0.00921630859375,
-0.09912109375,
-... | 39,313 | 39313 | |
Integral Approximation
October 9th 2012, 11:22 AM
renolovexoxo
Integral Approximation
I got this assignment and I honestly don't even know where to begin. My teacher isn't making much sense to me at the moment, so if anybody can help me I would greatly appreciate it!
October 9th 2012, 11:45 AM
TheEmptySet
Re:... | 5 | [
-0.03759765625,
-0.0223388671875,
0.06103515625,
-0.01007080078125,
-0.03759765625,
0.0169677734375,
-0.03857421875,
0.111328125,
-0.0247802734375,
0.0301513671875,
-0.06689453125,
0.06982421875,
0.051025390625,
-0.0732421875,
-0.0245361328125,
-0.09375,
0.0517578125,
-0.0110473632... | 39,314 | 39314 | |
solving system by substitution Help
January 9th 2008, 05:15 PM
yvonne
solving system by substitution Help
1. $Y=\sqrtX$
$Y=x-6$
2. $Y=|X|$
$Y=X+2$
3. Point $P$ is on the line $3X+Y=26$ and it is 10 units from the origin. Determine the coordinates of P
January 9th 2008, 05:32 PM
galactus
... | 4 | [
-0.004180908203125,
-0.0625,
-0.0673828125,
-0.02099609375,
-0.0225830078125,
0.0654296875,
-0.0260009765625,
0.034912109375,
0.000579833984375,
-0.0634765625,
0.173828125,
0.07275390625,
0.0111083984375,
0.040283203125,
-0.041015625,
0.0016937255859375,
-0.08740234375,
-0.04589843... | 39,315 | 39315 | |
positive element
Positive elements
Idea
In classical mathematics, an element of a poset is positive if and only if it not a bottom element.
A more subtle definition is needed in constructive mathematics; analogously to how “nonempty sets” may need to be replaced by inhabited sets. In mathematics that is both constru... | 4 | [
0.017822265625,
-0.007598876953125,
0.042236328125,
-0.0732421875,
0.000377655029296875,
-0.034423828125,
0.0107421875,
0.05615234375,
0.076171875,
0.054443359375,
0.01483154296875,
0.0091552734375,
0.1328125,
-0.0128173828125,
0.0791015625,
0.050048828125,
0.09228515625,
-0.019409... | 39,316 | 39316 | |
Two logarithmetic problems, solve for x
December 18th 2008, 09:24 AM #1
Member
Joined
May 2008
Posts
112
Two logarithmetic problems, solve for x
Attached are the problems.
For the first problem, the x cancels out each other. So how do I solve for x?
For the second problem, I don't know how to m... | 4 | [
-0.037353515625,
0.0087890625,
-0.003509521484375,
0.034912109375,
-0.01226806640625,
-0.1298828125,
0.031494140625,
-0.0245361328125,
-0.0089111328125,
-0.0018768310546875,
0.036376953125,
-0.043212890625,
0.026611328125,
0.052734375,
0.07275390625,
0.0194091796875,
-0.09033203125,
... | 39,317 | 39317 | |
Midpoint of a Line Segment
Midpoint in 3D
If A = (x[1], y[1], z[1]) and B = (x[2], y[2], z[2]) are the endpoints of a line segment, the midpoint of the line segment is given by:
Examples
Calculate the coordinates of the midpoint from the line segment AB.
Calculate the coordinates of Point C in the line segment AC,... | 4 | [
-0.04736328125,
0.0072021484375,
-0.043701171875,
-0.0576171875,
0.033203125,
-0.019775390625,
0.006683349609375,
0.0771484375,
-0.03662109375,
0.0103759765625,
-0.020751953125,
-0.076171875,
0.014892578125,
0.022216796875,
-0.0284423828125,
0.0927734375,
-0.052978515625,
-0.041748... | 39,318 | 39318 | |
Optimal reference for tensor product of symmetric bilinear forms?
up vote 7 down vote favorite
1
This is just a reference request on a relatively elementary level (for which I apologize in advance), but every time I bump into this question I suspect I'm missing the "correct" conceptual setting.
In the simplest case, o... | 4 | [
-0.08837890625,
-0.05859375,
0.055908203125,
0.0181884765625,
-0.026611328125,
0.0693359375,
-0.0458984375,
-0.0086669921875,
-0.07080078125,
-0.041748046875,
-0.048828125,
0.068359375,
-0.061279296875,
0.040283203125,
0.01220703125,
0.1513671875,
-0.03955078125,
0.036376953125,
... | 39,319 | 39319 | |
How do I find the derivative of this problem?
October 6th 2013, 07:01 AM
rhcprule3
How do I find the derivative of this problem?
f(x)=x2+2(3x2−3)(x2−2)http://webwork.morris.umn.edu/webwor...144/char3A.png
Do I just multply out the top to get f(x) and then get the derivative by the quotient rule from the... | 5 | [
0.00408935546875,
-0.0184326171875,
-0.03173828125,
-0.037109375,
0.0033111572265625,
-0.015625,
-0.029296875,
0.0135498046875,
0.02587890625,
0.04296875,
0.103515625,
-0.052734375,
-0.0035552978515625,
-0.03173828125,
0.00811767578125,
0.03857421875,
-0.03271484375,
0.025146484375... | 39,320 | 39320 | |
a special measurable function
September 4th 2011, 11:51 AM #1
Newbie
Joined
Jan 2011
Posts
24
a special measurable function
Hi,
I have a bdd Lebesgue measurable function $h$ on $\mathbb{R}$ such that h(x)=h(x+1) a.e. on $\mathbb{R}$. Define $h_k(x)=h(kx)$.
How do I prove the following:
(i)... | 5 | [
-0.045654296875,
0.041259765625,
0.0291748046875,
-0.08740234375,
-0.005401611328125,
0.0908203125,
0.107421875,
0.0194091796875,
-0.10302734375,
-0.041748046875,
-0.061767578125,
-0.033203125,
0.07470703125,
-0.0277099609375,
-0.053466796875,
0.005645751953125,
0.054931640625,
-0.... | 39,321 | 39321 | |
Pseudo-Geometric Series
October 4th 2008, 05:59 PM
icemanfan
Pseudo-Geometric Series
Find a way to obtain an explicit formula, in terms of r such that -1 < r < 1, for $\sum_{n=1} ^{\infty} n^pr^{n-1}$, for any positive integral choice of p.
October 4th 2008, 07:03 PM
Soroban
Hello, icemanfan!
I haven... | 5 | [
-0.07958984375,
-0.00012493133544921875,
-0.032470703125,
0.0274658203125,
0.013916015625,
-0.032958984375,
-0.035400390625,
0.09228515625,
0.01373291015625,
-0.0223388671875,
-0.146484375,
0.05078125,
0.0242919921875,
0.0537109375,
-0.00640869140625,
-0.07763671875,
0.03662109375,
... | 39,322 | 39322 | |
Math Help
October 3rd 2007, 06:41 AM #1
Member
Joined
Sep 2007
Posts
222
Solving
Hey i got a questions, im not sure how to solve the following equation for 't'. How would i do it?
2.4 = sqrt(2.1^2 + (0.049*t^2)^2)
Thanks
First square:
$<br /> <br /> 2.4^2 = 2.1^2 + 0.049^2 t^4<br />$... | 4 | [
0.05810546875,
0.0233154296875,
0.08251953125,
0.031494140625,
-0.08056640625,
-0.0576171875,
-0.061279296875,
0.0791015625,
0.054931640625,
-0.04150390625,
0.0296630859375,
-0.00506591796875,
0.01422119140625,
0.03125,
-0.06689453125,
0.033447265625,
-0.02099609375,
-0.06201171875... | 39,323 | 39323 | |
Behavior of externally-infinite elements in ultrapowers of $\langle HF,\epsilon\rangle$
up vote 3 down vote favorite
Consider the structure $\langle HF,\epsilon\rangle$ (the hereditarily finite sets with the epsilon-relation). An ultrapower of this structure will have externally-infinite elements -- elements not
gener... | 4 | [
-0.03271484375,
-0.049072265625,
-0.0673828125,
0.031982421875,
0.00182342529296875,
-0.0159912109375,
0.047607421875,
-0.0255126953125,
0.003936767578125,
-0.0615234375,
-0.040283203125,
-0.0128173828125,
0.0128173828125,
-0.03857421875,
-0.011474609375,
-0.0023651123046875,
0.04736... | 39,324 | 39324 | |
log-likelihood of ito diffusion
up vote 3 down vote favorite
2
Consider a diffusion process:
$ \text{d}X_t = f(X_t)\text{d}t + \text{d}W_t$
I've seen it given that the log-likelihood of the path is proportional to the Onsager-Machlup functional
$ \int_0^T \left(\frac{1}{2} \left|\dot{x}-f(x)\right|^2+\frac{1}{2}\na... | 4 | [
-0.08447265625,
-0.1123046875,
0.058837890625,
-0.0341796875,
0.07666015625,
-0.0205078125,
0.035400390625,
0.06982421875,
0.06103515625,
0.059326171875,
0.01519775390625,
0.054443359375,
0.0400390625,
-0.038818359375,
0.01287841796875,
0.0771484375,
0.00579833984375,
0.0068359375,... | 39,325 | 39325 | |
Arithmetic Sequence
December 13th 2009, 04:50 AM #1
Newbie
Joined
Apr 2009
Posts
16
Arithmetic Sequence
The rth term of an arithmetic progression is 1+4r. Find, in terms of n, the sum of the first n terms of the progression?
Thanks
Hello p4pri
When $r=1$ we get the first term, which is $1+4... | 4 | [
-0.04150390625,
0.00156402587890625,
0.072265625,
-0.115234375,
-0.051513671875,
0.046875,
-0.02587890625,
0.0869140625,
-0.04931640625,
0.01312255859375,
-0.059326171875,
0.037841796875,
-0.00133514404296875,
-0.00482177734375,
-0.083984375,
-0.0264892578125,
0.01312255859375,
-0.... | 39,326 | 39326 | |
INSTRUCTIONS
instructions to the proof checker
Major Section: PROOF-CHECKER
See proof-checker for an introduction to the interactive ``proof-checker'' goal manager, which supports much more direct control of the proof process than is available by direct calls to the prover
(as are normally made using defthm or thm)... | 5 | [
-0.038330078125,
0.06689453125,
-0.01171875,
-0.01336669921875,
0.08544921875,
-0.02294921875,
0.039306640625,
0.0517578125,
-0.0035400390625,
0.06396484375,
0.007110595703125,
-0.0712890625,
0.030029296875,
0.0174560546875,
0.036865234375,
-0.029541015625,
-0.0341796875,
-0.023559... | 39,327 | 39327 | |
CELESTIAL MECHANICS 8
1
CHAPTER 8
PLANETARY MOTIONS
8.1 Introduction
The word “planet” means “wanderer” (πλάνητες αστέρες − wandering stars); in
contrast to the “fix... | 5 | [
0.018310546875,
0.01226806640625,
0.050048828125,
0.01397705078125,
0.032958984375,
-0.0169677734375,
0.054931640625,
-0.00156402587890625,
0.07080078125,
0.06298828125,
0.028076171875,
-0.029052734375,
-0.00145721435546875,
-0.0888671875,
-0.0167236328125,
-0.08447265625,
-0.0996093... | 39,328 | 39328 | |
Algrbra help
July 30th 2008, 01:10 PM #1
Member
Joined
Jul 2008
Posts
89
Algrbra help
I am working on a project for school and there is one question I do not understand. Could someone please help me?
Project:
1.Find the high temperature for a certain city in the US. Use the internet to find tem... | 4 | [
0.01397705078125,
0.0181884765625,
0.016845703125,
0.033935546875,
-0.01361083984375,
0.020751953125,
-0.036376953125,
-0.00909423828125,
-0.039794921875,
0.0595703125,
0.060546875,
-0.0693359375,
0.040283203125,
-0.057861328125,
0.06591796875,
0.060791015625,
-0.06494140625,
-0.11... | 39,329 | 39329 | |
Finding x in fraction with scientific notation
September 30th 2010, 09:34 AM #1
Newbie
Joined
Sep 2010
Posts
1
Finding x in fraction with scientific notation
Hi I need help with this problem...I cant figure it out...help would be appreciated! (Trying to find x)
$\frac{\ 10^8}{10^5} = \frac{\ x}{10^9... | 4 | [
-0.049072265625,
0.0693359375,
0.017822265625,
0.06201171875,
0.019775390625,
-0.0380859375,
-0.001007080078125,
0.01214599609375,
-0.04248046875,
-0.011474609375,
0.0284423828125,
-0.061279296875,
0.03955078125,
0.1259765625,
0.009033203125,
0.06884765625,
-0.044921875,
0.07080078... | 39,330 | 39330 | |
Need help with a definite integral please
May 27th 2006, 07:38 AM #1
Junior Member
Joined
Apr 2006
Posts
25
I would appreciate advice on solving the following problem.
Evaluate the definite integral:
integral (upper limit 2, lower limit 1) [ 2x (x^2 +1 )] dx
Here is my own attempt.
Ste... | 5 | [
-0.07958984375,
0.033203125,
0.103515625,
0.010009765625,
0.04052734375,
-0.0089111328125,
-0.05029296875,
0.022216796875,
0.00164031982421875,
-0.09326171875,
0.0081787109375,
-0.11376953125,
-0.022216796875,
0.040283203125,
-0.0830078125,
-0.051025390625,
-0.006591796875,
0.04345... | 39,331 | 39331 | |
Is a rhombus rigid on a sphere or torus? And generalizations.
up vote 15 down vote favorite
5
If a rectangle is formed from rigid bars for edges and joints at vertices, then it is flexible in the plane: it can flex to a parallelogram. On any smooth surface with a metric, one can define a
linkage (e.g., a rectangle) wh... | 5 | [
0.00531005859375,
-0.0546875,
-0.05908203125,
-0.061279296875,
0.00823974609375,
0.037109375,
0.0281982421875,
0.08935546875,
0.0177001953125,
0.000812530517578125,
-0.029541015625,
0.05419921875,
0.00079345703125,
0.045654296875,
-0.036376953125,
-0.10009765625,
-0.0023651123046875,... | 39,332 | 39332 | |
help
In the second equation, solve for $\dfrac{1}{p}$. First $q = \dfrac{9}{2p}$. Then, multiply both sides by $\dfrac{2}{9}$. So, $\dfrac{2q}{9} = \dfrac{1}{p}$. Then $\dfrac{2q}{9} + \dfrac{1}{q} = 1$.
Now, solve for $q$.
Note: There are a number of ways to solve the system of equations. You first need an expression... | 4 | [
-0.07275390625,
0.00616455078125,
0.055908203125,
0.033447265625,
-0.029296875,
0.0322265625,
0.027099609375,
0.09326171875,
0.007659912109375,
-0.026123046875,
-0.009033203125,
-0.040771484375,
0.029541015625,
0.0927734375,
-0.015625,
-0.006500244140625,
-0.091796875,
0.0041198730... | 39,333 | 39333 | |
de moivre ques involving tan
August 4th 2011, 08:42 AM
blueyellow
de moivre ques involving tan
how does one go from
[Im(cos theta + i sin theta)^3]/[Re(cos theta + i sin theta)^3]
to
=[3cos^2 theta sin theta - sin^3 theta]/[cos^3 theta - 3 cos theta sin^2 theta]
I heard it's something to do w... | 5 | [
-0.11669921875,
0.087890625,
-0.10400390625,
0.044189453125,
-0.021240234375,
-0.007110595703125,
0.035888671875,
-0.07763671875,
0.115234375,
0.00799560546875,
0.048583984375,
-0.0021514892578125,
0.037353515625,
0.056884765625,
0.055419921875,
0.0164794921875,
-0.0634765625,
0.04... | 39,334 | 39334 | |
Homework Help
Posted by G on Thursday, June 12, 2008 at 12:25pm.
Quadratic Formula
Using +/- for plus or minus
Using \/ radical sign
*****************_________
Formula: -b +/- \/b^2-4ac
********____________________
*****************2a
Equation:
x^2 - 25 = 0
Books says answer is 5 and -5. I can get the 5. I do... | 4 | [
-0.04833984375,
-0.00970458984375,
0.06640625,
0.021728515625,
-0.03173828125,
0.02685546875,
-0.01129150390625,
0.046875,
0.048095703125,
-0.025634765625,
0.0517578125,
-0.020751953125,
0.04296875,
0.06494140625,
0.0118408203125,
0.1337890625,
0.005859375,
-0.0289306640625,
-0.0... | 39,335 | 39335 | |
FIND sin alpha and sin beta
April 17th 2006, 07:08 AM #1
Junior Member
Joined
Dec 2005
Posts
40
FIND sin alpha and sin beta
I do not have any idea to deal with this question, can anyone help?
It is given that
$<br /> y = \sin (x) + 4 \sin (x)<br />$,
where 0 <= x <= 2x.
If y has the maxi... | 4 | [
0.00628662109375,
-0.00677490234375,
-0.018310546875,
-0.0225830078125,
-0.0439453125,
0.052001953125,
-0.0206298828125,
0.03564453125,
-0.00072479248046875,
-0.054931640625,
0.0255126953125,
-0.02783203125,
-0.03662109375,
0.055908203125,
0.0458984375,
0.0986328125,
0.03662109375,
... | 39,336 | 39336 | |
how would prove this using for set operations is..... idempotent laws associa........
April 23rd 2010, 07:32 AM #1
Newbie
Joined
Apr 2010
Posts
23
how would i prove this using Set operations
i.e.
the operations i've been given are ........
idempotent laws
associative laws
commutative l... | 5 | [
0.0673828125,
0.0162353515625,
0.05419921875,
-0.05810546875,
-0.0084228515625,
-0.044921875,
0.109375,
-0.03173828125,
-0.037841796875,
0.015869140625,
-0.0380859375,
-0.061767578125,
0.01019287109375,
0.00933837890625,
0.09375,
0.09423828125,
0.012451171875,
0.03515625,
-0.1044... | 39,337 | 39337 | |
Mean number of $n$-simplices per $(n-2)$-simplex in a triangulated $n$-manifold
up vote 4 down vote favorite
Work by Tamura (extending results by Luo and Stong) shows the following.
Theorem: For any closed 3-manifold $M$ and any rational number $4.5 < r < 6$ there is a triangulation $T$ of $M$ for which the aver... | 4 | [
0.00726318359375,
0.040283203125,
0.00799560546875,
-0.052734375,
-0.12060546875,
0.015869140625,
-0.047119140625,
0.04736328125,
0.006317138671875,
0.04541015625,
0.037109375,
-0.11083984375,
0.01123046875,
-0.032470703125,
-0.0126953125,
-0.068359375,
0.050048828125,
-0.033447265... | 39,338 | 39338 | |
Volume 6,
Volume 6, Issue 8, August 1965
•
View Description Hide Description
The structure of cluster expansion which is widely used in statistical mechanics is studied from an algebraic point of view. In doing this, a commutative algebra is constructed which is generated
by partitions of a finite set... | 4 | [
-0.0703125,
-0.0189208984375,
0.053955078125,
0.06982421875,
-0.019775390625,
0.080078125,
0.07666015625,
0.02978515625,
0.08154296875,
-0.05908203125,
0.052490234375,
-0.0299072265625,
0.07080078125,
-0.01275634765625,
-0.02685546875,
-0.00933837890625,
0.0010833740234375,
0.04370... | 39,339 | 39339 | |
he
The ModulaTor
Oberon-2 and Modula-2 Techni... | 4 | [
-0.08740234375,
0.004608154296875,
-0.0732421875,
-0.039306640625,
-0.07373046875,
-0.06396484375,
0.017578125,
0.10595703125,
-0.0185546875,
0.007537841796875,
0.036865234375,
0.0380859375,
0.07421875,
-0.06884765625,
-0.052490234375,
0.03466796875,
-0.07373046875,
-0.041748046875... | 39,340 | 39340 | |
PROJECTILE MOTION AND THE BALLISTIC PENDULUM
Objective
To measure and compare the momentum and kinetic energy before and after an inelastic collision.
Theory
This is a two-parts experiment. In the first part we study projectile motion. In the second part we study the ballistic p... | 4 | [
-0.002166748046875,
0.0732421875,
-0.061279296875,
-0.05419921875,
-0.005462646484375,
0.0162353515625,
-0.00089263916015625,
0.06103515625,
-0.0027618408203125,
0.049072265625,
0.0235595703125,
-0.0029296875,
-0.00115966796875,
0.004638671875,
-0.01055908203125,
-0.02197265625,
0.06... | 39,341 | 39341 | |
Best Numerical Method for Evaluating a Hilbert transform
up vote 3 down vote favorite
2
I have to evaluate a Hilbert transform for some $\mathcal{L}^p(\mathbb{R},\mathbb{C})$-function ($1\leq p<\infty$). I know there are a number of algorithms out there to do it, but I don't have a full
literature overview. I am aware... | 4 | [
-0.11328125,
-0.0172119140625,
0.004150390625,
-0.06201171875,
0.00836181640625,
-0.060546875,
-0.07421875,
0.056640625,
-0.057861328125,
-0.0001773834228515625,
-0.003021240234375,
0.0208740234375,
-0.00927734375,
0.002349853515625,
-0.035888671875,
-0.0283203125,
-0.0074462890625,
... | 39,342 | 39342 | |
The Techniques For Solving Linear Equations And Linear Inequalities
The Techniques For Solving Linear Equations And Linear Inequalities Are Similar, Yet Different. Can You Explain And Give An Example Of Both A Linear Equation And A Linear Inequality That Demonstrates
This Difference?
Linear equations vs. Linear inequa... | 4 | [
-0.07568359375,
0.00506591796875,
0.033935546875,
-0.040771484375,
-0.021240234375,
-0.0289306640625,
-0.09521484375,
0.052734375,
0.003082275390625,
0.044921875,
0.01611328125,
0.01019287109375,
0.07421875,
-0.002716064453125,
0.00067901611328125,
0.061767578125,
-0.038330078125,
... | 39,343 | 39343 | |
Some probability help again please...
March 13th 2008, 03:45 AM #1
Some probability help again please...
Hey guys, just 3 questions this time...
1. Three different machines M1, M2, and M3 were used for producing a large
batch of similar manufactured items. Suppose that 20% of the items were
produced ... | 4 | [
0.00262451171875,
0.042236328125,
0.010498046875,
-0.007049560546875,
0.0302734375,
-0.056884765625,
0.0142822265625,
0.0322265625,
-0.10009765625,
0.032958984375,
0.1259765625,
-0.0263671875,
0.111328125,
-0.039794921875,
-0.0062255859375,
0.07373046875,
0.058837890625,
-0.0578613... | 39,344 | 39344 | |
F
Answers
Here is the proof of the section formula.
Consider any two points A (x [ 1 ], y [ 1 ]) and B (x [ 2 ], y [ 2 ]) and assume that P (x, y) divides AB internally in the ratio m: n i.e. PA: PB = m: n
Draw AR, PS and BT perpendicular to the x-axis. Draw AQ and PC perpendiculars to PS and BT respectively.
In... | 4 | [
-0.0869140625,
-0.00982666015625,
-0.0390625,
-0.0771484375,
0.0269775390625,
0.060791015625,
0.0101318359375,
-0.0191650390625,
-0.00121307373046875,
-0.0537109375,
0.060791015625,
-0.059326171875,
0.0595703125,
0.061279296875,
-0.0263671875,
0.0242919921875,
-0.027099609375,
-0.0... | 39,345 | 39345 | |
Exponential Series Proof
Date: 05/05/2001 at 22:55:22
From: Jake
Subject: Exponents/Algebra
Hi,
I'm having trouble with an exponential question.
In previous parts of the question, they give it that e^x is greater
than or equal to 1 + x for all real values of x. They also tell you
that:
(1+1)(1+(1/2))(1+(1/3)... | 4 | [
-0.0712890625,
0.0517578125,
0.05517578125,
0.02490234375,
-0.03955078125,
-0.08935546875,
0.00640869140625,
0.043212890625,
0.06787109375,
0.0086669921875,
-0.07763671875,
-0.051025390625,
0.0245361328125,
0.04638671875,
0.053466796875,
-0.00823974609375,
-0.025146484375,
0.010620... | 39,346 | 39346 | |
Coin probability problem!
March 18th 2010, 08:46 AM
BabyMilo
Coin probability problem!
A fair coin is flipped 60 times, what is the percent chance of flipping heads 25 or fewer times?
would you solve it this way?
Quote:
binomal
B-(60,0.5)
P(X< or = 25)
so it's 60Cr * 0.5^(r) * 0.5^... | 5 | [
0.046142578125,
0.07421875,
-0.02685546875,
0.00116729736328125,
-0.004058837890625,
-0.0810546875,
0.029052734375,
0.10009765625,
-0.01953125,
0.1513671875,
0.02880859375,
-0.0615234375,
0.02734375,
0.055419921875,
0.051513671875,
0.1142578125,
-0.0078125,
-0.0162353515625,
-0.0... | 39,347 | 39347 | |
Expansions by cube roots of 1 (mod n)
up vote 3 down vote favorite
Fix some integer $n$. I would like to know when it is possible to find a cube root of 1 mod $n$, say $r$, so that it is possible to write
$m = a(r^{2} - 1) + b(r - 1) + c$ mod n
for all $0 \leq m \leq n-1$, with coefficients $a$, $b$ and $c$ that are... | 5 | [
-0.07080078125,
0.0203857421875,
-0.09912109375,
0.1298828125,
-0.00860595703125,
0.01171875,
-0.0269775390625,
0.006591796875,
0.03759765625,
-0.0546875,
-0.0673828125,
0.01324462890625,
0.0234375,
0.034423828125,
-0.000881195068359375,
0.03466796875,
-0.0164794921875,
0.057373046... | 39,348 | 39348 | |
MHF Integral Bee!
August 16th 2009, 02:14 AM #1
MHF Contributor
Joined
May 2008
Posts
2,295
Thanks
7
MHF Integral Bee!
This thread is for pros! If you have a complete and correct solution, post it. Otherwise do not post anything please!
So you post your solution and also your own problem (integr... | 5 | [
0.00311279296875,
0.06201171875,
0.07177734375,
-0.060546875,
0.0027923583984375,
0.002227783203125,
0.020751953125,
0.0302734375,
-0.03515625,
0.0206298828125,
-0.03955078125,
-0.09228515625,
0.0113525390625,
0.0257568359375,
-0.04443359375,
0.03076171875,
0.0791015625,
-0.0065917... | 39,349 | 39349 | |
A few flux questions
May 11th 2011, 04:39 PM #1
Junior Member
Joined
Dec 2010
Posts
30
A few flux questions
1. Let S be the surface $z=x, x^2+y^2<=1$ Find
$\iint (x^2 +y^2)dS$
I know the answer is supposed to be $\sqrt{2}*\pi/ 2$ but can't seem to get there. I've tried evaluating it with the di... | 5 | [
0.01202392578125,
0.020263671875,
0.01904296875,
-0.040283203125,
0.05859375,
-0.0458984375,
-0.03466796875,
0.142578125,
-0.03466796875,
-0.01025390625,
-0.08349609375,
0.044189453125,
0.00031280517578125,
0.0439453125,
-0.055908203125,
0.0267333984375,
0.0269775390625,
-0.0451660... | 39,350 | 39350 | |
i.d. proofs
February 19th 2010, 01:43 PM #1
Member
Joined
Feb 2010
Posts
93
i.d. proofs
Hi:
I am asked to prove the following identities:
a) 2cot2θ≡cotθ-tanθ
b) tan3θ≡3tanθ-tan³θ/1-3tan²θ
I think I should tackle the most complicated side as it is easier to aim for the easier looking side... | 4 | [
-0.04638671875,
-0.02734375,
0.0341796875,
-0.039794921875,
0.06005859375,
-0.0091552734375,
0.06201171875,
-0.0546875,
0.01080322265625,
-0.0184326171875,
0.07177734375,
-0.1123046875,
-0.008056640625,
0.0654296875,
0.04931640625,
-0.017333984375,
-0.05419921875,
0.0869140625,
-... | 39,351 | 39351 | |
tangent bundle of a fiber bundle
up vote 4 down vote favorite
3
my question is very basic (i don't know too much of differential geometry): given a fiber bundle, is there a necessary and sufficient condition for its tangent bundle to be trivial?
i have some ideas, but submitted to some conditions on the cohomology ri... | 4 | [
-0.107421875,
-0.025634765625,
0.05712890625,
-0.00018310546875,
0.0208740234375,
0.03271484375,
0.09228515625,
0.07080078125,
-0.05078125,
-0.004791259765625,
0.08642578125,
-0.0252685546875,
-0.07666015625,
0.001983642578125,
0.0546875,
-0.02294921875,
0.016845703125,
-0.00078964... | 39,352 | 39352 | |
Simplifying complex fraction
October 30th 2010, 08:48 PM #1
Member
Joined
Mar 2010
Posts
150
Simplifying complex fraction
I know I shoudl know this, but it's late and for some reason I am drawing a blank. Any help would be appreciated. Thanks
How does $\frac{\frac{3}{x}}{1+\frac{4}{x^2}}$ simplify t... | 4 | [
0.02685546875,
-0.015625,
0.0031585693359375,
0.05859375,
0.01141357421875,
-0.07568359375,
-0.0164794921875,
0.028564453125,
0.055908203125,
-0.052001953125,
0.05126953125,
-0.09814453125,
-0.02099609375,
0.035400390625,
-0.051513671875,
0.042724609375,
0.0546875,
0.064453125,
-... | 39,353 | 39353 | |
Finding X (Quite easy..)
Your title said to 'find x' and your expression is in 'y'. I'm having trouble untangling your expression. Is it one of these: (1) $3y-1-\frac{1}{2}\left(\frac{2y+6}{8-y}-\frac{5}{3}\right)$ (2)
$3y-1-\frac{1}{2}\left(2y+\frac{6}{8}-y-\frac{5}{3}\right)$ (3) $3y-1-\frac{1}{2}\left(\frac{2y+6}{8}... | 4 | [
-0.09375,
-0.056884765625,
0.031982421875,
-0.037109375,
0.023193359375,
0.0137939453125,
-0.039306640625,
0.01025390625,
-0.006927490234375,
0.01483154296875,
0.03857421875,
-0.045654296875,
-0.00994873046875,
0.0269775390625,
0.0245361328125,
0.031982421875,
-0.0830078125,
0.0061... | 39,354 | 39354 | |
Categories presented with Arrows only, no objects: partial monoids
up vote 1 down vote favorite
2
Hi,
I received an answer to a question a while back. The question was about how we can present a category as a collection of arrows and a large list of algebraic relations between them. One of the
answers I got was about... | 4 | [
-0.017333984375,
-0.06591796875,
-0.01031494140625,
0.001251220703125,
-0.083984375,
-0.010986328125,
-0.055419921875,
0.0242919921875,
0.01318359375,
-0.0238037109375,
-0.032470703125,
-0.07177734375,
-0.05224609375,
-0.0020904541015625,
0.03076171875,
0.04736328125,
0.0322265625,
... | 39,355 | 39355 | |
Mental Math Tricks: Finding Cube Roots of Large Numbers
Date: 06/07/2004 at 11:44:34
From: Karim
Subject: finding the cube root of very large numbers in your head
A friend asked me to pick a number between 100 and 200, cube it, and
give him the answer. After thinking about it, he gave me the original
number that I h... | 4 | [
0.02587890625,
0.04638671875,
-0.043212890625,
-0.020263671875,
-0.07763671875,
-0.0206298828125,
-0.0537109375,
0.08154296875,
-0.05126953125,
-0.020751953125,
-0.059814453125,
0.0625,
0.0284423828125,
0.049560546875,
-0.055419921875,
-0.0233154296875,
-0.0810546875,
0.04516601562... | 39,356 | 39356 | |
Under what hypotheses are schematic fixed points of a flat deformation themselves flat?
up vote 5 down vote favorite
1
This is something of a follow-up question to this one; I hope people won't think this is a duplicate. At least in my head, it seems like a distinct enough question to merit a fresh start.
All my sche... | 4 | [
-0.044921875,
0.0196533203125,
0.011962890625,
-0.0001621246337890625,
0.040283203125,
0.0230712890625,
0.0166015625,
0.01202392578125,
0.00138092041015625,
0.004486083984375,
0.009521484375,
-0.023193359375,
0.00933837890625,
-0.025390625,
0.0093994140625,
0.01953125,
-0.041015625,
... | 39,357 | 39357 | |
uantization
The Story of Nth Quantization
John Baez
September 7, 2013
This is a story that leads up to a puzzle. I wrote it with some help from Toby Bartels.
Chapter 0: Zeroth Quantization
In the beginning there is the empty set. But since we're doing quantum theory, we'll hit the empty set with the functor F: Set... | 4 | [
-0.0537109375,
-0.004058837890625,
-0.004730224609375,
0.04248046875,
-0.053466796875,
0.039306640625,
0.07666015625,
-0.044189453125,
0.05322265625,
-0.037841796875,
0.05419921875,
-0.061767578125,
-0.043701171875,
-0.00445556640625,
-0.00506591796875,
0.022216796875,
-0.04125976562... | 39,358 | 39358 | |
Simple question about vector.
September 17th 2010, 03:58 PM #1
Junior Member
Joined
Nov 2009
Posts
58
Simple question about vector.
Let $\vec{A}$ be a vector with length $|\vec{ A}|$
$\hat{A} \;=\; \frac{\vec{A}}{|\vec{ A}|}$
What is $\frac{\vec{A}}{|\vec{ A}|}$ If $|\vec{A}|$ = 0?
What is... | 5 | [
-0.01519775390625,
0.0034942626953125,
-0.07568359375,
-0.00089263916015625,
0.078125,
0.0732421875,
-0.029541015625,
-0.0625,
0.044677734375,
0.0654296875,
0.08935546875,
-0.015625,
0.0201416015625,
0.027099609375,
-0.048828125,
0.0306396484375,
-0.0537109375,
-0.044189453125,
-... | 39,359 | 39359 | |
Field of Fractions and Extensions
October 8th 2010, 03:10 PM #1
Junior Member
Joined
Aug 2009
Posts
34
Field of Fractions and Extensions
Hello, I'd like some help regarding field extensions.
Let L:K be a field extension. $\alpha \in L$ is algebraic if and only if $K[\alpha] = K(\alpha) \simeq F[X]/(f... | 4 | [
0.0028076171875,
0.0208740234375,
-0.0015106201171875,
0.013916015625,
0.0361328125,
-0.017333984375,
0.0712890625,
-0.0033111572265625,
0.02783203125,
-0.050048828125,
-0.006683349609375,
0.01104736328125,
-0.0177001953125,
-0.017822265625,
-0.051513671875,
0.050048828125,
-0.011962... | 39,360 | 39360 | |
Number of parameters needed to specify a Hermitian matrix of rank r.
up vote 1 down vote favorite
Hi,
i have two questions that seem to bother me lately. Maybe you could help me and/or point me in any related literature.
1) Assume hermitian matrix $H \in \mathcal{C}^{n \times n}$ that has rank $r$. How many real val... | 5 | [
-0.06689453125,
-0.03466796875,
-0.111328125,
-0.0031890869140625,
-0.01806640625,
0.0654296875,
0.0086669921875,
-0.0400390625,
-0.10205078125,
-0.0174560546875,
0.006072998046875,
-0.016357421875,
0.00994873046875,
-0.02490234375,
-0.0172119140625,
-0.0093994140625,
-0.005462646484... | 39,361 | 39361 | |
Linear Matrix question
October 27th 2008, 06:23 PM #1
Member
Joined
Jan 2008
Posts
175
Linear Matrix question
if A is any mxn matrix such that m > n, is it possible to find an nxm matrix B such that $BA=I_n$? why or why not?
the second question is identical just switch m<n.
I dont understand th... | 5 | [
-0.09814453125,
-0.04052734375,
-0.039306640625,
-0.035400390625,
-0.01129150390625,
-0.07177734375,
0.0205078125,
-0.06982421875,
-0.0137939453125,
0.0498046875,
-0.01361083984375,
0.037841796875,
0.04248046875,
-0.0196533203125,
0.02685546875,
0.08251953125,
0.068359375,
0.030395... | 39,362 | 39362 | |
Surface Metric Tensor
Next: Parametric Space Meshing Up: Indirect Triangulation of 3D Surfaces Previous: Surface Representation
Surface Metric Tensor
The basic idea of the indirect triangulation technique consists in the meshing of the planar parametric space and in mapping that mesh to the surface. In order to... | 4 | [
-0.0888671875,
0.00469970703125,
0.0081787109375,
-0.10498046875,
-0.0252685546875,
0.0712890625,
-0.019775390625,
0.07763671875,
-0.00927734375,
-0.036865234375,
0.04443359375,
-0.058349609375,
-0.040283203125,
0.03369140625,
0.0380859375,
-0.056884765625,
-0.01708984375,
0.053710... | 39,363 | 39363 | |
two non-degenerate quadratic forms on $GF(2)^2r$
up vote 0 down vote favorite
I know this:
There are two non-degenerate quadratic forms on $GF(2)^2r$. The hyperbolic form may be taken to be $Q^+(x)=x_0 x_1 + \cdots +x_{2r-2}x_{2r-1}$ ,
and the elliptic form to be
$Q^-(x)=x^2_0 +x_0x_1 +x^2_1 +x_2x_3 + \cdots +x_{2r... | 4 | [
-0.0654296875,
-0.050048828125,
0.0126953125,
-0.017333984375,
-0.048828125,
-0.000522613525390625,
-0.0849609375,
-0.0439453125,
0.00885009765625,
-0.0111083984375,
0.1220703125,
-0.005706787109375,
-0.033935546875,
-0.005615234375,
0.0194091796875,
0.076171875,
-0.06005859375,
-0... | 39,364 | 39364 | |
What makes a distance?
up vote 9 down vote favorite
1
In the answers to my previous question, I learned that there are different concepts of distance, that is of distance-like functions with the usual metric being only the most popular and important
one.
All distance-like functions seem to agree in being
• nonnega... | 4 | [
-0.044189453125,
-0.02392578125,
-0.00909423828125,
-0.109375,
-0.0556640625,
-0.01025390625,
-0.076171875,
0.0859375,
0.087890625,
0.043701171875,
0.0191650390625,
-0.036376953125,
-0.021484375,
0.062255859375,
0.06298828125,
-0.06396484375,
0.142578125,
-0.0712890625,
-0.106933... | 39,365 | 39365 | |
Homework Help
Posted by John on Monday, November 5, 2012 at 9:52am.
A random sample of 384 people in Dalto City, a mid-sized city, revealed 112 individuals who work at more than one job. A second random sample of 432 workers from East Dettweiler, another mid-sized
city, found 91 people who work at more than one job. T... | 4 | [
0.0264892578125,
0.01092529296875,
0.09423828125,
0.029052734375,
0.04736328125,
-0.006134033203125,
-0.03515625,
0.064453125,
-0.008544921875,
0.00095367431640625,
0.00372314453125,
0.005401611328125,
-0.0654296875,
-0.0028076171875,
0.015625,
-0.0634765625,
-0.006317138671875,
0.... | 39,366 | 39366 | |
A Linear Algebra Question
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Let $M$ be a symmetric square matrix with integer coefficients and $M_k$ the matrix obtained by deleting the k-th line and k-th column. If det(M)=0 d... | 5 | [
-0.0089111328125,
0.0235595703125,
-0.00023937225341796875,
0.006439208984375,
0.00909423828125,
0.0220947265625,
0.0146484375,
-0.0986328125,
0.007781982421875,
0.004486083984375,
0.07666015625,
0.0830078125,
0.040771484375,
-0.0185546875,
-0.09033203125,
0.05224609375,
-0.000164031... | 39,367 | 39367 | |
Pi and Probability
Date: 12/21/97 at 19:34:02
From: Leduc
Subject: Hi
I'm doing a report for my math class on the relation between pi and
probability. I've been looking on the Internet for information, but
eveything I come across is way beyond my level. Could you send me some
info? I'm an 11th grader taking Advanced... | 4 | [
-0.0264892578125,
-0.0185546875,
-0.0576171875,
-0.0142822265625,
-0.08935546875,
-0.0272216796875,
0.043212890625,
0.1337890625,
-0.01904296875,
0.021728515625,
0.0272216796875,
0.006378173828125,
0.0712890625,
0.036376953125,
-0.056396484375,
-0.033203125,
-0.01806640625,
-0.0310... | 39,368 | 39368 | |
Q. on polynomials, plz help!
August 31st 2008, 07:27 PM #1
Newbie
Joined
Aug 2008
Posts
1
Q. on polynomials, plz help!
p(x) is a polynomial of degree>2. When p(x) is divided by x-2, it leaves remainder 1, and when divided by x-3, leaves rem. 3. Find the remainder when p(x) is divided by (x-2)(x-3)
H... | 4 | [
-0.10498046875,
0.016357421875,
-0.04541015625,
-0.002777099609375,
0.022705078125,
0.03955078125,
0.049560546875,
-0.01519775390625,
-0.002838134765625,
-0.01055908203125,
0.01177978515625,
-0.057861328125,
0.04736328125,
-0.01373291015625,
0.017578125,
-0.0712890625,
-0.04174804687... | 39,369 | 39369 | |
Urgent Help Quadratic Fuctions/Relations
July 26th 2007, 10:35 AM #1
Newbie
Joined
Jul 2007
Posts
22
Urgent Help Quadratic Fuctions/Relations
Heres the problem
Your a US general serving in Iraq and have been given orders to bomb a target 20km away. The missile launcher has been programed with an equ... | 4 | [
0.035888671875,
0.04150390625,
0.0263671875,
-0.03466796875,
0.00958251953125,
0.0693359375,
0.013671875,
0.057373046875,
-0.06787109375,
0.0927734375,
0.12109375,
-0.003692626953125,
0.046875,
0.0146484375,
-0.01495361328125,
0.11083984375,
-0.022705078125,
-0.018310546875,
-0.1... | 39,370 | 39370 | |
Normal Distribution
You are here
Normal Distribution
Quick revise
A continuous random variable X follows a normal distribution if it has the following probability density function (p.d.f.):
The parameters of the distribution are m and s^2, where m is the mean (expectation) of the distribution and s^2 is the varianc... | 5 | [
0.0274658203125,
0.046875,
0.00189208984375,
0.048583984375,
-0.0458984375,
-0.047607421875,
-0.0390625,
0.06005859375,
0.01385498046875,
0.02685546875,
0.080078125,
0.046142578125,
0.1240234375,
-0.0198974609375,
-0.0024566650390625,
-0.083984375,
0.09814453125,
-0.01190185546875,... | 39,371 | 39371 | |
Finding the $J$ for a symplectic vector space
up vote 0 down vote favorite
1
I found something strange when I was working on some other problems.
I thought the triple intersection description of the unitary group said that any two of $(g, \omega, J)$ determines the third pointwisely. Then I found I was very wrong: wh... | 4 | [
-0.123046875,
-0.044677734375,
0.05810546875,
0.01007080078125,
-0.0966796875,
-0.0262451171875,
0.03759765625,
-0.054443359375,
0.035888671875,
-0.099609375,
0.07763671875,
0.061279296875,
-0.05029296875,
-0.06884765625,
0.048828125,
0.01953125,
-0.08544921875,
0.05078125,
-0.05... | 39,372 | 39372 | |
Maximal area coverable by $k$ disjoint isosceles triangles contained in a triangle of area 1.
up vote 5 down vote favorite
Given a triangle $\Delta$ of unit area, how much area can always be covered by $k$ isosceles triangles contained in $\Delta$ and intersecting at most at their boundaries?
The answer is easy for ... | 5 | [
0.03125,
0.045166015625,
-0.01007080078125,
-0.0458984375,
-0.0322265625,
-0.1005859375,
0.08251953125,
-0.04833984375,
-0.05078125,
0.049560546875,
-0.038818359375,
-0.09423828125,
-0.017822265625,
0.0274658203125,
0.0634765625,
0.004150390625,
0.08935546875,
-0.052734375,
-0.04... | 39,373 | 39373 | |
: The Breathless Horror and Disgust
HISTOGRAM: The Breathless Horror and Disgust -- by JD Smith
There is something at work in my soul which I do not understand . . . there is a love for the marvellous, a belief in the marvellous, intertwined in all my projects, which hurries me out of the
common pathways of me... | 5 | [
-0.0003833770751953125,
0.0218505859375,
0.0189208984375,
0.056396484375,
0.0191650390625,
-0.00537109375,
0.06396484375,
0.03515625,
-0.006195068359375,
-0.068359375,
-0.08056640625,
0.0262451171875,
0.0361328125,
-0.0478515625,
-0.049072265625,
0.0264892578125,
-0.0439453125,
-0.... | 39,374 | 39374 | |
GCD between a complex and integer
March 25th 2011, 11:33 PM #1
Member
Joined
Jun 2008
Posts
148
GCD between a complex and integer
Suppose I wanted to find the GCD between a complex integer z and an integer. How would I go about doing this?
For instance, suppose $z = 6 + 4i$ and $I = 39$.
We kno... | 5 | [
-0.0294189453125,
0.028564453125,
-0.1201171875,
-0.054443359375,
0.04052734375,
-0.08154296875,
0.004364013671875,
0.072265625,
-0.048095703125,
-0.0712890625,
0.04248046875,
0.0130615234375,
0.0498046875,
0.0361328125,
0.005859375,
-0.0908203125,
0.004974365234375,
0.08984375,
... | 39,375 | 39375 | |
Study on integro-differential equation with generalized p-Laplacian operator
Abstract
We tackle the existence and uniqueness of the solution for a kind of integro-differential equations involving the generalized p-Laplacian operator with mixed boundary conditions. This is achieved by
using some results on the ranges f... | 5 | [
-0.044921875,
-0.0291748046875,
0.1279296875,
-0.07421875,
-0.00164794921875,
-0.0277099609375,
0.04296875,
0.00482177734375,
-0.031982421875,
-0.00543212890625,
-0.0030975341796875,
-0.00067138671875,
-0.05419921875,
0.07177734375,
0.05078125,
0.022216796875,
-0.02734375,
-0.03295... | 39,376 | 39376 | |
Equations: the
Equations: the "Elimination" Method
Date: 11/20/96 at 19:12:23
From: collin
Subject: Easier Ways to Solve Two Equations
Solve the system by using the substitution method
5x - 3y = -36
3x - y = -10
This is what I did, but it seems so involved. Is there an easier way?
... | 4 | [
-0.07421875,
-0.00506591796875,
-0.0299072265625,
-0.0133056640625,
0.03759765625,
0.0164794921875,
-0.01177978515625,
0.0220947265625,
-0.06591796875,
0.0014801025390625,
0.07763671875,
0.052490234375,
0.04931640625,
0.07177734375,
0.031005859375,
0.0294189453125,
-0.0615234375,
0... | 39,377 | 39377 | |
AR(1): Variance of Sample Mean
September 25th 2012, 06:06 AM
lpd
AR(1): Variance of Sample Mean
Hi.
I have an auto-regressive process of order 1, AR(1). Assuming sample size n.
i) I would like to find, $Var(\bar{X})$ of AR(1). Would someone kindly show a source for this result? The correlation is denot... | 4 | [
-0.051025390625,
-0.0732421875,
0.0301513671875,
0.057373046875,
0.0147705078125,
0.0311279296875,
0.059814453125,
0.0302734375,
0.01165771484375,
0.03173828125,
0.0189208984375,
0.08837890625,
0.0216064453125,
-0.049560546875,
-0.03857421875,
-0.0189208984375,
-0.01544189453125,
-... | 39,378 | 39378 | |
Dividing Positive and Negative Exponents
Date: 12/18/97 at 21:21:01
From: Matt
Subject: Dividing positive and negative exponents
I have the problem:
(3^2)^-1 M^-1 N^-2
-------------------
3^-3 M^0 N^3
I am pretty sure that I take care of the 3^2 = 9 first. I think after
that I take 9^-1 = 1/9 But the fractions ... | 4 | [
-0.00113677978515625,
0.03125,
-0.05810546875,
0.07568359375,
-0.007659912109375,
-0.05224609375,
0.00127410888671875,
-0.0076904296875,
0.044189453125,
-0.0031280517578125,
0.0198974609375,
-0.01708984375,
0.044921875,
0.1083984375,
0.0003986358642578125,
0.00439453125,
-0.043212890... | 39,379 | 39379 | |
Help with trigonometric integration
August 5th 2012, 10:22 AM
Giestforlife
Help with trigonometric integration
I have to prove that the integral of 1/(u^2+2) is tan^(-1)(u/sqrt(2)))/sqrt(2)
So far, I've been able to show that 1/(u^2+2) = 1/4(Θ +sin(Θ)cost(Θ)) where Θ=tan^(-1)(u/sqrt(2))
Any help would ... | 5 | [
0.0037841796875,
-0.0299072265625,
0.072265625,
0.0517578125,
0.054443359375,
-0.05908203125,
-0.0634765625,
0.0224609375,
0.06591796875,
-0.006988525390625,
0.0216064453125,
-0.052490234375,
-0.040771484375,
0.0654296875,
-0.07080078125,
-0.0137939453125,
0.08154296875,
-0.0119018... | 39,380 | 39380 | |
Finding change of volume in cylinder - related rate
February 11th 2013, 09:18 AM #1
Member
Joined
Sep 2011
Posts
75
Finding change of volume in cylinder - related rate
Engine cylinder 15 cm deep, being bored out
radius increases by .10 mm/min
How fast does volume change when dia is 9.5 cm?
p... | 5 | [
-0.022216796875,
0.0673828125,
0.0240478515625,
-0.056640625,
0.0283203125,
-0.050048828125,
-0.09912109375,
0.08349609375,
0.0203857421875,
-0.0286865234375,
-0.012939453125,
-0.0322265625,
0.01019287109375,
0.06298828125,
-0.0181884765625,
-0.001068115234375,
0.0289306640625,
0.0... | 39,381 | 39381 | |
Summation of Euler's φ-Function
July 7th 2010, 11:45 AM
elemental
Summation of Euler's φ-Function
Euler's φ-function measures the number of positive integers equal to or less than n,
which are relatively prime to n.
Compute the following:
∑ φ(d)
d|n
Prove this is correct.
The only obser... | 5 | [
-0.0654296875,
0.0186767578125,
0.04736328125,
-0.0079345703125,
0.035888671875,
0.009521484375,
0.09619140625,
0.0262451171875,
0.0537109375,
-0.0186767578125,
0.0096435546875,
0.0732421875,
0.01190185546875,
-0.08935546875,
-0.045166015625,
0.03857421875,
-0.0205078125,
-0.017456... | 39,382 | 39382 | |
Find volume of region, double integrals?
March 30th 2014, 10:28 AM #1
Newbie
Joined
Feb 2014
From
United States
Posts
6
Find volume of region, double integrals?
Third semester calculus; What I'm I doing wrong? I'm being mark wrong for the answer I got.
My problem:
Find the volume of the reg... | 5 | [
0.037353515625,
-0.0107421875,
0.09765625,
-0.10888671875,
-0.0224609375,
-0.0947265625,
-0.095703125,
0.031982421875,
-0.0234375,
-0.040283203125,
-0.02392578125,
0.037841796875,
-0.0166015625,
0.11669921875,
-0.031494140625,
0.0263671875,
0.00738525390625,
-0.1015625,
-0.045410... | 39,383 | 39383 | |
change of variables
January 31st 2009, 05:37 PM #1
Member
Joined
Jan 2009
Posts
91
change of variables
part (a)
use the substitution u = (y-x) to find the general family of solutions of the differential equation:
dy/dx = sin(y-x)
part (b)
show that if a new independant variable is defin... | 4 | [
-0.1552734375,
0.06787109375,
-0.00994873046875,
0.0322265625,
-0.024169921875,
0.054931640625,
0.03759765625,
-0.0771484375,
-0.0263671875,
0.00830078125,
0.0257568359375,
-0.0106201171875,
-0.007659912109375,
0.0096435546875,
-0.03173828125,
-0.06591796875,
-0.047119140625,
-0.04... | 39,384 | 39384 | |
Paradox about high-dimensional spheres!
I have been out of puzzle world for sometime. Leaving IIT Kanpur meant leaving company of theoretical souls such as Ramprasad, Deepanjan and Sagarmoy. Interactions with them drove me to write most of
the articles I write here.
Anyways, I had an interesting chat with Ramprasad a... | 5 | [
0.037353515625,
-0.08837890625,
-0.04443359375,
0.00518798828125,
0.01708984375,
-0.08984375,
-0.0025482177734375,
0.039794921875,
0.07421875,
-0.016845703125,
-0.032958984375,
-0.0274658203125,
0.00921630859375,
0.031982421875,
0.005401611328125,
-0.12109375,
0.046142578125,
-0.05... | 39,385 | 39385 | |
Fredholmness and invertibility in a C* algebra generated convolution-type operators
up vote 1 down vote favorite
1
Let $PC$ be the algebra of complex-valued, piecewise-continuous functions from $[-\infty,+\infty]$, $SO$ be the algebra of bounded, continuous, complex-valued functions on $\mathbb R$ which are
slowly osc... | 5 | [
-0.01806640625,
-0.03125,
0.0098876953125,
0.04296875,
-0.046630859375,
0.07080078125,
-0.01019287109375,
-0.037109375,
0.01904296875,
-0.06787109375,
0.0274658203125,
0.0213623046875,
-0.044921875,
-0.0198974609375,
-0.0234375,
0.0213623046875,
-0.0146484375,
-0.00537109375,
-0.... | 39,386 | 39386 | |
Partial & Implicit Problem ! Help !
Last edited by Zachary; August 5th 2009 at 09:30 PM.
For the first $\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_3}}} = \frac{{{R_1}{R_2} + {R_1}{R_3} + {R_2}{R_3}}}<br /> {{{R_1}{R_2}{R_3}}} \Leftrightarrow R = \frac{{{R_1}{R_2}
{R_3}}}<br /> {{{R_1}{R_2} + {R... | 5 | [
-0.0712890625,
-0.06103515625,
-0.0037384033203125,
-0.003997802734375,
0.0286865234375,
-0.05224609375,
-0.033447265625,
-0.01116943359375,
0.0361328125,
0.005462646484375,
-0.078125,
-0.058837890625,
0.037841796875,
0.03125,
0.08935546875,
-0.01141357421875,
-0.07568359375,
0.030... | 39,387 | 39387 | |
Constructing a cone
Hi Steve,
If you have a cone and cut it, by a line perpendicular to the circular base, and lay it out flat, you will have a sector of a circle. You can construct a cone by reversing this process.
In the diagram above I have labeled the radius of the sector as r inches, the length of the arc as a i... | 4 | [
0.036376953125,
0.05322265625,
-0.04833984375,
0.01507568359375,
-0.04150390625,
-0.0277099609375,
0.004241943359375,
0.11328125,
0.0537109375,
0.04541015625,
-0.004791259765625,
0.0008087158203125,
-0.00408935546875,
0.055908203125,
-0.0162353515625,
-0.031494140625,
-0.11083984375,... | 39,388 | 39388 | |
2.
2. 5 Derivatives of Higher Orders
2.5.1 Definition of higher order derivatives: A derivative of the second order or the second derivative of the function y=f(x) is the derivative of its derivative, i.e.,
The second derivative may be... | 5 | [
-0.07568359375,
-0.038818359375,
0.12890625,
-0.032470703125,
0.033203125,
0.04052734375,
-0.015380859375,
-0.0010833740234375,
0.024169921875,
0.059326171875,
0.0654296875,
0.1005859375,
-0.002227783203125,
-0.03076171875,
-0.002471923828125,
-0.01312255859375,
-0.03662109375,
0.0... | 39,389 | 39389 | |
understanding Steenrod squares
up vote 23 down vote favorite
22
There is a function on Z/2Z-cohomology called Steenrod squaring: Sq^i:H^k(X,Z/2Z) --> H^k+i(X,Z/2Z). (Coefficient group suppressed from here on out.) Its notable axiom (besides things like
naturality), and the reason for its name, is that if a∈H^k(X), the... | 4 | [
-0.0673828125,
0.0439453125,
0.0177001953125,
0.044921875,
0.01214599609375,
0.0556640625,
0.072265625,
-0.039794921875,
-0.01409912109375,
0.0068359375,
0.0291748046875,
-0.02734375,
0.006622314453125,
-0.037353515625,
-0.0306396484375,
0.0244140625,
-0.078125,
0.05322265625,
-0... | 39,390 | 39390 | |
Chemistry and Derivatives!
February 9th 2010, 04:42 PM #1
Newbie
Joined
Feb 2010
Posts
1
Chemistry and Derivatives!
I have a calculus project due tomorrow and help would be greatly appreciated!
The problem: Imagine that .00158 moles of CO2 is contained in a closed pipette whose volume is decreasing a... | 5 | [
-0.060546875,
0.0230712890625,
0.078125,
0.057373046875,
0.0078125,
-0.09521484375,
-0.03662109375,
0.07568359375,
0.03515625,
0.035400390625,
-0.020751953125,
-0.0301513671875,
0.0177001953125,
0.038330078125,
-0.00640869140625,
0.006683349609375,
-0.024169921875,
0.0198974609375,... | 39,391 | 39391 | |
Restart SARSA
Rook Jumping Maze Instructions: Starting at the circled cell in the upper-left corner, find a path to the goal cell marked “G”. From each numbered cell, one may move that exact number of cells
horizontally or vertically in a straight line. How many moves does the shortest path have?
... | 5 | [
-0.0024261474609375,
0.0006256103515625,
-0.060302734375,
-0.0947265625,
-0.062255859375,
0.048095703125,
-0.00250244140625,
0.00469970703125,
-0.00885009765625,
0.080078125,
-0.1064453125,
0.043701171875,
0.016357421875,
-0.003997802734375,
-0.083984375,
0.018310546875,
-0.020019531... | 39,392 | 39392 | |
Family of subsets such that there are at most two sets containing two given elements
up vote 7 down vote favorite
We have a set $S$ with $k$ elements, a positive integer $n$, and subsets $S_1, S_2, \cdots, S_n,$ each with n elements. For any two elements $a,b$ of $S$, there are at most two sets $S_i$ containing
both $... | 4 | [
-0.0240478515625,
0.0235595703125,
0.001556396484375,
-0.01312255859375,
0.00958251953125,
0.0830078125,
0.04345703125,
-0.06201171875,
0.005584716796875,
-0.03564453125,
-0.09326171875,
-0.0302734375,
0.10302734375,
-0.07421875,
-0.01385498046875,
0.0478515625,
0.05908203125,
-0.0... | 39,393 | 39393 | |
probability problem counting techniques.
September 26th 2007, 10:23 PM #1
Junior Member
Joined
Aug 2007
Posts
26
probability problem counting techniques.
can anyone helpe with this problem?:
Companies A,B,C,D, and E each send three delegates to a conference. A committee of 4 delegates, selected by lo... | 4 | [
0.041748046875,
0.0101318359375,
-0.042724609375,
-0.07958984375,
-0.05908203125,
0.05810546875,
0.057373046875,
-0.040771484375,
0.0693359375,
0.03955078125,
0.000537872314453125,
-0.05078125,
0.0004634857177734375,
0.006256103515625,
-0.03076171875,
0.037109375,
0.0341796875,
0.0... | 39,394 | 39394 | |
Converting Logs to Another Base
Date: 04/27/98 at 01:50:52
From: Ashraf Suleman
Subject: Finding the nth log
Hello,
I'm taking a computer programming course in Grade 12 (Pascal), and on
the side I've decided to write a calculator program for use in DOS.
The compiler I'm using, however, only performs logarithms to t... | 4 | [
-0.01202392578125,
0.0201416015625,
-0.033203125,
0.00860595703125,
-0.0023651123046875,
-0.052978515625,
0.017578125,
0.037841796875,
-0.019287109375,
0.0625,
0.006378173828125,
0.002685546875,
-0.013671875,
0.050537109375,
0.02490234375,
0.05078125,
-0.1650390625,
0.11279296875,
... | 39,395 | 39395 | |
Integration: General Power Formula
April 30th 2013, 02:40 PM #1
Member
Joined
Sep 2011
Posts
75
Integration: General Power Formula
Hi. Question - integrate the following function:
28-1-19
(int) (4 + ((e^x))^3) e^x dx
The answer is 1/4(4 + (e^x))^4 + C
doing the work myself, du = 3((4 ... | 5 | [
0.04736328125,
0.01068115234375,
0.057373046875,
0.00494384765625,
-0.043701171875,
-0.0537109375,
0.020263671875,
-0.0174560546875,
0.0185546875,
0.00927734375,
0.07568359375,
-0.08740234375,
-0.0225830078125,
0.012451171875,
0.053466796875,
-0.054443359375,
0.0174560546875,
0.108... | 39,396 | 39396 | |
Proving the binomial coeficient is always a natural number?
July 20th 2010, 06:59 AM #1
Proving the binomial coeficient is always a natural number?
How would one go about proving that:
${ n \choose k }$
is always a natural number? That is, assuming $0 \leq k \leq n$ and that $n = 1, 2, 3, 4...$ and that... | 5 | [
0.08203125,
0.0091552734375,
0.0380859375,
0.0308837890625,
-0.0267333984375,
0.0673828125,
0.00738525390625,
-0.00141143798828125,
-0.00640869140625,
0.1298828125,
-0.12890625,
-0.0235595703125,
-0.04638671875,
0.007415771484375,
0.06298828125,
0.048828125,
0.0693359375,
0.0588378... | 39,397 | 39397 | |
Higher order differential equations, undetermined coefficients?
October 13th 2011, 01:55 PM
stupidoldman
Higher order differential equations, undetermined coefficients?
y''+y=2*x*sin(x)
my Yp=(Ax+B)cos(x)+(Cx+D)sin(x)
but the answers say that Yp is supposed to be (Ax^2+Bx)cos(x)+(Cx^2+Dx)sin(x)
Can... | 4 | [
-0.1328125,
-0.057373046875,
0.029296875,
0.031494140625,
0.029052734375,
0.08935546875,
-0.053955078125,
-0.06298828125,
0.0289306640625,
0.03759765625,
0.11962890625,
-0.0233154296875,
-0.033935546875,
0.018798828125,
0.00555419921875,
0.042724609375,
-0.0103759765625,
0.00619506... | 39,398 | 39398 | |
Math Help
May 29th 2009, 06:28 PM #1
growth
1. Prove that $\log x$ grows more slowly than $x^c$ for any positive number $c$.
Proof. So for $x > (c+1)!$, we have $e^x > \frac{x^{c+1}}{(c+1)!} > x^c$. If we fix $c$ we could probably prove this by induction on $x$ (e.g. fix $c=1$). Now can we somehow "take inv... | 5 | [
-0.04345703125,
-0.0240478515625,
0.008544921875,
0.0208740234375,
0.037109375,
-0.056640625,
-0.0074462890625,
0.0169677734375,
0.0419921875,
0.07080078125,
-0.025634765625,
-0.031494140625,
0.037109375,
0.0133056640625,
-0.0003204345703125,
0.0103759765625,
-0.04052734375,
0.0520... | 39,399 | 39399 |