content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Famous Theorems of Mathematics/Logic
Gödel's completeness theoremEdit
In the following, we state two equivalent forms of the theorem, and show their equivalence.
Later, we prove the theorem. This is done in the following steps:
1. Reducing the theorem to sentences (formulas with no free variables) in prenex form, i... | 4 | [
-0.05517578125,
-0.01312255859375,
0.12109375,
-0.0250244140625,
0.048583984375,
0.10205078125,
0.01092529296875,
0.005706787109375,
0.087890625,
0.08154296875,
0.056640625,
0.03955078125,
0.0181884765625,
-0.00141143798828125,
0.11279296875,
0.006317138671875,
-0.035888671875,
0.0... | 23,500 | 23500 | |
Dirac Lagr in Hermitian form
Is there any way to write the Dirac lagrangian to have symmetric derivatives (acting on both sides)? Of course someone can do that by trying to make the Lagrangian completely hermitian by adding the
hermitian conjugate, and he'll get the same equations of motion (a 1/2 must exist in that ca... | 4 | [
-0.0732421875,
-0.08056640625,
0.06640625,
-0.057373046875,
-0.09716796875,
0.06787109375,
0.06640625,
-0.058837890625,
-0.0302734375,
0.0712890625,
0.11962890625,
-0.01220703125,
-0.033935546875,
0.02685546875,
0.0751953125,
0.06005859375,
-0.068359375,
0.1123046875,
-0.07275390... | 23,501 | 23501 | |
Spiraling integers
I came across a challenge at a site I visit regularly and decided to give it a go.
The challenge was to write a program (in any language) to get a spiraling printout of integers based upon the user input. For example if the user input "5" then the output would be:
1 2 3 4 5
16 17 18 19 6
... | 5 | [
-0.041259765625,
0.03564453125,
-0.0272216796875,
-0.08447265625,
-0.1240234375,
-0.003692626953125,
0.01470947265625,
-0.046875,
0.03173828125,
-0.057373046875,
0.04833984375,
0.04833984375,
0.06982421875,
-0.0157470703125,
-0.068359375,
0.032958984375,
-0.09130859375,
0.047607421... | 23,502 | 23502 | |
Help substituting !
April 15th 2010, 06:04 AM #1
Junior Member
Joined
Jan 2009
Posts
39
Help substituting !
I have
(D^2theta/ds^2)+((2/s)dtheta/ds)+((k^2)/s)theta=0
I am asked to make the subtitution x=2k*sqrt(s) in order to get the above in terms of theta and x.
How do i do this?
I'm... | 5 | [
-0.07958984375,
0.02197265625,
0.027587890625,
0.0145263671875,
-0.0294189453125,
-0.0224609375,
-0.033935546875,
0.01055908203125,
0.06982421875,
0.023193359375,
0.0625,
-0.040283203125,
0.006134033203125,
0.0255126953125,
-0.047607421875,
0.052001953125,
0.034423828125,
0.0961914... | 23,503 | 23503 | |
Inequality question
August 16th 2009, 12:47 PM #1
Newbie
Joined
Aug 2009
Posts
8
Inequality question
If x, y, z are real numbers, show that
(y + z - x)^2 + (z + x - y)^2 + (x + y - z)^2 >= yz + zx + xy.
I simplified it to
x^2 + y^2 + z^2 >= xy + xz + yz
not really sure what Im suppose... | 4 | [
-0.040771484375,
0.031982421875,
0.0030059814453125,
0.05078125,
0.00811767578125,
0.0262451171875,
-0.048828125,
-0.01202392578125,
-0.060546875,
0.01446533203125,
-0.0390625,
0.0478515625,
0.09814453125,
0.00958251953125,
-0.0118408203125,
0.064453125,
0.0030975341796875,
-0.0211... | 23,504 | 23504 | |
Calculating integral value based on similar integral
August 10th 2012, 09:40 AM #1
Newbie
Joined
Jul 2012
From
Seattle
Posts
18
Thanks
2
Calculating integral value based on similar integral
The following definite integral has a known value of say 23.
$\int_{0}^{10}\frac{h(t)dt}{11-t}$
W... | 5 | [
-0.07275390625,
0.018798828125,
0.0103759765625,
-0.12060546875,
-0.0184326171875,
0.0023651123046875,
-0.0201416015625,
0.08447265625,
-0.026611328125,
-0.06005859375,
0.0140380859375,
0.0185546875,
-0.00469970703125,
0.04833984375,
-0.060302734375,
-0.061767578125,
-0.0048217773437... | 23,505 | 23505 | |
Probability -
March 27th 2006, 11:29 PM #1
Junior Member
Joined
Feb 2006
From
New Zealand
Posts
26
A traffic officer has a concealed radar unit that she uses to measure the speed of traffic crossing a bridge. She finds that the mean speed is 84km/h and the standard deviation is 5km/h.
a) What pro... | 5 | [
0.02734375,
0.044189453125,
0.03466796875,
-0.0081787109375,
0.0062255859375,
-0.00518798828125,
-0.027099609375,
0.0556640625,
-0.04638671875,
0.048828125,
0.046630859375,
-0.05517578125,
0.0478515625,
0.0419921875,
-0.0286865234375,
0.029541015625,
0.041015625,
-0.03271484375,
... | 23,506 | 23506 | |
Prove that psquared +qsquared +rsquared +2pqr =1
mathelord
if arc cos[p] +arc cos[q] +arc cos[r] =180,
prove that psquared +qsquared +rsquared +2pqr =1
i need a comprehensive solution
You could start by doing:
[tex]\cos ((arc cos p + arc cos q) + arc cos r)=-1[/tex]
[tex]\cos (arc cosp + arc cosq)cos(arc cosr) - \s... | 5 | [
-0.0810546875,
0.041015625,
0.00012111663818359375,
0.059326171875,
-0.056640625,
0.08642578125,
0.033447265625,
0.0213623046875,
0.06494140625,
-0.00052642822265625,
0.0203857421875,
-0.032958984375,
0.06201171875,
0.11865234375,
0.03271484375,
-0.016357421875,
-0.0120849609375,
-... | 23,507 | 23507 | |
A Simpler Way to Handle Complex Analysis
A better way for designers and engineers to analyze their work is with an FE program that emulates conventional handbooks.
BARNA SZABO
Professor of Mechanics
Washington University
St. Louis, Mo.
szabo@ccm.wustl.edu
IVO BABUSKA
Professor of Aerospace Engineering
University of T... | 5 | [
-0.10009765625,
0.042724609375,
-0.00860595703125,
0.06005859375,
0.01434326171875,
-0.0498046875,
-0.08544921875,
0.099609375,
-0.00970458984375,
-0.002105712890625,
-0.119140625,
0.0079345703125,
0.029541015625,
-0.010498046875,
0.0027313232421875,
-0.08544921875,
-0.00128936767578... | 23,508 | 23508 | |
Linear algebra problem
February 25th 2009, 01:30 PM #1
Member
Joined
Mar 2008
Posts
78
Linear algebra problem
Let ${x}=[x_{1}, x_{2}, ... ,x_{n}]$ be a vector in $\mathbb{R}^{n}$. Prove that $||x|| \leq\sum_{i=1}^n |x_{i}|$.
I am not sure how to start this. I'm guessing I need to use induction but I... | 4 | [
-0.045166015625,
0.0203857421875,
-0.01239013671875,
-0.050048828125,
0.0111083984375,
-0.032958984375,
0.0098876953125,
-0.017578125,
0.00640869140625,
0.00083160400390625,
-0.0615234375,
0.0673828125,
0.041015625,
-0.0030364990234375,
-0.123046875,
0.07763671875,
0.07666015625,
-... | 23,509 | 23509 | |
Vector Space and Linear Transformation
February 2nd 2009, 07:25 AM #1
Vector Space and Linear Transformation
Let V and W be vector spaces over the field F ; suppose that $<br /> \{\vec v_i : i \in I \}$ is a basis for V , listed without redundancy.
Also suppose that for each $<br /> i \in I$, there exists $<br... | 4 | [
-0.0849609375,
-0.058349609375,
-0.0142822265625,
0.032958984375,
0.03759765625,
0.0126953125,
0.022216796875,
-0.047607421875,
0.046875,
-0.058837890625,
-0.053955078125,
-0.045654296875,
0.031494140625,
0.03369140625,
-0.03369140625,
0.02099609375,
0.0252685546875,
0.025512695312... | 23,510 | 23510 | |
Is this correct?
February 28th 2010, 07:48 PM
jzellt
Is this correct?
Solve 3x + 3 = x + 5 mod 11 (= is congruence not equality...)
(3x - x) = (5 - 3) mod 11
2x = 2 mod 11
2x = 13 mod 11
x = 13/2 mod 11
Is this correct?
February 28th 2010, 08:27 PM
dani
No. To be able to divide by an... | 4 | [
-0.1376953125,
0.031494140625,
-0.0021209716796875,
-0.00860595703125,
0.031005859375,
-0.059326171875,
0.052734375,
-0.00970458984375,
-0.052734375,
-0.015380859375,
0.08203125,
-0.00185394287109375,
0.031494140625,
-0.0419921875,
-0.0196533203125,
-0.0167236328125,
-0.0712890625,
... | 23,511 | 23511 | |
differentiation again
May 12th 2008, 02:52 AM #1
Member
Joined
Sep 2007
Posts
176
differentiation again
given $x^{\frac 2 3} + y^{\frac 2 3} = a ^{\frac 2 3}$
find d^2 y / dx^2
my working:
dy/dx = $-(\frac y x )^{1/3}$
d^2 y / dx^2 = ${- \frac 1 3} (\frac y x)^ {- \frac 2 3}$$\mbox{ }$${... | 5 | [
0.0341796875,
-0.0986328125,
-0.03955078125,
-0.017333984375,
-0.06201171875,
-0.041748046875,
-0.056640625,
-0.021728515625,
0.04931640625,
0.0478515625,
0.06787109375,
0.05517578125,
-0.003875732421875,
0.0693359375,
0.050048828125,
0.043701171875,
-0.02392578125,
0.0062866210937... | 23,512 | 23512 | |
vectors problem
February 25th 2007, 04:12 PM #1
Junior Member
Joined
Dec 2006
Posts
28
vectors problem
i know that the definition of a unit vector is one such that if you square all the vectors, add them together, and take the square root, you get 1.
i also know that in order for a vector to be perp... | 4 | [
-0.04150390625,
-0.078125,
-0.0281982421875,
-0.06201171875,
-0.06689453125,
-0.0303955078125,
-0.05126953125,
-0.07763671875,
0.0169677734375,
0.040771484375,
0.01092529296875,
0.0361328125,
0.02099609375,
0.05810546875,
-0.1162109375,
-0.02978515625,
-0.06201171875,
0.0654296875,... | 23,513 | 23513 | |
Parallelogram Help
May 3rd 2007, 05:31 AM #1
Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. State your plan and give proof.
Given: ABCD is a parallelogram with angle 1 congruent to angle 2.
To Prove: ABCD is a rhombus
Plan: ______________... | 4 | [
-0.02783203125,
0.0869140625,
-0.0130615234375,
-0.1494140625,
-0.0198974609375,
0.052001953125,
0.01458740234375,
0.064453125,
-0.01385498046875,
0.0810546875,
0.025146484375,
-0.08349609375,
0.03515625,
0.005035400390625,
0.0196533203125,
-0.05029296875,
-0.034912109375,
0.005737... | 23,514 | 23514 | |
Probability for playing cards
March 4th 2010, 12:31 AM #1
Junior Member
Joined
Aug 2009
Posts
62
Probability for playing cards
Mr.A has 13 cards of the same suit. He withdraws 4 cards from it and makes a number using the digits in the units place of each chosen card, i.e he will take 3 from king whose va... | 4 | [
0.0247802734375,
0.087890625,
-0.10693359375,
-0.0361328125,
-0.034912109375,
0.030029296875,
0.095703125,
0.044921875,
-0.006256103515625,
-0.037353515625,
-0.00506591796875,
-0.040771484375,
-0.0537109375,
0.0306396484375,
-0.034912109375,
-0.0130615234375,
-0.0546875,
0.03393554... | 23,515 | 23515 | |
Differentiability
May 20th 2008, 12:26 AM #1
Member
Joined
Mar 2008
Posts
91
Differentiability
f(x) = x sin(1/x) for every x not equal to 0
0 for x = 0
How do i show whether this function is differentiable or not at x=0. First of all i know that if a function is differentiable at a then lim(h->0... | 5 | [
-0.031494140625,
0.01373291015625,
-0.057861328125,
-0.021484375,
0.005584716796875,
-0.00007152557373046875,
-0.003753662109375,
-0.06884765625,
0.0277099609375,
-0.014892578125,
0.11572265625,
-0.034912109375,
-0.0079345703125,
0.04052734375,
-0.0281982421875,
-0.0281982421875,
-0.... | 23,516 | 23516 | |
Brevet US5917739 - Calculating the average of four integer numbers rounded towards zero in a single instruction cycle
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to calculating the average of four integer numbers, and more particularly to single instruction cycle calculation of... | 4 | [
0.0019683837890625,
-0.002532958984375,
-0.07421875,
-0.11669921875,
0.0072021484375,
-0.04931640625,
-0.0576171875,
0.07080078125,
0.0130615234375,
-0.049072265625,
-0.09423828125,
0.007781982421875,
-0.0198974609375,
-0.0072021484375,
-0.07421875,
-0.058349609375,
0.000463485717773... | 23,517 | 23517 | |
A closer look
Next: Normalization for final result Up: The Angular Component Previous: The Angular Component
Let us take a careful look at the equation,
We note that the x derivative of
If we have instead
This latter equation is in the same form as our original equation. That is,
Or, if we so choose,
This is the... | 4 | [
-0.0859375,
0.025634765625,
0.0291748046875,
0.00860595703125,
-0.0123291015625,
0.040771484375,
-0.01123046875,
-0.056640625,
0.01177978515625,
0.0732421875,
0.05322265625,
0.009765625,
-0.0009765625,
-0.01226806640625,
0.033447265625,
0.08740234375,
-0.07763671875,
0.02294921875,... | 23,518 | 23518 | |
Patent US5528533 - DCT/inverse DCT arithmetic unit using both of a first and second different algorithm to thereby provide an improved combination of speed and accuracy
This application is a continuation of application Ser. No. 08/207,144, filed on Mar. 8, 1994, now abandoned.
BACKGROUND OF THE INVENTION
1. Field of ... | 4 | [
-0.138671875,
0.06884765625,
-0.076171875,
-0.07958984375,
-0.031494140625,
-0.060302734375,
-0.01397705078125,
0.06494140625,
0.054931640625,
-0.034423828125,
0.03564453125,
0.01068115234375,
0.031005859375,
-0.017822265625,
-0.06982421875,
-0.06396484375,
-0.033935546875,
0.14648... | 23,519 | 23519 | |
[SOLVED] Trig equation - Why can't I get it right?!?
May 4th 2010, 10:34 AM
UltraGirl
[SOLVED] Trig equation - Why can't I get it right?!?
Hi. I've been trying to solve this trig. equation 4sin4t + 3cos4t = 0. The answer is meant to be t = $\frac{\pi}{4}-\frac{1}{4}\arctan(\frac{3}{4})$
$<br /> 4sin4t + 3co... | 5 | [
-0.0281982421875,
0.00506591796875,
0.0084228515625,
0.03173828125,
-0.01446533203125,
-0.0113525390625,
-0.06884765625,
0.09521484375,
0.03564453125,
-0.00909423828125,
0.057373046875,
-0.10400390625,
0.040283203125,
0.01519775390625,
-0.006683349609375,
0.01300048828125,
-0.0064697... | 23,520 | 23520 | |
need help with descrete math please
December 6th 2008, 02:29 PM #1
Junior Member
Joined
Nov 2008
Posts
50
need help with descrete math please
Let f:A->B be a function. Prove that f^7 = f°f°f°f°f°f°f is a bijection if and only if f is a bijection.
help meeeeeeeeeeeeeee, thnx!!!
Just prove in g... | 5 | [
-0.038330078125,
-0.01220703125,
0.08447265625,
0.037353515625,
-0.06640625,
0.03369140625,
0.061279296875,
0.003814697265625,
-0.024658203125,
0.05419921875,
-0.037353515625,
-0.06298828125,
0.0072021484375,
0.045654296875,
-0.0118408203125,
0.0301513671875,
0.00066375732421875,
0... | 23,521 | 23521 | |
Halstead Metrics
Halstead Metrics
CodeSonar computes various Halstead metrics, as defined by Maurice H. Halstead in Elements of Software Science (1977). Halstead metrics are based on definitions of operators and operands. These are
language dependent; CodeSonar uses the following definitions when computing Halstead m... | 5 | [
-0.07177734375,
-0.041748046875,
-0.045654296875,
-0.040771484375,
-0.1650390625,
-0.04296875,
-0.053955078125,
0.00848388671875,
0.01953125,
-0.080078125,
0.06884765625,
-0.107421875,
0.01025390625,
-0.0003414154052734375,
-0.072265625,
0.00469970703125,
-0.048828125,
0.0256347656... | 23,522 | 23522 | |
Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain
Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 421657, 24 pages
http://dx.doi.org/10.1155/2010/421657
Research Article
Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain
... | 5 | [
-0.142578125,
0.057373046875,
0.1083984375,
0.09765625,
-0.0322265625,
-0.0198974609375,
0.00106048583984375,
-0.00142669677734375,
-0.0194091796875,
0.055419921875,
-0.00494384765625,
-0.030517578125,
0.0458984375,
0.00009250640869140625,
-0.0130615234375,
-0.0201416015625,
0.013610... | 23,523 | 23523 | |
A sequence, a1=64, a2=66, a3=67, an=8+a(n-3), which of the
Author Message
TAGS:
A sequence, a1=64, a2=66, a3=67, an=8+a(n-3), which of the [#permalink] 29 Mar 2007, 17:53
... | 4 | [
-0.0537109375,
0.04248046875,
-0.0157470703125,
-0.044677734375,
-0.04833984375,
0.0615234375,
0.012451171875,
-0.0169677734375,
0.07373046875,
0.00958251953125,
0.02001953125,
-0.00634765625,
0.05078125,
-0.0859375,
-0.0732421875,
0.05908203125,
-0.0791015625,
-0.0546875,
-0.011... | 23,524 | 23524 | |
finding linear/exponential formulas
suppose f(-3)=5/8 and f(2)=20. Find a formula for f assuming it is
a. linear y=mx +b so slope was 155/8. If I put it into the formula y=19 3/8x -18 3/4
b. exponential
f(20) =20. P=f(t)=ab^t
f(2)=ab[2]=20
f(-3)=ab^-3=5/8
then put one equation over th eother to get b^5=32, so b=2
... | 4 | [
-0.0654296875,
0.002349853515625,
-0.0267333984375,
-0.017822265625,
0.002288818359375,
0.015869140625,
-0.03271484375,
0.04296875,
0.034912109375,
0.08203125,
0.10302734375,
-0.043701171875,
0.021484375,
0.0634765625,
0.10107421875,
0.11962890625,
-0.1455078125,
0.0155029296875,
... | 23,525 | 23525 | |
Simple 3D Vectors question!
March 4th 2010, 11:35 AM
Yehia
Simple 3D Vectors question!
The points A(4,5,10) B(2,3,4) and C(1,2,-1) are three vertices of a parallelogram ABCD. Find vector and Cartesian equations for the sides AB and BC and find the coordinates of D.
I need help please! Very much appreciated!... | 4 | [
-0.10400390625,
0.017578125,
-0.041015625,
-0.1162109375,
0.007720947265625,
0.07421875,
0.0020904541015625,
0.09521484375,
-0.07861328125,
0.061279296875,
-0.0301513671875,
-0.044189453125,
0.0238037109375,
0.018310546875,
-0.08349609375,
0.056640625,
-0.0693359375,
-0.02404785156... | 23,526 | 23526 | |
Math Help
Winter, we're here to help you, but unless you have a try of them yourself, what's the point? The rule of thumb is simplify the easiest parts first, then move to the harder parts... What we have here
is... $\frac{49x}{3(\frac{1}{2})}$. Here the bottom is easiest to simplify. $3(\frac{1}{2})=3 \times \frac{1}... | 4 | [
0.0269775390625,
0.00408935546875,
0.07958984375,
0.001556396484375,
-0.06787109375,
-0.03369140625,
0.04248046875,
0.007354736328125,
0.00173187255859375,
0.0654296875,
-0.04296875,
-0.07568359375,
0.0263671875,
0.0732421875,
0.00189971923828125,
0.033203125,
-0.0947265625,
0.1127... | 23,527 | 23527 | |
Dynamics of a Stochastic Cooperative Predator-Prey System with Beddington-DeAngelis Functional Response
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 927217, 15 pages
http://dx.doi.org/10.1155/2014/927217
Research Article
Dynamics of a Stochastic Cooperative Predator-Prey System with Beddington-DeAngel... | 5 | [
-0.0157470703125,
-0.04248046875,
-0.0205078125,
-0.004180908203125,
-0.0211181640625,
-0.03369140625,
-0.03759765625,
-0.037841796875,
0.06298828125,
0.01904296875,
0.03076171875,
0.0002727508544921875,
0.0693359375,
0.0263671875,
-0.04736328125,
-0.01171875,
0.061279296875,
-0.02... | 23,528 | 23528 | |
Quadratic Equations
April 23rd 2008, 03:49 PM #1
Member
Joined
Apr 2008
Posts
78
Quadratic Equations
5b^2 - 14b - 3 = 0
This is what I did
14 = 14^2 - 4 (5)(-3) / 2(5)
14= 196 + 60 / 10
14= 256 / 10
How do I get the answer?
12x^2 - 5x = 2
I subtracted 2 and got
12x^2 - 5x... | 4 | [
-0.04296875,
0.0218505859375,
0.03759765625,
-0.0162353515625,
-0.10498046875,
0.0830078125,
-0.038330078125,
0.0458984375,
0.025390625,
-0.059326171875,
0.0908203125,
-0.0118408203125,
0.01458740234375,
0.05712890625,
-0.036376953125,
0.08984375,
0.005615234375,
-0.053466796875,
... | 23,529 | 23529 | |
Existence Results for General Mixed Quasivariational Inequalities
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 701858, 8 pages
http://dx.doi.org/10.1155/2012/701858
Research Article
Existence Results for General Mixed Quasivariational Inequalities
Department of Mathematics, COMSATS Institute of Info... | 5 | [
-0.048583984375,
-0.0390625,
0.11376953125,
-0.03662109375,
-0.06884765625,
0.05419921875,
0.00121307373046875,
-0.00872802734375,
0.01104736328125,
-0.010498046875,
0.01953125,
0.06494140625,
0.08837890625,
-0.016845703125,
0.0172119140625,
0.003204345703125,
0.05029296875,
-0.013... | 23,530 | 23530 | |
Implicit Iterative Method for Hierarchical Variational Inequalities
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 472935, 14 pages
http://dx.doi.org/10.1155/2012/472935
Research Article
Implicit Iterative Method for Hierarchical Variational Inequalities
^1Scientific Computing Key Laboratory of Shangh... | 5 | [
-0.006317138671875,
0.01904296875,
0.123046875,
-0.0263671875,
-0.0859375,
-0.015625,
-0.044189453125,
0.087890625,
0.053466796875,
-0.010986328125,
0.00482177734375,
0.02001953125,
0.09326171875,
0.03466796875,
-0.00003886222839355469,
-0.04833984375,
0.0380859375,
-0.058349609375... | 23,531 | 23531 | |
I need help with maths please
March 1st 2009, 07:34 AM #1
I need help with maths please
Hi i have a problem, my exams are coming up in two months but i have no idea about maths, such questions as:
Differentiate withrespect to x
(i)
3x8
(the 8 is the small 8 that does be on the top right hand cor... | 4 | [
-0.0257568359375,
-0.022705078125,
0.029541015625,
0.01806640625,
-0.05517578125,
0.03076171875,
0.0020599365234375,
0.0634765625,
0.006103515625,
-0.0057373046875,
0.0654296875,
-0.07568359375,
0.033447265625,
0.0267333984375,
-0.01007080078125,
0.052490234375,
-0.07275390625,
0.0... | 23,532 | 23532 | |
Factoring help
July 7th 2007, 01:39 PM
starswept
Factoring help
Hi, I need help with this question:
Factor the expressions px^3 + (p-q)x^2 + (-2p-q)x + 2q and abx^3 + (a-2b-ab)x^2 + (2b-a-2)x + 2
I've tried a few different ways, but none of them work out. Thank you for any help!
July 7th 2007, 01:51 P... | 4 | [
-0.0654296875,
0.01409912109375,
0.061279296875,
0.05908203125,
0.04052734375,
0.12060546875,
0.01190185546875,
-0.0517578125,
-0.012451171875,
0.001251220703125,
0.03515625,
-0.0233154296875,
0.0693359375,
0.0087890625,
0.03271484375,
0.07763671875,
-0.033203125,
-0.02392578125,
... | 23,533 | 23533 | |
\documentclass[reqno]{amsart} \usepackage{hyperref} \AtBeginDocument{{\noindent\small 2006 International Conference in Honor of Jacqueline Fleckinger. \newline {\em Electronic Journal of Differential
Equations}, Conference 16, 2007, pp. 1--13. \newline ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.m... | 4 | [
-0.07861328125,
0.06884765625,
0.05029296875,
0.04833984375,
0.06298828125,
-0.0032958984375,
-0.042236328125,
0.062255859375,
0.07373046875,
0.0107421875,
0.049560546875,
-0.060302734375,
-0.0032958984375,
-0.0184326171875,
-0.0556640625,
0.08154296875,
-0.08154296875,
-0.05395507... | 23,534 | 23534 | |
Relative efficiency
December 6th 2008, 10:34 PM #1
Relative efficiency
Suppose that $Y_1, \ Y_2, \ \dotso,\ Y_n$ is a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. Given two unbiased estimators, find their relative efficiency.
$\sigma^2_1 = S^2 = \frac{1}{n-1} \sum^n_{i=1}... | 5 | [
0.013427734375,
-0.0712890625,
0.0247802734375,
0.00848388671875,
0.06689453125,
-0.05224609375,
-0.07666015625,
0.03662109375,
0.01019287109375,
-0.03271484375,
0.01263427734375,
0.07275390625,
0.0247802734375,
-0.058837890625,
0.0390625,
0.05419921875,
0.06396484375,
0.0190429687... | 23,535 | 23535 | |
Testing series for convergence or divergence
April 27th 2010, 08:09 PM
CalculusCrazed
Testing series for convergence or divergence
$\sum _{n=1}^{\infty }{\frac {n!}{{e}^{{n}^{2}}}}$
I tried the ratio test, from my figuring, I got that it diverges. However, the back of the book says otherwise ;)
I end u... | 5 | [
-0.048095703125,
-0.0595703125,
-0.0159912109375,
0.02392578125,
0.0286865234375,
0.0030670166015625,
-0.06787109375,
-0.03271484375,
0.040283203125,
0.006195068359375,
0.0888671875,
0.00885009765625,
-0.0546875,
0.056884765625,
-0.031982421875,
-0.0390625,
0.033203125,
-0.04467773... | 23,536 | 23536 | |
limit of exponential function
August 30th 2010, 03:40 AM #1
Newbie
Joined
Nov 2008
Posts
8
limit of exponential function
Hi there,
I found this line in a book which I would like to understand:
$K \int^{+\infty}_{-\infty}e^{-ax^{2}}dx = K \left(\frac{\pi}{a}\right)^{\frac{1}{2}}$
I tried to... | 4 | [
0.06640625,
-0.01263427734375,
-0.0172119140625,
-0.04150390625,
0.03759765625,
-0.034912109375,
0.033447265625,
-0.0186767578125,
0.0167236328125,
0.126953125,
0.12255859375,
0.05810546875,
0.0211181640625,
-0.01202392578125,
-0.01708984375,
-0.029052734375,
0.01348876953125,
-0.0... | 23,537 | 23537 | |
Favorite challenging math puzzles
You are here: Home → Online resources → Favorite puzzles
Favorite challenging math puzzles
In February 2014, I asked my subscribers for their favorite math puzzle. This collection is the result—a list of puzzles chosen by teachers and parents! This page lists the more challenging puz... | 4 | [
-0.0220947265625,
-0.0145263671875,
0.0118408203125,
0.0038909912109375,
-0.068359375,
-0.026123046875,
0.08642578125,
-0.0184326171875,
0.0106201171875,
0.076171875,
0.00445556640625,
-0.0322265625,
0.031982421875,
0.041259765625,
-0.053466796875,
0.021240234375,
0.0223388671875,
... | 23,538 | 23538 | |
Patent US20040093470 - Parallel processing method for inverse matrix for shared memory type scalar parallel computer
CROSS REFERENCE
[0001] This patent application is a continuation in part application of the previous U.S. patent application, titled “PARALLEL PROCESSING METHOD FOR INVERSE MATRIX FOR SHARED MEMORY TYPE... | 4 | [
-0.10595703125,
0.03076171875,
-0.09619140625,
-0.06298828125,
-0.09716796875,
-0.05517578125,
-0.040283203125,
0.02197265625,
-0.00946044921875,
0.0267333984375,
0.0277099609375,
0.158203125,
0.061279296875,
-0.06787109375,
-0.08154296875,
-0.00244140625,
-0.0284423828125,
0.06030... | 23,539 | 23539 | |
Slope of the perpendicular line on the other line
One way to look at it is this: if y= mx+ b is the equation of a line, then the slope, m, is the tangent of the angle, [itex]\theta[/itex], the line makes with the x-axis. If two lines are
perpendicular then they form a right triangle with the x-axis as hypotenuse. The ... | 4 | [
-0.10400390625,
0.0185546875,
0.04541015625,
-0.10400390625,
-0.042724609375,
0.051513671875,
0.00014209747314453125,
0.06005859375,
0.031494140625,
0.0074462890625,
0.09326171875,
0.00885009765625,
0.08203125,
0.030517578125,
-0.021728515625,
0.08447265625,
-0.059326171875,
0.0368... | 23,540 | 23540 | |
Dynamic system model
Philip Wong
aha! so x[1] = [0 1.1; 0.3 0.5] *[80 20]
Yes.
so say if I want to work out [10], would I do this:
[0^10,1.1; 0.3,0.5^10]*[80,20]
No. The definition of your model really says x
[i+1]
= A x
[i]
, that is, to get state for generation i+1 you matrix multiply A with the state vecto... | 4 | [
-0.05029296875,
0.0498046875,
-0.032470703125,
0.0126953125,
-0.001220703125,
-0.00604248046875,
0.0045166015625,
-0.0113525390625,
0.004302978515625,
-0.04736328125,
0.0458984375,
-0.00408935546875,
0.0546875,
-0.0179443359375,
-0.0189208984375,
0.03369140625,
-0.07666015625,
0.04... | 23,541 | 23541 | |
Problem with an algebra exercice
August 14th 2010, 09:20 AM #3
Newbie
August 14th 2010, 12:47 AM #2
Newbie
August 14th 2010, 12:30 AM #1
Newbie
Completing the square
Expand and simplify the forumla and then use apply Quadratic formula to solve it.
$3(x^2 - 4 \sqrt{3}) - 8x(\sqrt{3} - 1) + 19 = 0$
$3... | 4 | [
-0.0869140625,
-0.036865234375,
-0.00360107421875,
0.05029296875,
-0.0286865234375,
0.12890625,
-0.03759765625,
0.01397705078125,
0.060302734375,
-0.058349609375,
0.09521484375,
-0.0458984375,
0.009765625,
0.0172119140625,
0.020751953125,
0.04150390625,
-0.021728515625,
-0.01226806... | 23,542 | 23542 | |
How can I show f(x)=x2-cosx=0 has exactly 2 solutions?
Originally posted by Hurkyl
One of the cuter ways to prove a function has no zeroes in a certain interval (e.g. [1, ∞) )is to prove that it's left endpoint is positive and that it's increasing throughout the interval
I've already shown that f(x) cannot be ze... | 5 | [
-0.078125,
0.036865234375,
0.0419921875,
0.044921875,
-0.000484466552734375,
0.02734375,
-0.06005859375,
0.111328125,
0.00811767578125,
0.0299072265625,
0.05029296875,
-0.07666015625,
0.036865234375,
0.06884765625,
0.01080322265625,
-0.06396484375,
0.03125,
-0.126953125,
0.083984... | 23,543 | 23543 | |
Properties of Continuous Functions
December 6th 2012, 06:34 PM #1
Member
Joined
Sep 2010
Posts
151
Thanks
1
Properties of Continuous Functions
If i have a continuous function "f" from the reals to the reals and a bounded subset of real numbers "B," is f(B) always bounded?
I'm trying to find some... | 4 | [
-0.041259765625,
-0.00860595703125,
-0.08056640625,
0.031982421875,
-0.040771484375,
0.07080078125,
0.0302734375,
0.002532958984375,
-0.0234375,
-0.0299072265625,
-0.049072265625,
0.076171875,
-0.0047607421875,
0.04736328125,
0.0546875,
0.00665283203125,
0.0299072265625,
-0.0996093... | 23,544 | 23544 | |
Carrier-Based Common Mode Voltage Control Techniques in Three-Level Diode-Clamped Inverter
Advances in Power Electronics
Volume 2012 (2012), Article ID 327157, 12 pages
http://dx.doi.org/10.1155/2012/327157
Research Article
Carrier-Based Common Mode Voltage Control Techniques in Three-Level Diode-Clamped Inverter
^... | 4 | [
-0.02001953125,
0.0235595703125,
-0.015869140625,
0.034912109375,
0.0064697265625,
-0.0245361328125,
-0.045654296875,
0.052978515625,
-0.00958251953125,
0.01177978515625,
0.06494140625,
-0.00396728515625,
0.03173828125,
-0.0498046875,
0.078125,
0.111328125,
-0.04833984375,
0.023315... | 23,545 | 23545 | |
Need help with finding density
1. The problem statement, all variables and given/known data
Assuming the Earth to be comprised of only a uniform density mantle and a uniform density
core and the mean density of the mantle to be 4700 kg=m3, determine the mean density of
the Earth's core. Take Earth's radius to be 6400 k... | 4 | [
0.0546875,
0.0751953125,
0.03466796875,
0.00469970703125,
0.0018463134765625,
-0.011962890625,
-0.06884765625,
0.08544921875,
-0.08935546875,
-0.00714111328125,
-0.0169677734375,
-0.11962890625,
0.0380859375,
0.0185546875,
0.01318359375,
-0.0299072265625,
0.0223388671875,
0.0281982... | 23,546 | 23546 | |
Orthogonal projection onto span of vectors using weighted inner product
July 14th 2008, 06:11 PM #1
Find the orthogonal projection of
$v=\begin{pmatrix}1 \\ 2 \\ -1 \\ 2 \end{pmatrix}$
onto the span of $\begin{pmatrix}1 \\ -1 \\ 2 \\ 5 \end{pmatrix}$ and $\begin{pmatrix}2 \\ 1 \\ 0 \\ -1 \end {pmatrix}$
... | 4 | [
-0.06982421875,
-0.05810546875,
-0.005126953125,
-0.0400390625,
0.028564453125,
-0.032958984375,
-0.003936767578125,
-0.03369140625,
-0.012939453125,
-0.01953125,
-0.048828125,
-0.0595703125,
-0.002105712890625,
-0.02001953125,
-0.12060546875,
0.078125,
0.00860595703125,
-0.0133666... | 23,547 | 23547 | |
Pascal's Trianglw
December 11th 2006, 02:30 PM #1
Newbie
Joined
Sep 2006
Posts
8
Pascal's Trianglw
Oops, sorry for the typo in the title. :|
Need help with these please:
In the expansion of (1-ax)^n, the first three terms are 1-12x-63x^2. Find the values of a and n.
and
In the expansi... | 4 | [
-0.06103515625,
0.09033203125,
-0.00982666015625,
0.041259765625,
-0.07666015625,
0.03173828125,
0.0225830078125,
-0.08203125,
-0.01483154296875,
0.0302734375,
0.0771484375,
-0.01507568359375,
-0.0059814453125,
-0.037841796875,
-0.00982666015625,
0.002166748046875,
-0.06298828125,
... | 23,548 | 23548 | |
solving equation
November 10th 2010, 01:24 PM #1
Newbie
Joined
Nov 2010
Posts
9
solving equation
Hi. I have a maths question on finding the turning points and determining their nature but I can't find the value of x and w.
The equation is z= e^(2x) + e^(-y) + e^(w^2) - e^(ln2x) - 2e^(w) + y
I d... | 4 | [
-0.013671875,
-0.0284423828125,
0.04296875,
0.0712890625,
0.0341796875,
-0.005523681640625,
-0.0189208984375,
0.01220703125,
0.025634765625,
0.016357421875,
0.1455078125,
-0.0791015625,
-0.01129150390625,
0.08349609375,
0.053466796875,
0.07666015625,
-0.11962890625,
-0.06494140625,... | 23,549 | 23549 | |
A bit of Quadratics No calculas answers
June 12th 2009, 10:16 PM #1
A bit of Quadratics No calculas answers
A farmer has 60m of fencing with which to construct three sides of a rectangular yard connected to an existing fence.
a) if the width of the paddock is x metres and the area inside the yard A square met... | 4 | [
0.06787109375,
0.033447265625,
-0.032470703125,
-0.103515625,
0.00156402587890625,
-0.051025390625,
-0.028564453125,
0.009765625,
-0.07177734375,
0.09423828125,
0.03515625,
0.0045166015625,
0.0791015625,
0.10791015625,
0.024169921875,
0.11083984375,
-0.01025390625,
-0.026123046875,... | 23,550 | 23550 | |
On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear Differential Equation
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 787920, 18 pages
http://dx.doi.org/10.1155/2012/787920
Research Article
On the Zeroes and the Critical Points of a Solution of a Second Order Half-Linear... | 5 | [
-0.0859375,
0.038330078125,
0.0849609375,
0.052490234375,
0.0279541015625,
0.02685546875,
-0.09814453125,
0.0986328125,
0.00970458984375,
-0.030029296875,
0.09765625,
-0.0164794921875,
0.03515625,
-0.00677490234375,
-0.03515625,
-0.0179443359375,
-0.054931640625,
-0.13671875,
-0.... | 23,551 | 23551 | |
Free Convection Heat and Mass Transfer MHD Flow in a Vertical Porous Channel in the Presence of Chemical Reaction
Journal of Fluids
Volume 2013 (2013), Article ID 297493, 14 pages
http://dx.doi.org/10.1155/2013/297493
Research Article
Free Convection Heat and Mass Transfer MHD Flow in a Vertical Porous Channel in the... | 5 | [
-0.0042724609375,
-0.031494140625,
0.0390625,
0.0145263671875,
0.008544921875,
-0.06494140625,
0.005218505859375,
-0.0020751953125,
0.044921875,
0.01324462890625,
-0.07666015625,
-0.06298828125,
0.07861328125,
0.0177001953125,
0.014892578125,
-0.037353515625,
-0.0198974609375,
-0.0... | 23,552 | 23552 | |
The meaning of the curvature
September 29th 2009, 05:39 PM
Kaitosan
The meaning of the curvature
Basically, the curvature of a curve at a given point measures how quickly the curve changes direction at that point. But what exactly does that mean? What "direction" changes.... is it an angle?
Suppose the curva... | 4 | [
-0.0654296875,
-0.053955078125,
-0.002471923828125,
-0.02099609375,
-0.045166015625,
0.0179443359375,
-0.05712890625,
0.04052734375,
0.039794921875,
0.0223388671875,
0.07861328125,
0.0263671875,
0.0106201171875,
0.0634765625,
-0.010986328125,
-0.036376953125,
-0.044677734375,
0.008... | 23,553 | 23553 | |
Prove Sequence is Bounded
Definitions: Let {x[n]} be a bounded sequence in Reals.
We define {y[k]} and {z[k]} by
y[k]=sup{x[n]: n [tex]\geq[/tex] k}, z[k]=inf{x[n]: n [tex]\geq[/tex] k}
Claim: (i) Both y[k] and z[k] are bounded sequences
(ii){y[k]} is a decreasing sequence
(iii){z[k]} is an increasing sequence
Proof:... | 5 | [
-0.087890625,
0.020751953125,
-0.000820159912109375,
-0.0159912109375,
0.0308837890625,
0.044189453125,
0.06103515625,
-0.03466796875,
-0.008544921875,
-0.10595703125,
-0.060546875,
0.12109375,
0.0361328125,
0.0235595703125,
-0.00909423828125,
0.0283203125,
0.06396484375,
0.0234375... | 23,554 | 23554 | |
Proof by Induction
August 31st 2010, 07:50 PM #1
Newbie
Joined
Aug 2010
Posts
2
Proof by Induction
n
$\sum$ i(2^i) = (n-1) * 2^(n+1) + 2
i=1
So far if have the base case 1(2^1) = (1-1) * (1+1) + 2
Induction part is giving me problems:
k
$\sum$ i(2^i) = (k-1) * 2^(k+1) + 2 = ((k+1... | 4 | [
-0.08251953125,
0.05419921875,
0.07763671875,
0.07470703125,
0.07373046875,
-0.09521484375,
0.047119140625,
0.04931640625,
-0.01007080078125,
0.02685546875,
-0.1396484375,
-0.107421875,
0.0751953125,
-0.0069580078125,
-0.0135498046875,
0.057373046875,
-0.0196533203125,
0.0278320312... | 23,555 | 23555 | |
Patente US5812992 - Method and system for training a neural network with adaptive weight updating and adaptive pruning in principal component space
CROSS REFERENCE TO RELATED APPLICATION
This application is a continuation of patent application Ser. No. 08/448,770 entitled "METHOD AND SYSTEM FOR TRAINING A NEURAL NETWO... | 4 | [
-0.1171875,
-0.053955078125,
-0.03759765625,
-0.041015625,
-0.0380859375,
0.07421875,
-0.0123291015625,
0.0250244140625,
-0.01519775390625,
-0.07275390625,
0.0240478515625,
0.0986328125,
0.0673828125,
-0.044189453125,
-0.083984375,
-0.027099609375,
-0.008544921875,
0.0966796875,
... | 23,556 | 23556 | |
linearly dependent
April 19th 2009, 02:41 PM #1
Newbie
Joined
Apr 2009
Posts
5
linearly dependent
Hi guys, I need help with the following question:
Given that {X1, X2,..., Xk} is a linearly independent set, show that {X1, X2,..., Xk, y} is linearly dependent if and only if y is in the span {X1, X2,.... | 5 | [
-0.08447265625,
-0.040283203125,
-0.01397705078125,
0.0673828125,
0.05078125,
0.041015625,
0.08056640625,
-0.087890625,
0.00738525390625,
-0.017333984375,
0.051513671875,
-0.00433349609375,
0.0235595703125,
-0.0091552734375,
-0.047607421875,
0.10400390625,
-0.002410888671875,
-0.02... | 23,557 | 23557 | |
Dynamics Question using nonconstant acceleration
1. The problem statement, all variables and given/known data
A particle has an initial speed of 27 m/s. If it experiences a deceleration of a = -(6t) m/s^2, where t is in seconds, determine the distance traveled before it stops.
2. Relevant equations
a = dv/dt
v = ds/... | 5 | [
-0.0302734375,
-0.03466796875,
0.00799560546875,
-0.017822265625,
-0.00115966796875,
0.02294921875,
-0.0634765625,
0.043701171875,
-0.024169921875,
0.0751953125,
0.142578125,
-0.0240478515625,
0.0001888275146484375,
-0.042236328125,
-0.058349609375,
-0.0076904296875,
-0.0009727478027... | 23,558 | 23558 | |
HKC: An Algorithm to Predict Protein Complexes in Protein-Protein Interaction Networks
Journal of Biomedicine and Biotechnology
Volume 2011 (2011), Article ID 480294, 14 pages
http://dx.doi.org/10.1155/2011/480294
Research Article
HKC: An Algorithm to Predict Protein Complexes in Protein-Protein Interaction Networks
... | 4 | [
-0.126953125,
-0.08203125,
-0.005218505859375,
0.01019287109375,
0.059814453125,
-0.01806640625,
-0.019775390625,
0.028076171875,
-0.02587890625,
-0.033447265625,
-0.027587890625,
-0.004974365234375,
0.046630859375,
0.08349609375,
-0.068359375,
0.0224609375,
-0.06982421875,
-0.0112... | 23,559 | 23559 | |
Least-Mean-Square Receding Horizon Estimation
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 631759, 19 pages
http://dx.doi.org/10.1155/2012/631759
Research Article
Least-Mean-Square Receding Horizon Estimation
^1Department of Control and Instrumentation Engineering, Kangwon National University,... | 4 | [
-0.0157470703125,
0.0299072265625,
0.0771484375,
0.05517578125,
0.02587890625,
0.0208740234375,
-0.078125,
0.0279541015625,
0.048828125,
0.0673828125,
-0.032470703125,
-0.044189453125,
0.08056640625,
-0.050537109375,
-0.1513671875,
0.01092529296875,
0.0458984375,
-0.0419921875,
0... | 23,560 | 23560 | |
Weak Form of the Effective Mass Schrodinger Equation
Hi,
I am numerically solving the 2D effective-mass Schrodinger equation
[itex]\nabla \cdot (\frac{-\hbar^2}{2} c \nabla \psi) + (U - \epsilon) \psi = 0[/itex]
where [itex]c[/itex] is the effective mass matrix
[itex]\left( \begin{array}{cc}
1/m^*_x & 1/m^*_{xy} \\... | 4 | [
0.0189208984375,
-0.01226806640625,
0.0279541015625,
-0.0390625,
0.025390625,
0.046630859375,
-0.021728515625,
0.00933837890625,
-0.12255859375,
-0.039306640625,
0.0556640625,
0.0111083984375,
-0.049560546875,
0.020751953125,
0.07568359375,
0.1162109375,
0.0196533203125,
-0.0351562... | 23,561 | 23561 | |
Latest content added for UNT Digital Library Collection: UNT Theses and DissertationsA Comparative Study of Non Linear Conjugate Gradient MethodsCenters of Invariant Differential Operator Algebras for Jacobi Groups of Higher RankNatural Smooth Measures on the Leaves of the Unstable Manifold of Open Billiard Dynamical S... | 4 | [
-0.1591796875,
-0.0322265625,
0.02001953125,
0.0179443359375,
-0.02685546875,
0.0169677734375,
0.00173187255859375,
0.035888671875,
-0.05078125,
-0.10986328125,
0.05859375,
-0.04736328125,
-0.025146484375,
-0.00274658203125,
-0.0225830078125,
-0.037109375,
-0.0179443359375,
-0.0078... | 23,562 | 23562 | |
What Is The Subject? I Need Help!
March 27th 2008, 12:20 AM
phillychum
What Is The Subject? I Need Help!
Okay.. it says on my assignment ..
"to solve an equation we sometimes have to change the subject"
first of all.. what is the subject?
thats the first question. and then the second question says... | 4 | [
-0.0419921875,
0.04736328125,
0.00518798828125,
0.0400390625,
-0.00579833984375,
0.0771484375,
0.0341796875,
-0.034912109375,
0.10546875,
0.07958984375,
-0.005157470703125,
0.0289306640625,
-0.032470703125,
0.056396484375,
0.052001953125,
0.03369140625,
-0.09326171875,
-0.060058593... | 23,563 | 23563 | |
Patent US4843607 - Multiple error trapping
BACKGROUND OF THE INVENTION
Error trapping is a well-known shortcut in the art of error detection and correction. It is described, for example, in Peterson and Weldon, Error-Correcting Code, The MIT Press, 1984, at pages
237-240 and 364-367. Whenever applicable, error trappin... | 4 | [
-0.07763671875,
0.0771484375,
0.0135498046875,
0.035888671875,
-0.010498046875,
-0.033935546875,
-0.0247802734375,
0.0263671875,
-0.01104736328125,
0.0052490234375,
0.0272216796875,
0.057373046875,
0.123046875,
-0.1015625,
-0.1220703125,
-0.0128173828125,
-0.03759765625,
0.04833984... | 23,564 | 23564 | |
trigonometric equation system
September 23rd 2008, 05:24 AM #1
Newbie
Joined
Sep 2008
Posts
1
trigonometric equation system
40 - W*sin(theta) = 0 ......equation 1
69.28 - W -W*cos(theta)=0 .........equation 2
solve for W and theta:
The final answer: W=46.19 N, theta = 60 deg,
but How ca... | 4 | [
-0.08349609375,
0.038330078125,
-0.0810546875,
0.076171875,
-0.072265625,
0.013916015625,
-0.033203125,
0.0205078125,
0.041259765625,
0.0306396484375,
0.1025390625,
-0.08251953125,
0.0308837890625,
0.0673828125,
-0.005157470703125,
0.0537109375,
-0.10498046875,
-0.033447265625,
-... | 23,565 | 23565 | |
Patent US7328164 - Pricing optimization apparatus and method
RELATED PATENT APPLICATION
This application is a National Phase Application of PCT/IL03/00036 International Filing Date 14 Jan. 2003, which claims priority from U.S. Provisional Patent Application No. 60/348,380 filed 16 Jan.
2002.
FIELD OF THE INVENTION
T... | 4 | [
-0.0849609375,
0.048095703125,
-0.0302734375,
-0.087890625,
-0.07568359375,
0.03466796875,
0.07666015625,
0.166015625,
0.032958984375,
0.024169921875,
0.004669189453125,
0.041259765625,
0.0291748046875,
-0.0012969970703125,
-0.01904296875,
-0.083984375,
0.07958984375,
0.03881835937... | 23,566 | 23566 | |
Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 128520, 20 pages
http://dx.doi.org/10.1155/2012/128520
Research Article
Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals
Department of Ma... | 5 | [
-0.035400390625,
-0.02099609375,
0.01239013671875,
-0.09326171875,
-0.033935546875,
0.00750732421875,
0.0576171875,
0.050537109375,
-0.039794921875,
-0.01544189453125,
-0.0390625,
0.0634765625,
0.0234375,
-0.0576171875,
-0.049072265625,
0.04345703125,
0.00592041015625,
0.0397949218... | 23,567 | 23567 | |
Prove that there is no positive integer between 0 and 1
October 14th 2007, 03:17 AM #1
Newbie
Joined
Oct 2007
Posts
7
Prove that there is no positive integer between 0 and 1
Theorem : Prove that there is no positive integer between 0 and 1
<proof>
Suppose there is a positive integer 'a' between... | 4 | [
-0.0189208984375,
0.12158203125,
0.08056640625,
0.042724609375,
0.0390625,
0.0712890625,
0.046875,
0.0380859375,
0.0830078125,
0.0191650390625,
-0.04248046875,
0.048828125,
0.154296875,
-0.0279541015625,
-0.0810546875,
-0.07421875,
0.0478515625,
-0.0556640625,
0.01422119140625,
... | 23,568 | 23568 | |
99 questions/54A to 60
From HaskellWiki
< 99 questions
(Difference between revisions)
m (move data definition into 54A)
← Older edit Newer edit →
Line 7: ... | 5 | [
0.0027008056640625,
0.043701171875,
0.0537109375,
0.0206298828125,
0.0263671875,
-0.0419921875,
0.0010986328125,
0.03662109375,
-0.014404296875,
0.06787109375,
0.03466796875,
-0.055419921875,
0.054931640625,
-0.051513671875,
0.013671875,
0.11572265625,
-0.12255859375,
-0.0164794921... | 23,569 | 23569 | |
CALCULUS three questions
5a) Use the chain rule. $(uv)'=u'v+uv'$ 5b) Use the chain rule. For logarithmic differentiation, you the formula $\log_a x=\frac {\ln x}{\ln a}$ 5c) $(\ln |x|)'=\frac {x'}{x}$, so $\frac {1}{(\cos ^
2e^{-x})(\tan (e^{-x}))}$ 6) Rewrite for y. For example, $x=e^y, y=\ln x$ Use the tangent line f... | 5 | [
0.017822265625,
0.0023040771484375,
0.051513671875,
-0.056884765625,
0.050537109375,
0.000759124755859375,
0.020751953125,
0.036865234375,
-0.03955078125,
0.0732421875,
0.11767578125,
0.00830078125,
-0.022705078125,
0.048095703125,
0.062255859375,
0.0087890625,
-0.0859375,
-0.03295... | 23,570 | 23570 | |
Intuitive reason absolute values are used for transformations in statistics?
phiiota
well, if say X distributed as f(X), and say i have Y=g(X), and I want to know the distribution of Y, in a simple case I can say that Y~f(g^-1(y))|d/dy g^-1(y)|.
I don't know why we'd always want the absolute value, as opposed to th... | 4 | [
-0.07568359375,
-0.053466796875,
0.11669921875,
-0.0615234375,
0.03369140625,
-0.06982421875,
-0.049560546875,
0.051513671875,
0.0927734375,
0.07861328125,
0.048828125,
0.1494140625,
0.03564453125,
0.002655029296875,
0.0208740234375,
0.007568359375,
0.064453125,
0.01019287109375,
... | 23,571 | 23571 | |
Measures for Human Reproduction Should Be Linked to Both Men and Women
International Journal of Population Research
Volume 2014 (2014), Article ID 908385, 10 pages
http://dx.doi.org/10.1155/2014/908385
Research Article
Measures for Human Reproduction Should Be Linked to Both Men and Women
^1Department of Economics, ... | 4 | [
0.00811767578125,
-0.00028228759765625,
-0.06884765625,
0.080078125,
0.0390625,
0.041259765625,
-0.045654296875,
0.039794921875,
-0.0169677734375,
0.060791015625,
0.0771484375,
-0.107421875,
-0.0291748046875,
0.006805419921875,
0.01239013671875,
-0.047607421875,
0.044677734375,
-0.... | 23,572 | 23572 | |
Patent US7398162 - Quantum mechanical model-based system and method for global optimization
TECHNICAL FIELD
This invention relates generally to global optimization of functions, and more specifically to computer implemented model-based global optimization of functions.
BACKGROUND OF THE INVENTION
“Optimization” is a... | 4 | [
-0.072265625,
0.0458984375,
-0.01806640625,
-0.03662109375,
-0.115234375,
-0.0517578125,
-0.050048828125,
0.0498046875,
-0.032958984375,
-0.00299072265625,
-0.052490234375,
0.00775146484375,
0.0869140625,
0.042724609375,
-0.08984375,
-0.00021266937255859375,
0.001708984375,
-0.0008... | 23,573 | 23573 | |
Please Help Asap Homework Questions!!
November 11th 2007, 05:05 PM #1
Newbie
Joined
Mar 2007
Posts
16
Please Help Asap Homework Questions!!
1) Suppose y is directly proportial to the product of x and the square of w and inversely proportional to the sum of r and s. If x=2, w=3, r=1, and s=5, then y=15. F... | 4 | [
-0.08203125,
-0.01611328125,
0.00213623046875,
-0.0030670166015625,
0.041259765625,
0.039306640625,
0.04296875,
0.007080078125,
-0.09619140625,
0.032470703125,
0.023681640625,
0.0012054443359375,
-0.007171630859375,
0.03564453125,
-0.07666015625,
0.0751953125,
-0.04345703125,
-0.01... | 23,574 | 23574 | |
Need some help on a couple integrations
December 2nd 2006, 02:18 PM #1
Newbie
Joined
Sep 2006
Posts
5
Need some help on a couple integrations
You dont need to do them all but one would be nice. I want to see how to do it rather than just get answers. Thanks.
Integral of [(e^x + cos(x)]^2 dx
I tr... | 5 | [
0.061767578125,
0.037109375,
0.0208740234375,
-0.02978515625,
0.0595703125,
-0.002410888671875,
-0.021240234375,
-0.024169921875,
-0.032958984375,
0.041259765625,
0.061767578125,
0.035888671875,
-0.05029296875,
-0.052490234375,
0.031982421875,
-0.0123291015625,
0.046875,
0.05200195... | 23,575 | 23575 | |
Prove that the Image of a Continuous Function on a Dense Set is Dense
June 20th 2010, 10:55 AM #1
Member
Joined
Jun 2010
Posts
205
Thanks
1
Prove that the Image of a Continuous Function on a Dense Set is Dense
I've been working on this for days and have made no progress, so any advice would be apprec... | 4 | [
0.037841796875,
0.04931640625,
0.05712890625,
0.00457763671875,
-0.0026092529296875,
0.09130859375,
0.1181640625,
0.0125732421875,
-0.0005950927734375,
-0.01708984375,
-0.05029296875,
-0.0296630859375,
0.039794921875,
0.1298828125,
0.0986328125,
-0.00909423828125,
0.076171875,
-0.0... | 23,576 | 23576 | |
graded/filtered noetherian algebras
January 8th 2011, 09:31 PM
hp32
graded/filtered noetherian algebras
Hi, I'm having a bit of bother proving the following statement:
Let A be a filtered algebra and gr(A) the associated graded algebra. If gr(A) is noetherian without zero-divisors, then so is A.
Here... | 5 | [
-0.04833984375,
0.0157470703125,
0.00897216796875,
-0.04541015625,
0.053466796875,
-0.0037078857421875,
0.041748046875,
-0.07666015625,
-0.03662109375,
-0.0537109375,
0.00714111328125,
-0.046142578125,
0.0093994140625,
-0.030517578125,
-0.0267333984375,
-0.0078125,
-0.00628662109375,... | 23,577 | 23577 | |
Patent US7292660 - Delta-phase detection method and system
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to wireless communication systems, and more particularly, to a method of maintaining synchronization by detecting a burst sequence in wireless communication systems.
2. Descr... | 4 | [
-0.11865234375,
-0.00003814697265625,
-0.09375,
-0.1025390625,
-0.058837890625,
0.033935546875,
0.0225830078125,
0.043701171875,
-0.017333984375,
-0.0245361328125,
0.01611328125,
0.0537109375,
0.10400390625,
-0.0849609375,
0.00482177734375,
-0.08935546875,
0.0654296875,
-0.05004882... | 23,578 | 23578 | |
Equation of the Tangent
October 8th 2009, 08:46 AM #1
Junior Member
Joined
Nov 2008
From
Far away.
Posts
47
Hello! I have this question about tangents, which I have solved partly. But I have some difficulties in solving the ii - part. I would appreciate your help
Here is the question:
Conside... | 4 | [
-0.0235595703125,
-0.017822265625,
0.0771484375,
-0.001800537109375,
0.030029296875,
-0.007415771484375,
0.041748046875,
0.027587890625,
0.033935546875,
0.08544921875,
0.08447265625,
-0.0167236328125,
0.007568359375,
0.08642578125,
0.02294921875,
0.150390625,
-0.0576171875,
-0.0544... | 23,579 | 23579 | |
Generalizations of Hölder’s and Some Related Integral Inequalities
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 198405, 9 pages
http://dx.doi.org/10.1155/2013/198405
Research Article
Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space
Department of Constr... | 5 | [
-0.00665283203125,
0.0250244140625,
0.0859375,
-0.0546875,
0.0103759765625,
0.031005859375,
0.005645751953125,
0.0537109375,
0.041259765625,
-0.0206298828125,
-0.046142578125,
-0.0101318359375,
0.055419921875,
-0.03125,
-0.0546875,
-0.03564453125,
0.07275390625,
-0.025146484375,
... | 23,580 | 23580 | |
Elementary insight into Bertrand's postulate
June 18th 2009, 01:11 PM
Bruno J.
Elementary insight into Bertrand's postulate
Bertrand's postulate states that for any positive integer $n>1$ there is a prime with $n<p<2n$.
The following is not a rigorous proof but rather something I have thought of which makes ... | 4 | [
-0.03515625,
-0.041748046875,
0.029541015625,
-0.00823974609375,
0.10791015625,
0.045166015625,
0.0634765625,
0.130859375,
0.0286865234375,
-0.01031494140625,
-0.14453125,
0.07568359375,
0.0908203125,
-0.004852294921875,
0.00811767578125,
-0.07373046875,
0.07958984375,
-0.020141601... | 23,581 | 23581 | |
Cylindrical tank
October 25th 2010, 12:16 PM #1
Senior Member
Joined
Apr 2006
Posts
290
Cylindrical tank
A cylindrical tank has a radius of 30cm and a height of 45cm. The tank contains water to a depth of 36cm.
A metal sphere is dropped into the water and is completely covered. The water level rises... | 4 | [
-0.01470947265625,
0.0517578125,
-0.0162353515625,
-0.044677734375,
0.0546875,
-0.023681640625,
-0.01416015625,
0.06640625,
0.0021209716796875,
-0.03564453125,
-0.09375,
-0.0223388671875,
0.0751953125,
0.12255859375,
0.0147705078125,
-0.056640625,
-0.0185546875,
0.0400390625,
-0.... | 23,582 | 23582 | |
Please help me with this challenging math question probabilty
February 17th 2010, 10:53 AM #1
Newbie
Joined
Feb 2010
Posts
1
Please answer any of the following question and please show your work
For [ 2x^2 - 1/x]^6, determine
a) The middle term
b) The term containing x^3
Given the univer... | 5 | [
0.004150390625,
0.00872802734375,
0.02001953125,
-0.01123046875,
-0.07861328125,
0.0245361328125,
0.060302734375,
0.01043701171875,
-0.004913330078125,
0.047119140625,
0.004302978515625,
-0.08447265625,
0.037841796875,
0.0181884765625,
-0.0233154296875,
0.0062255859375,
0.0126953125,... | 23,583 | 23583 | |
Probaility venn diagram
May 21st 2011, 02:05 AM
helloying
Probaility venn diagram
A computer game stimulate a match beteewn A and B. The match consist of at most 3 sets. Each set is won by either A or B and the match is won by 1st player to win the two sets.
The stimulation uses the following rules:
-Th... | 5 | [
-0.0184326171875,
-0.005401611328125,
0.0120849609375,
-0.10400390625,
-0.05322265625,
0.080078125,
0.11328125,
0.00787353515625,
0.038818359375,
0.07763671875,
-0.060546875,
-0.07177734375,
0.0908203125,
-0.0181884765625,
0.0242919921875,
0.0830078125,
-0.0086669921875,
-0.0600585... | 23,584 | 23584 | |
Wolfram Demonstrations Project
Driven Spherical Pendulum
This Demonstration shows an animation of a driven spherical pendulum.
A free-swinging rigid pendulum is suspended inside a frame that can rotate around a vertical axis fixed by two frictionless bearings at its top and bottom. A motor at the bottom can transfer ... | 4 | [
-0.01141357421875,
0.00445556640625,
-0.06298828125,
-0.06787109375,
-0.02294921875,
0.032470703125,
-0.06298828125,
0.06396484375,
-0.005859375,
0.049072265625,
0.056396484375,
0.0260009765625,
0.050048828125,
-0.080078125,
-0.0302734375,
0.028564453125,
-0.01806640625,
0.06494140... | 23,585 | 23585 | |
Finding the angle between tangents
February 6th 2013, 04:39 PM #1
Newbie
Joined
Feb 2013
From
Guam
Posts
2
Finding the angle between tangents
Verify that the circles x^2+y^2 = 25 and (x−5)^2+(y−10)^2= 50 intersect at A = (4, 3).
Find the size of the acute angle formed at A by the intersecting c... | 4 | [
-0.0240478515625,
0.003662109375,
-0.005462646484375,
0.00104522705078125,
0.0096435546875,
-0.0380859375,
0.048583984375,
0.08984375,
-0.048095703125,
0.00109100341796875,
0.053955078125,
0.0174560546875,
0.0157470703125,
0.05712890625,
0.039794921875,
0.11083984375,
-0.0654296875,
... | 23,586 | 23586 | |
Find the minimum of an integral
December 18th 2011, 07:01 AM #1
Newbie
Joined
Dec 2011
Posts
15
Find the minimum of an integral
Find $\min_{a,b \in \mathbb{R}}\int_{0}^{2\pi }(1+x-(a+b\cos x))^{2}dx$ without using mathematical analysis or calculus.
Do you have any ideea how can I do this?
Re: Find ... | 5 | [
0.021240234375,
0.01287841796875,
0.0146484375,
-0.051025390625,
-0.07177734375,
0.10498046875,
0.023681640625,
0.1123046875,
-0.0283203125,
0.0341796875,
-0.037841796875,
0.017578125,
0.0703125,
-0.08935546875,
-0.00836181640625,
-0.03955078125,
0.076171875,
-0.029296875,
-0.054... | 23,587 | 23587 | |
derivative question, please help!
August 19th 2006, 02:09 AM #1
Junior Member
Joined
Dec 2005
Posts
40
derivative question, please help!
I don't know how to take out Δx when i do the question
If $y=sin x$, show that
$<br /> \frac{dy}{dx}= cos x<br />$
(by the first principles)
ling_c_... | 5 | [
-0.08251953125,
-0.0118408203125,
-0.046630859375,
-0.01165771484375,
-0.0213623046875,
0.04638671875,
-0.04931640625,
-0.06005859375,
-0.015869140625,
0.007354736328125,
0.08984375,
-0.033447265625,
-0.05224609375,
-0.02294921875,
0.1044921875,
-0.0189208984375,
0.013427734375,
-0... | 23,588 | 23588 | |
Two circles intersecting each other...
February 25th 2010, 07:30 AM #1
Member
Joined
Mar 2009
From
jharkhand
Posts
77
Two circles intersecting each other...
Two circles intersect each other at A and B as shown in the figure. The common chord AB is produced to meet a common tangent PQ to the circles a... | 4 | [
-0.1103515625,
0.0279541015625,
-0.047119140625,
0.00555419921875,
-0.03759765625,
-0.0224609375,
0.0296630859375,
0.039306640625,
0.03515625,
-0.0576171875,
0.029052734375,
-0.05517578125,
-0.0198974609375,
0.0284423828125,
0.017333984375,
0.054931640625,
-0.0849609375,
-0.0235595... | 23,589 | 23589 | |
[SOLVED] finding the volume of a beaker
February 20th 2010, 12:38 PM
ogglock
[SOLVED] finding the volume of a beaker
i need to find the volume of this beaker
http://img13.imageshack.us/img13/1264/72680665.png
other than the information given in the picture, you are also told that the diameter of the op... | 4 | [
-0.003875732421875,
0.076171875,
-0.037109375,
-0.0625,
0.02685546875,
-0.10888671875,
0.0057373046875,
0.06689453125,
0.04638671875,
-0.025634765625,
-0.06201171875,
-0.06298828125,
-0.07568359375,
0.08544921875,
-0.02392578125,
-0.10888671875,
-0.048828125,
-0.0732421875,
-0.01... | 23,590 | 23590 | |
CDF of the Weibull Distribution
November 26th 2009, 05:04 PM #1
Newbie
Joined
Oct 2009
Posts
20
CDF of the Weibull Distribution
I'm trying to find the CDF of the weibull distribution but have no idea how to integrate it from 0 to positive infinity. Can someone please show me how I can integrate this? k, ... | 4 | [
-0.041015625,
0.0169677734375,
-0.0108642578125,
-0.01312255859375,
-0.0380859375,
-0.0208740234375,
0.07421875,
-0.049072265625,
-0.0194091796875,
0.02685546875,
0.05419921875,
-0.10498046875,
0.123046875,
-0.0167236328125,
-0.011474609375,
-0.014892578125,
0.02197265625,
-0.12304... | 23,591 | 23591 | |
An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 505903, 29 pages
http://dx.doi.org/10.1155/2013/505903
Research Article
An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fract... | 5 | [
-0.0400390625,
0.03076171875,
0.09228515625,
0.01531982421875,
-0.038818359375,
-0.0196533203125,
-0.0927734375,
-0.03271484375,
0.033447265625,
0.033447265625,
0.049072265625,
0.01123046875,
0.008544921875,
0.00604248046875,
-0.048583984375,
0.024169921875,
-0.00885009765625,
-0.0... | 23,592 | 23592 | |
Field Theory - Nicholson - Splitting Fields - Section 6.3 - Example 1
October 19th 2013, 02:23 AM #1
Field Theory - Nicholson - Splitting Fields - Section 6.3 - Example 1
I am reading Nicholson: Introduction to Abstract Algebra, Section 6.3 Splitting Fields.
Example 1 reads as follows: (see attachment)
... | 5 | [
-0.01397705078125,
0.057373046875,
0.06640625,
0.01904296875,
0.1123046875,
0.041748046875,
0.0419921875,
0.023681640625,
-0.0032958984375,
0.0022735595703125,
0.1376953125,
-0.00860595703125,
0.00185394287109375,
-0.06884765625,
0.0037384033203125,
0.01043701171875,
-0.12060546875,
... | 23,593 | 23593 | |
help starting a triple integral/center of mass problem
November 3rd 2009, 03:36 PM #1
Member
Joined
Nov 2008
From
MD
Posts
165
i need help setting up the integral expressions to compute the centroid please!
the solid bounded by the paraboloids z=1+x^2+y^2 and z=5-x^2-y^2 with density proportional ... | 5 | [
0.0016632080078125,
0.0419921875,
-0.04833984375,
-0.07666015625,
-0.0291748046875,
-0.049072265625,
0.00640869140625,
0.002960205078125,
-0.064453125,
0.00555419921875,
-0.048828125,
-0.032470703125,
-0.0106201171875,
0.1015625,
-0.07470703125,
0.0230712890625,
-0.0033721923828125,
... | 23,594 | 23594 | |
Solving Quadratic Systems
July 23rd 2007, 02:07 PM #1
Junior Member
Joined
Jul 2007
Posts
49
Solving Quadratic Systems
Find the exact solutions of x^2 - (y - 5)^2 = 25 and y = -x^2
Do I try to isolate the y in the first equation first?
Would that be like x^2 - (-x^2 - 5)^2 = 25? Or should I ju... | 4 | [
-0.052001953125,
-0.01336669921875,
0.0203857421875,
0.003753662109375,
0.08642578125,
-0.057373046875,
0.006103515625,
-0.027099609375,
0.02099609375,
-0.03955078125,
0.130859375,
0.0341796875,
-0.0023345947265625,
0.049560546875,
0.00543212890625,
0.07470703125,
0.01263427734375,
... | 23,595 | 23595 | |
Newton's Method
Given the function: $f(x)=5e^{-x}-29x$ When, $x_{0}=\ln(6)$ $x_{1}=?$ I know... $x_{n+1}=x_{n}-\frac{5e^{-x}-29x}{-5e^{-x}-29}$
You will have: $x_1=\ln(6)-\frac{5e^{-\ln(6)}-29\ln(6)}{-5e^{-\ln(6)}-29}$ Now, use the two identities: $-\ln(y)=\ln\left(\frac{1}{y} \right)$ and $e^{\ln(y)}=y$ to simplify.
... | 4 | [
-0.083984375,
-0.05810546875,
0.017578125,
-0.031494140625,
0.048095703125,
-0.06982421875,
-0.01708984375,
0.041259765625,
-0.00152587890625,
0.140625,
0.09912109375,
-0.044921875,
-0.0322265625,
0.0279541015625,
0.0017242431640625,
0.0169677734375,
-0.1357421875,
0.00564575195312... | 23,596 | 23596 | |
He's Variational Iteration Method for Solving Fractional Riccati Differential Equation
International Journal of Differential Equations
Volume 2010 (2010), Article ID 764738, 8 pages
http://dx.doi.org/10.1155/2010/764738
Research Article
He's Variational Iteration Method for Solving Fractional Riccati Differential Equ... | 5 | [
-0.061279296875,
-0.019775390625,
0.03564453125,
0.041748046875,
-0.07470703125,
0.0361328125,
-0.00775146484375,
0.05078125,
0.0224609375,
0.01239013671875,
0.0142822265625,
0.032958984375,
-0.039794921875,
0.044921875,
-0.00592041015625,
0.00176239013671875,
0.0181884765625,
0.06... | 23,597 | 23597 | |
Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems
Advances in Operations Research
Volume 2013 (2013), Article ID 708979, 9 pages
http://dx.doi.org/10.1155/2013/708979
Research Article
Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Probl... | 5 | [
-0.09130859375,
-0.037353515625,
-0.029052734375,
-0.0458984375,
-0.028076171875,
0.01214599609375,
-0.017578125,
-0.0498046875,
0.0172119140625,
0.0771484375,
-0.056884765625,
0.0001888275146484375,
0.018798828125,
0.08642578125,
-0.0245361328125,
0.051513671875,
0.1142578125,
0.0... | 23,598 | 23598 | |
Problem Set
Electricity: Electric Circuits
Electric Circuits: Problem Set
Problem 1:
Over the course of an 8 hour day, 3.8x10^4 C of charge pass through a typical computer (presuming it is in use the entire time). Determine the current for such a computer.
Problem 2:
The large window air conditioner in Anita Breez... | 4 | [
0.0179443359375,
0.11865234375,
0.01202392578125,
0.028564453125,
-0.00164794921875,
-0.033203125,
0.0673828125,
0.01556396484375,
-0.0118408203125,
0.06982421875,
-0.002655029296875,
-0.08642578125,
0.060302734375,
0.05859375,
0.015869140625,
0.0341796875,
-0.01031494140625,
-0.04... | 23,599 | 23599 |