content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Equation of The Plane
March 10th 2009, 11:37 PM #1
Newbie
Joined
Nov 2008
Posts
24
Equation of The Plane
Find the equation of the plane (if it exists) containing the two lines:
A) R1(t)= <1-t, t, 3+2t> ; R2(t)= <t, 1+t, 5-2t>
B) R1(t)= <1+3t, -2t, -1+t> ; R2(t)= <6t,1-4t,3+2t>
C) R1(t)= <t... | 4 | [
-0.11328125,
0.0130615234375,
0.01275634765625,
-0.017333984375,
0.028564453125,
0.0198974609375,
0.0189208984375,
0.0869140625,
-0.037353515625,
0.107421875,
-0.0301513671875,
-0.012451171875,
0.00028228759765625,
-0.00130462646484375,
-0.054443359375,
0.02294921875,
-0.080078125,
... | 33,900 | 33900 | |
What is an Euler-Fokker genus?
In ancient times the Greeks made a distinction between different genera. The fourth was the interval between the two extreme tones of the tetrachord. Two other tones divided this distance into three
intervals, in various different ways. This multiformity gave rise to a system of classifi... | 4 | [
-0.038818359375,
0.034423828125,
0.0303955078125,
-0.11669921875,
-0.0751953125,
-0.044921875,
-0.0625,
0.0291748046875,
0.08740234375,
0.037841796875,
0.021240234375,
-0.1435546875,
-0.00131988525390625,
-0.0810546875,
-0.0126953125,
-0.0615234375,
-0.048095703125,
-0.026123046875... | 33,901 | 33901 | |
Which subsets of R^3 are subspaces?
April 19th 2010, 08:44 PM
iExcavate
Which subsets of R^3 are subspaces?
SUBSPACES (Headbang)!
Hi, I don't understand subspaces! I came across this question in homework tasks, and I'm guessing it's very important to the course?!
Which of the following subsets of R^3 a... | 4 | [
-0.027587890625,
-0.038330078125,
-0.068359375,
-0.0177001953125,
0.034912109375,
0.05712890625,
0.040283203125,
0.0169677734375,
0.007781982421875,
-0.002593994140625,
-0.0137939453125,
-0.00927734375,
0.0242919921875,
-0.042724609375,
0.034912109375,
-0.061279296875,
-0.01599121093... | 33,902 | 33902 | |
definite integral answer different from Riemann Sum calc
May 18th 2008, 07:15 PM #1
Newbie
Joined
Feb 2008
Posts
9
definite integral answer different from Riemann Sum calc
Hi everybody,
I have to calculate a definite integral using the oh so necessary Riemann Sum.
I first calculated the integral... | 5 | [
-0.0255126953125,
-0.043212890625,
0.08447265625,
-0.0079345703125,
0.020751953125,
-0.06884765625,
0.0654296875,
0.10400390625,
0.025146484375,
-0.03173828125,
-0.044189453125,
-0.04736328125,
-0.031982421875,
-0.046875,
-0.0693359375,
-0.08935546875,
0.051513671875,
-0.05078125,
... | 33,903 | 33903 | |
Math Help
October 28th 2008, 11:38 AM #1
Junior Member
Joined
Oct 2008
Posts
25
INDICES
a) express 27 to the power of a 1/2 as a power of 3
b) express root 2 as a power of 8
c) express root 2 divided by 16 as a power of 2
how exactly do you go about these Q's and what does it mean by expr... | 4 | [
-0.0252685546875,
0.037109375,
-0.09423828125,
0.0966796875,
-0.06103515625,
-0.0654296875,
0.044677734375,
-0.00168609619140625,
0.072265625,
0.0218505859375,
-0.0167236328125,
-0.06396484375,
0.06103515625,
0.048095703125,
0.0546875,
0.0927734375,
-0.1318359375,
0.0546875,
-0.0... | 33,904 | 33904 | |
Homology theory constructed in a homotopy-invariant way
up vote 17 down vote favorite
7
Singular homology sends homotopic morphisms on equal morphisms and weakly equivalent spaces on isomorphic objects. So singular homology is in fact defined on the homotopy category of topological
spaces.
But the usual definition of... | 4 | [
-0.025390625,
-0.0157470703125,
0.00970458984375,
0.0289306640625,
-0.06201171875,
0.051025390625,
-0.050048828125,
-0.005035400390625,
-0.0101318359375,
-0.054931640625,
-0.01043701171875,
-0.068359375,
-0.0155029296875,
-0.0091552734375,
0.0289306640625,
0.003326416015625,
-0.02746... | 33,905 | 33905 | |
What axioms are stronger than the Axiom of choice?
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
What other axioms in set theory are stronger than AC ? I mean what are those axioms that will imply AC ?
up vote 4 down ... | 4 | [
-0.01416015625,
-0.04052734375,
-0.048828125,
-0.0537109375,
0.08349609375,
0.0274658203125,
-0.07177734375,
0.029541015625,
0.0303955078125,
0.05126953125,
-0.04638671875,
0.0169677734375,
-0.002197265625,
0.007659912109375,
0.07275390625,
-0.0230712890625,
0.03515625,
-0.01940917... | 33,906 | 33906 | |
Acceptance Sampling
A tutorial on how to develop sampling plans that detect and prevent the use of unacceptable materials and services.
By Stan Hilliard
© 1999 H & H Servicco Corp.
Outline
┌──────┬────────────────────────────────────────────────────────┐
│ PAGE │ TUTORIAL... | 5 | [
-0.037841796875,
0.05322265625,
-0.02001953125,
-0.035400390625,
0.06982421875,
-0.08251953125,
0.09521484375,
0.0186767578125,
-0.06494140625,
-0.006744384765625,
-0.020751953125,
0.002655029296875,
0.02197265625,
-0.006011962890625,
0.027587890625,
-0.08447265625,
0.1015625,
-0.0... | 33,907 | 33907 | |
sicp-ex-2.5
;; Constructor
(define (cons a b) (* (expt 2 a) (expt 3 b)))
;; Enables us to calculate the log of n in base b
(define (logb b n) (floor (/ (log n) (log b))))
;; Selectors
(define (car x) (logb 2 (/ x (gcd x (expt 3 (logb 3 x))))))
(define (cdr x) (logb 3 (/ x (gcd x (expt 2(logb 2 x))))))
I had ori... | 4 | [
-0.0712890625,
0.0019683837890625,
-0.054443359375,
-0.0576171875,
0.01904296875,
-0.0341796875,
0.04248046875,
0.00579833984375,
0.00162506103515625,
-0.04296875,
0.041748046875,
-0.06982421875,
0.0191650390625,
0.0634765625,
0.05322265625,
0.0279541015625,
-0.0859375,
0.137695312... | 33,908 | 33908 | |
Generalized Towers of Hanoi - Optimal Algorithm
Generalized Towers of Hanoi - Optimal Algorithm Follow
... | 4 | [
-0.041015625,
0.048095703125,
-0.044189453125,
-0.08251953125,
-0.09228515625,
-0.078125,
-0.03125,
0.0225830078125,
0.00970458984375,
0.08203125,
-0.02734375,
0.0625,
0.0595703125,
0.00482177734375,
-0.05712890625,
0.0498046875,
-0.0390625,
-0.0234375,
0.0264892578125,
-0.0329... | 33,909 | 33909 | |
Determining all the zeros of a function
March 5th 2011, 09:20 AM #1
Junior Member
Joined
Feb 2011
Posts
58
Determining all the zeros of a function
Determine the zero's
f(x) = kx^3 - 8x -x +3k + 1 k=3 and has a zero when x = 2
3x^3 - 8x^2 - x + 3(3) + 1
= 3x^3 - 8x^2 - x +10 <<<<< don't k... | 4 | [
-0.0439453125,
0.034912109375,
-0.05078125,
0.007354736328125,
-0.0283203125,
0.048583984375,
0.000537872314453125,
0.0166015625,
0.025634765625,
-0.0101318359375,
0.0673828125,
-0.10107421875,
0.09716796875,
0.026123046875,
-0.0084228515625,
-0.0198974609375,
-0.03662109375,
-0.01... | 33,910 | 33910 | |
Quadratic formula
May 27th 2008, 04:40 PM #1
Newbie
Joined
May 2008
Posts
2
Quadratic formula
Can someone help me?
Please, I'm really confused. Anyone help would be appreciated.
I'm not really sure what to do w/ the x's in the equation....
heres the link to the equation:
http://img100.im... | 4 | [
-0.08544921875,
-0.0240478515625,
0.03564453125,
0.0120849609375,
-0.0272216796875,
0.0137939453125,
0.083984375,
-0.0267333984375,
-0.0037841796875,
-0.00537109375,
0.0703125,
-0.10888671875,
0.06005859375,
0.0150146484375,
0.01239013671875,
0.058837890625,
0.0069580078125,
0.0415... | 33,911 | 33911 | |
Complex analysis - integrating over a contour
November 16th 2012, 06:59 PM
alphabeta89
Complex analysis - integrating over a contour
Let $0 < |\alpha| < 1$. Find
$\displaystyle{\int_{\gamma}\frac{\mathrm{Re}(z)}{z-\alpha}dz}$
in terms of $\alpha$, where $\gamma$ is the circle $|z| = 1$ oriented in the ... | 5 | [
-0.00830078125,
-0.00921630859375,
-0.0262451171875,
-0.0037078857421875,
0.0184326171875,
0.0118408203125,
0.0157470703125,
0.07275390625,
-0.037109375,
0.059814453125,
0.00537109375,
0.0186767578125,
-0.0245361328125,
0.046875,
-0.06201171875,
-0.02392578125,
-0.01422119140625,
-... | 33,912 | 33912 | |
Stepper/time equation problem
June 27th 2012, 02:44 PM #1
Newbie
Joined
Jun 2012
From
London
Posts
1
Stepper/time equation problem
Hi, I have an equation that I have been staring at for hours. Hope this is in the right section, it's a weird one.
i have a stepper motor attached to a clock to essen... | 4 | [
-0.1025390625,
0.045654296875,
-0.0115966796875,
0.0238037109375,
-0.044677734375,
-0.00909423828125,
-0.01214599609375,
0.0400390625,
0.03125,
-0.08056640625,
0.0498046875,
-0.054931640625,
0.00066375732421875,
0.03857421875,
0.033447265625,
0.004425048828125,
-0.078125,
-0.037353... | 33,913 | 33913 | |
Models of separable equations (population growth, half life, interest)
September 14th 2013, 06:10 PM #1
Newbie
Joined
Sep 2013
From
Broken Arrow
Posts
4
Models of separable equations (population growth, half life, interest)
Hey all,
I'm working the odd problems in section 3.1 of Christian Consta... | 5 | [
-0.10791015625,
-0.015625,
0.09326171875,
0.01287841796875,
0.0113525390625,
-0.01080322265625,
-0.042724609375,
0.03076171875,
-0.05419921875,
0.0137939453125,
0.142578125,
-0.07763671875,
-0.0135498046875,
0.007049560546875,
-0.00830078125,
0.05029296875,
-0.072265625,
-0.0776367... | 33,914 | 33914 | |
Factoring quadratics
March 24th 2009, 03:57 AM #1
Junior Member
Joined
Jan 2009
Posts
52
Factoring quadratics
For example:
$<br /> 6x^2 +11x -35<br />$
I've been doing this by trial and error but it takes too long. I tried googling "factoring quadratics" but when it comes to examples like this, ... | 4 | [
-0.0281982421875,
-0.0152587890625,
0.041748046875,
0.006317138671875,
-0.0087890625,
0.052001953125,
-0.043212890625,
-0.0089111328125,
-0.047119140625,
0.03662109375,
0.021728515625,
-0.0047607421875,
0.056640625,
0.048095703125,
-0.0096435546875,
0.09228515625,
0.0284423828125,
... | 33,915 | 33915 | |
Simple exponential integral
That's good. But I'm looking for a solution in which integration by parts is NOT used.
Consider $y = t \sin t$. Then $\frac{dy}{dt} = \sin t + t \cos t$. Now integrate both sides: $y = \int \sin t + t \cos t \, dt = \int \sin t \, dt + \int t \cos t \, dt$. Substitute $y = t \sin t$:
$t \si... | 5 | [
-0.10888671875,
-0.03125,
-0.00726318359375,
0.0286865234375,
0.03271484375,
0.01361083984375,
-0.07080078125,
-0.001312255859375,
-0.07568359375,
0.006378173828125,
0.02685546875,
-0.03173828125,
-0.06640625,
0.0859375,
0.0546875,
-0.052490234375,
-0.033203125,
0.0771484375,
0.0... | 33,916 | 33916 | |
ing
Back to Mathematics and Politics
In many situations, voting is not "one person-one vote." For example, the stockholders of a company usually have one vote for each share of stock owned in the company. Thus, some people may have many
votes (have much power) while other voters may have only a few votes (have little ... | 5 | [
-0.0177001953125,
-0.07958984375,
0.015625,
-0.0308837890625,
-0.046875,
-0.0189208984375,
-0.0380859375,
0.06298828125,
0.06298828125,
0.06298828125,
-0.052978515625,
0.03466796875,
0.06591796875,
0.010986328125,
-0.03857421875,
-0.01904296875,
0.018310546875,
0.0673828125,
-0.0... | 33,917 | 33917 | |
Market equilibrium
March 23rd 2009, 03:59 PM #1
Newbie
Joined
Mar 2009
Posts
11
The supply function is 2p-q=50.
Demand function is pq=100=20q.
What are the price and quantity of market equilibrium?
I can't figure this out. I think you have to isolate "p" and set the two equations equal to ea... | 4 | [
-0.050537109375,
0.09716796875,
0.0947265625,
-0.01953125,
-0.04638671875,
0.10205078125,
0.048095703125,
0.04248046875,
0.005706787109375,
0.07177734375,
0.0908203125,
-0.06201171875,
0.07373046875,
0.1005859375,
0.05810546875,
0.049560546875,
-0.06494140625,
-0.00860595703125,
... | 33,918 | 33918 | |
Groups - discrete math
In G={x∈R | x>1} is defined operation * with x*y = xy-x-y+2. Show that {G,*} is Albelian group
thanks
Re: Groups - discrete math
Re: Groups - discrete math
we need to show 4 things:
1. * is an associative binary operation on G. this means two things:
a) x*y has to be in ... | 5 | [
-0.037353515625,
0.010498046875,
0.005828857421875,
-0.024658203125,
-0.04345703125,
-0.07080078125,
0.11376953125,
-0.107421875,
-0.0250244140625,
-0.045166015625,
-0.052490234375,
-0.056396484375,
0.057861328125,
-0.037841796875,
0.0400390625,
0.04345703125,
-0.00616455078125,
0.... | 33,919 | 33919 | |
Joint distrib of gamma distribs
October 31st 2009, 09:48 AM
isarutas
Joint distrib of gamma distribs
Let X_i, with i \epsilon {1,2,3} be independant r.v. and suppose that X_i \epsilon Gamma(r_i,1).
Now set:
Y_1= X_1/(X_1+X_2)
Y_2= (X_1+X_2)/(X_1+X_2+X_3)
Y_3= X_1+X_2+X_3
Determine the joint ... | 5 | [
-0.09765625,
-0.080078125,
-0.006011962890625,
-0.1240234375,
0.0380859375,
-0.06640625,
0.0859375,
-0.01263427734375,
0.0211181640625,
0.0224609375,
0.043212890625,
0.01177978515625,
0.03173828125,
0.01068115234375,
0.01226806640625,
0.02392578125,
-0.07958984375,
0.0291748046875,... | 33,920 | 33920 | |
Curve of intersection with two surfaces
May 10th 2008, 08:47 PM #1
Junior Member
Joined
Apr 2008
Posts
37
Curve of intersection with two surfaces
Show that the curve with vector equation $r(t) = <2 cos^2(t), sin(2t), 2sin(t)>$ is the curve of intersection of the surfaces $(x-1)^2+y^2 = 1$ and $x^2 + y^2 ... | 4 | [
-0.06103515625,
-0.0196533203125,
-0.0306396484375,
0.056396484375,
0.00799560546875,
-0.0179443359375,
0.008544921875,
0.0908203125,
-0.00860595703125,
-0.021728515625,
-0.039794921875,
-0.004730224609375,
0.0166015625,
0.050048828125,
-0.06689453125,
-0.032470703125,
-0.07568359375... | 33,921 | 33921 | |
Triple integration
August 22nd 2006, 01:42 PM #1
Newbie
Joined
Aug 2006
Posts
23
Triple integration
Hello,
Having problems with a homework question:
Part A asks to sketch the solid region bounded in the first octant by elliptic cylinder 2x^2 + y^2 =1, and the plane y + z = 1.
I know we hav... | 5 | [
-0.049072265625,
0.022705078125,
-0.035888671875,
-0.057373046875,
0.005706787109375,
-0.091796875,
-0.048583984375,
0.0174560546875,
-0.0194091796875,
-0.00041961669921875,
-0.06298828125,
0.04443359375,
0.006103515625,
0.107421875,
-0.00927734375,
-0.057861328125,
-0.0220947265625,... | 33,922 | 33922 | |
smallest-nonmember-problem
Given a finite set S of non-negative integers, the smallest-nonmember problem (Chapter 1) finds the smallest non-negative integer not in S. For example, { 0 1 3 } -> 2.
Here are three solutions, with successive solutions having asymptotically better worst-case behavior than the previous sol... | 4 | [
-0.01806640625,
0.03857421875,
0.001678466796875,
-0.035888671875,
0.03076171875,
0.01043701171875,
0.07373046875,
0.034912109375,
0.005126953125,
-0.00653076171875,
-0.03125,
-0.036376953125,
0.10400390625,
0.03955078125,
-0.0595703125,
-0.0096435546875,
0.058837890625,
0.01129150... | 33,923 | 33923 | |
Homework Help
Posted by Cynthia on Tuesday, August 7, 2012 at 5:52pm.
evaluate (integral) xe^2x dx
A. 1/6x^2 e^3x+C
B. 1/2xe^2x-1/2e^2x+C
C. 1/2xe^2x-1/4e^2x+C
D. 1/2x^2-1/8e^4x+C
Evaluate (integral) e^3x cosh 2x dx
A. 1/2e^5x + 1/2e^x +C
B. 1/10e^5x + 1/2e^x + C
C. 1/4e^3x + 1/2x + C
D. 1/10e^5x + 1/5x + C
... | 5 | [
-0.05712890625,
0.0576171875,
0.072265625,
-0.00057220458984375,
0.06884765625,
0.00457763671875,
-0.046630859375,
0.0712890625,
-0.013671875,
0.057861328125,
0.0322265625,
-0.10791015625,
-0.01104736328125,
0.005340576171875,
-0.040771484375,
-0.054931640625,
-0.025146484375,
-0.0... | 33,924 | 33924 | |
find the centroid (C.O.M) of a thin plane
May 17th 2011, 01:05 AM
[nuthing]
find the centroid (C.O.M) of a thin plane
hi,
find the center of mass (or centroid) of a thin plate of constant density covering the given region.
(a) The region bounded by y = x^2 and y = 4.
I can't seem to get this questi... | 5 | [
0.091796875,
0.059326171875,
-0.03857421875,
-0.0947265625,
0.0096435546875,
-0.0264892578125,
-0.0103759765625,
0.125,
-0.0081787109375,
0.004119873046875,
0.0302734375,
-0.021728515625,
-0.04736328125,
0.0174560546875,
-0.01495361328125,
0.0654296875,
0.0014190673828125,
-0.04760... | 33,925 | 33925 | |
Math Help
November 23rd 2008, 03:48 PM #1
Newbie
Joined
Jun 2008
From
Marion, VA
Posts
18
Inverse
Set up a system belw as a matrix multiplication of the form AB=C. Find the inverse A^-1 of A and use it to solve the system.
3x + -6y + -17z = 288
11x + -17y + 110z = 79
-5x + 7y + 8z = 2... | 5 | [
-0.09912109375,
0.03173828125,
-0.09619140625,
-0.02392578125,
0.0157470703125,
-0.0712890625,
0.01202392578125,
-0.0419921875,
-0.091796875,
0.09228515625,
0.01190185546875,
0.0233154296875,
0.05908203125,
-0.0537109375,
-0.039794921875,
0.045654296875,
-0.064453125,
0.04174804687... | 33,926 | 33926 | |
Verifying Identities?
March 31st 2009, 07:24 AM #1
Newbie
Joined
Feb 2009
Posts
11
Verifying Identities?
I have two questions that I am getting nowhere on:
1. Verify the identity: cotx+tanx=cscxsecx
I thought of working on the right side, but I came up with (1/tanx)+(sinx/cosx) and didn't know w... | 4 | [
-0.049072265625,
0.103515625,
0.078125,
0.059814453125,
0.01531982421875,
0.0179443359375,
0.053955078125,
-0.040771484375,
0.057861328125,
-0.02685546875,
0.048828125,
-0.12255859375,
-0.00860595703125,
0.0908203125,
-0.0286865234375,
0.0054931640625,
-0.0078125,
0.09619140625,
... | 33,927 | 33927 | |
m
Geometry Concepts: Line Intersection and its Applications
By lbackstrom
TopCoder Member
...read Section 1
Line-Line Intersection
Finding a Circle From 3 Points
Reflection
Rotation
Convex Hull
In the previous section we saw how to use vectors to solve geometry problems. Now we are going to learn how to use some b... | 4 | [
-0.1103515625,
-0.0517578125,
-0.07373046875,
-0.042724609375,
-0.059814453125,
-0.05322265625,
0.022705078125,
-0.024169921875,
-0.017822265625,
-0.0286865234375,
-0.0322265625,
-0.01007080078125,
-0.00823974609375,
-0.0294189453125,
-0.018310546875,
0.08203125,
-0.09033203125,
-0... | 33,928 | 33928 | |
PS - Looking for easy calculation trick
Author Message
TAGS:
PS - Looking for easy calculation trick [#permalink] 16 Feb 2009, 20:14
... | 4 | [
-0.0169677734375,
0.07763671875,
-0.04248046875,
0.0157470703125,
-0.0277099609375,
-0.0150146484375,
0.0673828125,
0.08447265625,
-0.028076171875,
0.055419921875,
0.013671875,
-0.07666015625,
0.06591796875,
-0.007110595703125,
-0.03125,
0.061279296875,
-0.0296630859375,
0.04028320... | 33,929 | 33929 | |
sine inequality
June 28th 2008, 06:11 AM #1
sine inequality
The set of all x in the interval [0, π] for which 2 sin^2 x - 3 sin x + 1 ≥ 0 is?
I got three values of x:
π/6, 5π/6 and π/2
Options for the question are:
A) [π/6, 5π/6] U {π/2}
B) [π/6, 5π/6] - {π/2}
C) [π/6, 5π/6]
D) None
... | 4 | [
-0.0267333984375,
0.052001953125,
-0.03662109375,
-0.06103515625,
-0.064453125,
0.09130859375,
-0.0026397705078125,
-0.03271484375,
-0.005340576171875,
-0.042236328125,
0.01409912109375,
-0.0556640625,
0.0260009765625,
-0.03369140625,
0.034423828125,
-0.0654296875,
0.0260009765625,
... | 33,930 | 33930 | |
Trapezoidal rule problem
August 25th 2008, 11:45 PM #1
Junior Member
Joined
Nov 2007
Posts
29
Trapezoidal rule problem
integral (limits: a = -1 and b = 1) or $5e^-2x^2$ (the Latex max confuse: 5e^-2x^2) using 4 strips.
Length = 2 and width = 0.6
$E = 0.677 + 0.677 = 1.354$
$M = 0.169 + 0.1... | 5 | [
0.045166015625,
0.03173828125,
0.076171875,
-0.046142578125,
-0.017578125,
-0.06982421875,
-0.01324462890625,
0.10986328125,
-0.048095703125,
0.07275390625,
0.0111083984375,
-0.054931640625,
0.068359375,
0.0252685546875,
-0.02197265625,
0.10888671875,
-0.046875,
-0.034912109375,
... | 33,931 | 33931 | |
Homework Help
Posted by Melinda on Tuesday, January 10, 2012 at 7:16pm.
I have no clue what to do on these questions.
1.Two resistors a and b are connected in parallel. The total resistance R in such a circuit is found by formula R= 1/a + 1/b. If R=5/6 ohms and b is one more ohm than a, find the number of ohms in a
a... | 4 | [
-0.0390625,
0.06787109375,
0.0067138671875,
-0.01397705078125,
-0.057861328125,
-0.0186767578125,
-0.016357421875,
0.050537109375,
0.036865234375,
0.06640625,
-0.00762939453125,
-0.044677734375,
0.08740234375,
0.005462646484375,
-0.0185546875,
0.10205078125,
-0.0888671875,
-0.03491... | 33,932 | 33932 | |
Integrate 3cos^2(x)
April 14th 2009, 12:47 AM
ZaZu
Integrate 3cos^2(x)
Hey guys,
Can you please show me a step by step integration for
Find the solution for the differential equation :
3Cos^2(x) , y= Pi , x = Pi/2
Thank you !
April 14th 2009, 01:25 AM
mr fantastic
April 14th 2009, 01:42 ... | 5 | [
-0.0185546875,
0.0262451171875,
-0.01226806640625,
0.034423828125,
-0.015869140625,
0.00022983551025390625,
-0.0615234375,
-0.004638671875,
0.0201416015625,
-0.021484375,
0.05712890625,
-0.02001953125,
0.005096435546875,
0.0002880096435546875,
0.0194091796875,
-0.06494140625,
0.01348... | 33,933 | 33933 | |
Definitions of Probability Measure Proof
October 11th 2010, 11:17 PM
AKTilted
Definitions of Probability Measure Proof
Hi, I'm wondering if someone can help me with the following questions relating to the following definitions:
Given sample space S with event space A probability measure is defined as:
1... | 4 | [
-0.0810546875,
-0.07763671875,
0.05615234375,
-0.01507568359375,
0.0054931640625,
0.1748046875,
0.15625,
-0.0135498046875,
0.0242919921875,
0.0194091796875,
-0.00299072265625,
-0.07275390625,
0.0179443359375,
0.00811767578125,
-0.0191650390625,
0.020263671875,
0.050537109375,
-0.02... | 33,934 | 33934 | |
Bowling balls
Solving the nice puzzle below, I found it easier to define a stream coinductively than to define a function from natural numbers inductively.
You’re standing in front of a 100 story building with two identical bowling balls. You’ve been tasked with testing the bowling balls’ resilience. The building ... | 5 | [
0.032470703125,
0.054443359375,
-0.026611328125,
-0.054931640625,
-0.00848388671875,
-0.0218505859375,
-0.053955078125,
0.00136566162109375,
0.03173828125,
0.053466796875,
-0.09765625,
-0.03271484375,
0.0096435546875,
0.0859375,
0.055419921875,
-0.02197265625,
0.00830078125,
0.0167... | 33,935 | 33935 | |
Confused by alternate method of finding f'(a)
February 12th 2011, 06:28 PM #1
Newbie
Joined
Mar 2010
Posts
13
Confused by alternate method of finding f'(a)
I'm having a hard time using:
$f'(a)=\lim_{x \to a}\dfrac{f(x)-f(a)}{x-a}$
to find the derivative of $f(x)=x^2-8x+9$
I need to do it u... | 4 | [
-0.0233154296875,
0.037109375,
0.031982421875,
-0.021240234375,
-0.0191650390625,
0.0927734375,
-0.06396484375,
0.05810546875,
0.0537109375,
0.060791015625,
0.18359375,
-0.027587890625,
0.033447265625,
0.0205078125,
0.00909423828125,
0.0211181640625,
-0.0289306640625,
0.00248718261... | 33,936 | 33936 | |
The division problem in distribution theory.
March 24th 2011, 04:02 PM
measureman
The division problem in distribution theory.
Hi all.
Given a distribution v and a smooth f (both on a set X) - how do we find the distribution u such that fu = v? If f is never zero, then u = v/f is the solution.
I am try... | 4 | [
-0.0517578125,
0.05908203125,
0.0032958984375,
0.0576171875,
0.06396484375,
0.04931640625,
0.09228515625,
-0.0654296875,
0.05078125,
0.00604248046875,
0.103515625,
-0.049560546875,
0.047607421875,
0.0654296875,
0.017822265625,
-0.051025390625,
-0.00457763671875,
-0.06298828125,
-... | 33,937 | 33937 | |
Limit of Sequence
Prove that the limit as n approaches infinity of (2^n)/n! = 0. Any help?
Maybe you can show me? Or not if you can't be bothered...
Congratulations topsquark on your 1 --- The name of that rule is called the ratio test. If you ever studied infinite series that is what is used. --- I have very elegant... | 5 | [
-0.052734375,
-0.06298828125,
-0.03955078125,
0.046875,
0.0322265625,
0.029296875,
-0.08154296875,
-0.0123291015625,
0.04248046875,
0.031494140625,
-0.05908203125,
-0.07373046875,
-0.0068359375,
0.0595703125,
-0.0211181640625,
-0.039794921875,
0.05859375,
0.04248046875,
0.0952148... | 33,938 | 33938 | |
Gaussian curvature
December 16th 2011, 02:00 PM
Sogan
Gaussian curvature
Hello everybody,
when we consider some regular surface $S\subset \mathbb{R}^3$ with constant gaussian curvature.
Then my question is: Why and how the curvature does changes, when i multiply the givin scalar product by a constant $a... | 5 | [
-0.0439453125,
-0.125,
0.060791015625,
-0.06689453125,
-0.0169677734375,
-0.038330078125,
0.061279296875,
0.0179443359375,
0.0751953125,
0.043212890625,
0.138671875,
0.043701171875,
0.042236328125,
-0.037353515625,
-0.000530242919921875,
-0.064453125,
-0.053466796875,
0.03662109375... | 33,939 | 33939 | |
Solving Second Order Differential Equations using Runge Kutta
December 20th 2010, 03:20 PM #1
Newbie
Joined
Dec 2010
Posts
3
Solving Second Order Differential Equations using Runge Kutta
1. The problem statement, all variables and given/known data
In aerodynamics, one encounters the following initial... | 4 | [
-0.0546875,
0.01708984375,
-0.026123046875,
-0.023681640625,
0.0159912109375,
-0.00836181640625,
-0.04345703125,
-0.03564453125,
-0.0296630859375,
-0.045166015625,
0.1103515625,
-0.0625,
-0.06591796875,
-0.04736328125,
-0.00057220458984375,
0.09326171875,
-0.10888671875,
-0.0291748... | 33,940 | 33940 | |
differential equation
November 4th 2012, 12:36 AM #1
Newbie
Joined
Oct 2012
From
canada
Posts
15
differential equation
Hello:
I have to solve the following differential equation as shown in the attachment
please help me how to solve this differential equation
Re: differential equation
... | 5 | [
-0.06689453125,
-0.00086212158203125,
0.07177734375,
0.0169677734375,
0.041259765625,
0.0032958984375,
0.007537841796875,
0.047119140625,
0.00830078125,
0.015625,
0.099609375,
-0.06640625,
0.013916015625,
0.051513671875,
-0.037109375,
0.04736328125,
-0.04833984375,
-0.060546875,
... | 33,941 | 33941 | |
Euclidean norm of U*x when norm of x is 1!
October 1st 2009, 10:26 AM #1
Newbie
Joined
Sep 2009
Posts
4
Let x be a nx1 vector in Cn and y = U*x is another vector in Cn, where U is a unitary matrix and * represents the conjugate transpose.
The Euclidean norm of y equals 1 if and only if the Euclidean ... | 5 | [
-0.033935546875,
-0.0498046875,
-0.0966796875,
-0.051513671875,
-0.018798828125,
-0.0556640625,
0.0771484375,
-0.0859375,
-0.09814453125,
-0.111328125,
0.0111083984375,
0.0174560546875,
0.06982421875,
0.0517578125,
-0.0242919921875,
0.02685546875,
0.0517578125,
-0.1171875,
-0.041... | 33,942 | 33942 | |
Homework Help
Posted by Shubham on Thursday, May 22, 2008 at 9:33am.
sin(x)+cos(x)=2/3
find the value of
sin(x)
• Maths - Reiny, Thursday, May 22, 2008 at 10:25am
square both sides
sin^2 x + 2sinxcosx + cos^2 x = 4/9
1 + sin 2x = 4/9
sin 2x = -5/9
2x = 213.75 or 2x = 326.25
x = 106.87º o... | 4 | [
-0.055419921875,
0.050048828125,
-0.0242919921875,
0.0478515625,
-0.016845703125,
0.001983642578125,
-0.017822265625,
-0.0093994140625,
0.00885009765625,
-0.033447265625,
0.0869140625,
-0.0206298828125,
0.005767822265625,
0.03759765625,
0.03271484375,
-0.07080078125,
-0.06494140625,
... | 33,943 | 33943 | |
Applications of general arrow notation?
December 7th 2006, 03:50 PM #1
Applications of general arrow notation?
I don't know where to put this, so I put it here cause it is so advanced...
Anyway, for those who knows what arrow notation is, I have some questions, and for those who don't know what it is, here's... | 4 | [
-0.0291748046875,
-0.046142578125,
-0.0849609375,
0.01129150390625,
-0.08251953125,
-0.0167236328125,
0.024658203125,
-0.0703125,
0.05126953125,
-0.000789642333984375,
0.0002593994140625,
0.068359375,
0.040283203125,
-0.0169677734375,
0.015869140625,
0.19140625,
-0.0546875,
-0.0099... | 33,944 | 33944 | |
2 calculus quesions
April 17th 2010, 07:32 AM #1
Member
Joined
Dec 2009
Posts
171
2 calculus quesions
Hey there,
I'll be glad to get some help in the following questions:
1. Let g(x) be a differentiable function at $(0,1]$ which satisfies: $x^{2}g(x)$ is a monotonic ascending function at
$(... | 4 | [
-0.0294189453125,
-0.07275390625,
0.03369140625,
0.044189453125,
-0.024169921875,
0.0062255859375,
0.07666015625,
0.0034332275390625,
-0.050537109375,
-0.00113677978515625,
0.02392578125,
0.11328125,
0.061767578125,
-0.0830078125,
-0.12890625,
-0.03955078125,
0.06689453125,
-0.0322... | 33,945 | 33945 | |
Strange question with improper integrals
April 29th 2010, 06:49 PM #1
Member
Joined
Oct 2009
Posts
229
Strange question with improper integrals
First off, the limits of integration are both infinites, and I've only worked with one so far, with the other being a number. What changes?
And finally... | 5 | [
-0.0230712890625,
0.0234375,
-0.0033416748046875,
0.01275634765625,
0.060546875,
-0.05029296875,
-0.0013580322265625,
-0.052978515625,
-0.01043701171875,
-0.0439453125,
0.03857421875,
0.004058837890625,
-0.037109375,
-0.00360107421875,
0.0103759765625,
0.055908203125,
0.0016555786132... | 33,946 | 33946 | |
Interesting problem, any proofs?
October 30th 2009, 10:00 AM #1
Member
Joined
Mar 2009
Posts
168
Interesting problem, any proofs?
Let $x_{1},x_{2},...,x_{n}$ be positive real numbers. Prove that
$n^2\leq(x_1+x_2+...+x_n)(\frac{1}{x_1}+\frac{1}{x_ 2}+...+\frac{1}{x_n})$ and
$\frac{x_1+x_2+...+x_... | 5 | [
-0.0625,
-0.07666015625,
0.002960205078125,
-0.02197265625,
-0.0294189453125,
-0.00034332275390625,
-0.035400390625,
-0.011474609375,
0.0074462890625,
0.0145263671875,
-0.05517578125,
0.08447265625,
0.0177001953125,
0.00958251953125,
-0.07080078125,
0.0869140625,
0.078125,
-0.04858... | 33,947 | 33947 | |
Finding a matrix and its transpose from a given matrix
August 4th 2007, 11:23 PM #1
Newbie
Joined
Aug 2007
Posts
9
Hi all, I'm new here. I'm currently doing a thesis on image compression and embedding. However, I'm stuck at a final part of my calculations.
Lets say you have a square matrix A. Taking t... | 5 | [
-0.00634765625,
-0.0166015625,
-0.103515625,
-0.09521484375,
-0.008056640625,
-0.033447265625,
0.00119781494140625,
-0.05419921875,
-0.02978515625,
0.06689453125,
0.024169921875,
0.01275634765625,
0.051025390625,
0.01190185546875,
-0.0172119140625,
0.1279296875,
-0.051513671875,
0.... | 33,948 | 33948 | |
Related Rates cont'd...
November 21st 2008, 09:07 PM
nivek516
Related Rates cont'd...
I have some more questions that I need help setting up. Please feel free to switch out the numbers for variables so I can learn how to solve these. Thanks in advance for your help!
Quote:
Two towers (A and B) are 150... | 5 | [
-0.0037689208984375,
0.031982421875,
0.0213623046875,
-0.048583984375,
-0.01904296875,
-0.0206298828125,
-0.052978515625,
0.0673828125,
-0.0439453125,
0.0167236328125,
0.0164794921875,
-0.05078125,
0.0223388671875,
0.006072998046875,
0.00506591796875,
0.12158203125,
-0.068359375,
0... | 33,949 | 33949 | |
Related Rates: Changing Dimensions in a Rectangle
November 16th 2009, 08:03 PM #1
Newbie
Joined
Nov 2009
Posts
1
Related Rates: Changing Dimensions in a Rectangle
I am so confused on this one. I don't know if I'm suppose to use implicit differentiation like my other problems or what.
Problem: The le... | 5 | [
0.03857421875,
-0.0089111328125,
-0.0057373046875,
-0.0264892578125,
0.019287109375,
0.01171875,
-0.09130859375,
0.037109375,
0.0216064453125,
-0.000972747802734375,
0.09716796875,
0.023681640625,
-0.014892578125,
0.052978515625,
0.0166015625,
0.07470703125,
-0.0018463134765625,
0.... | 33,950 | 33950 | |
sin (180 - c) = sin c how ?
April 1st 2011, 06:51 AM #1
Junior Member
Joined
Jul 2009
Posts
68
i was going through an example in my book and cam across a step
a + b + c = 180
a+ b+ = 180 - c
sin ( a + b) = sin (180 - c) = sin c
i am not being able to understand how
sin (180 - c) = sin... | 4 | [
-0.09228515625,
0.00341796875,
-0.02392578125,
0.047119140625,
-0.0247802734375,
0.032470703125,
-0.052001953125,
-0.017578125,
-0.0108642578125,
0.024169921875,
0.0546875,
-0.0712890625,
0.020263671875,
0.0201416015625,
0.021728515625,
-0.061279296875,
-0.11083984375,
0.0305175781... | 33,951 | 33951 | |
Math Help
February 24th 2007, 10:10 AM #1
Newbie
Joined
Feb 2007
Posts
5
Loan
James borrowed $5,000 from his friend 2 years ago; and, an additional $3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.
a) How much will James have to pay... | 5 | [
-0.0189208984375,
0.115234375,
0.0673828125,
0.00121307373046875,
-0.01336669921875,
-0.087890625,
0.0260009765625,
0.0859375,
-0.037353515625,
0.07568359375,
0.0009918212890625,
-0.06591796875,
0.0390625,
0.0546875,
-0.01177978515625,
0.046142578125,
-0.0498046875,
-0.030883789062... | 33,952 | 33952 | |
Multivariable Calculus - Chain Rule
March 16th 2010, 03:12 PM #1
Junior Member
Joined
Sep 2009
Posts
32
Multivariable Calculus - Chain Rule
I might have to keep coming back here, this assignment is killing me...
Given w = xy + yz, y = sin x and z = e^x, find dw/dx
$\frac{dw}{dx} = \frac{\partial... | 5 | [
-0.07373046875,
-0.0166015625,
-0.03759765625,
0.0419921875,
0.04052734375,
-0.01123046875,
0.008056640625,
-0.1015625,
-0.049560546875,
0.043212890625,
0.036865234375,
0.00909423828125,
0.01434326171875,
0.0576171875,
0.06689453125,
0.0277099609375,
-0.07568359375,
0.04931640625,
... | 33,953 | 33953 | |
A Circle Circumscribed about a hexagon
January 12th 2010, 05:30 AM #1
Newbie
Joined
Jan 2010
Posts
4
A Circle Circumscribed about a hexagon
i need your help again !
help me to solve this...please
God bless you more .
*A circle is circumscribed about a hexagon. The area outside the hexagon b... | 4 | [
0.033935546875,
0.09375,
-0.07568359375,
-0.0185546875,
-0.031494140625,
-0.018310546875,
-0.01220703125,
0.06689453125,
0.00185394287109375,
0.0322265625,
0.0133056640625,
-0.050537109375,
0.004730224609375,
0.05078125,
0.043701171875,
-0.01397705078125,
-0.0673828125,
0.009826660... | 33,954 | 33954 | |
Propositional Logic Proof
June 16th 2011, 06:03 AM #1
Senior Member
Joined
Dec 2008
Posts
288
Propositional Logic Proof
I was wondering if this proof was ok or if (as I suspect) I am wrong and if you could help point me in the right direction.
thanks for any help
Suppose that $\mathcal{F}$ is a... | 5 | [
0.0230712890625,
-0.0303955078125,
0.08447265625,
0.01080322265625,
0.0791015625,
-0.0289306640625,
0.10546875,
-0.0654296875,
-0.0140380859375,
0.029296875,
0.034912109375,
-0.01373291015625,
0.06982421875,
0.014892578125,
0.030029296875,
-0.008544921875,
0.0252685546875,
0.035400... | 33,955 | 33955 | |
Quadratic Functions... and... ranges?
November 29th 2009, 07:23 AM #1
Newbie
Joined
Oct 2009
Posts
24
Quadratic Functions... and... ranges?
Forgive me if this is in the wrong place. I'm at that transitional stage where the algebra stuff is mix in with the pre-calculus stuff.
The question:
Elect... | 4 | [
-0.0849609375,
0.0390625,
0.056396484375,
0.0299072265625,
0.0142822265625,
0.09326171875,
-0.0703125,
0.0322265625,
0.0015106201171875,
-0.0004711151123046875,
0.09912109375,
-0.10302734375,
0.0245361328125,
0.0208740234375,
0.010009765625,
-0.05029296875,
0.0093994140625,
-0.0212... | 33,956 | 33956 | |
asking if this squeeze theorem proof is correct
January 27th 2011, 12:07 AM #1
Junior Member
Joined
Jul 2008
From
Athens, Greece
Posts
48
Hello,
I would like to ask if the proof below, concerning the squeeze theorem is correct. I guess someone else must have come up with it but I didn't find anyt... | 4 | [
-0.146484375,
-0.0220947265625,
0.044677734375,
-0.04345703125,
-0.015380859375,
0.035400390625,
0.138671875,
0.002349853515625,
-0.02490234375,
-0.01556396484375,
0.0859375,
0.037109375,
0.00107574462890625,
0.0218505859375,
0.04443359375,
0.021240234375,
-0.0218505859375,
-0.0297... | 33,957 | 33957 | |
What is Double Sampling?
6. Process or Product Monitoring and Control
6.2. Test Product for Acceptability: Lot Acceptance Sampling
6.2.4. What is Double Sampling?
Double Sampling Plans
How double Double and multiple sampling plans were invented to give a questionable lot another chance. For examp... | 5 | [
-0.0673828125,
0.0390625,
0.0419921875,
-0.0546875,
0.0194091796875,
-0.0751953125,
0.040771484375,
0.12109375,
0.0189208984375,
0.03271484375,
-0.0306396484375,
0.01068115234375,
0.07763671875,
-0.08203125,
0.0556640625,
-0.01239013671875,
0.0093994140625,
-0.022705078125,
-0.06... | 33,958 | 33958 | |
Precalculus/Trigonometry
Posted by Amanda on Saturday, October 27, 2007 at 1:14am.
How can I write a polynomial equation for this problem and draw a labeled diagram?
A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a ... | 4 | [
0.054443359375,
0.10595703125,
0.00921630859375,
-0.095703125,
0.044921875,
0.0361328125,
-0.044921875,
0.05029296875,
-0.045166015625,
0.00909423828125,
0.05322265625,
-0.049560546875,
0.039794921875,
0.08251953125,
0.0576171875,
0.0947265625,
-0.000530242919921875,
-0.01239013671... | 33,959 | 33959 | |
slope of hill
August 17th 2008, 09:28 PM #1
Newbie
Joined
Apr 2008
Posts
23
slope of hill
The height of a certain hill (in meters) is given by
h(x,y)
= 10 ( 2x y - 3 x^2- 4 y^2- 18 x + 28 y + 12),
where y is the distance (in kilometers) North, x the distance East
(a) How steep is th... | 4 | [
-0.03466796875,
0.052490234375,
0.01068115234375,
-0.0693359375,
0.00848388671875,
0.04443359375,
-0.06201171875,
0.1171875,
-0.0216064453125,
-0.001953125,
0.033935546875,
-0.01708984375,
0.049072265625,
0.02734375,
0.041259765625,
0.091796875,
-0.08251953125,
0.041015625,
-0.06... | 33,960 | 33960 | |
Homework Help
Posted by Urgent on Friday, March 30, 2007 at 2:30pm.
I have a test soon.. and I really need to know how to do this problem.. please help!!!
lim as x-->0 sin^2(x)/tan(x^2)
the answer is 1, but I have no clue how to get that!
Use series expansions. Look up Taylor expansion on google and study that topi... | 5 | [
-0.0023040771484375,
0.06884765625,
0.0205078125,
0.1171875,
0.0517578125,
-0.046630859375,
0.010009765625,
-0.04248046875,
0.053466796875,
-0.08154296875,
0.039306640625,
0.02197265625,
-0.024169921875,
0.005126953125,
-0.04443359375,
0.053955078125,
0.032958984375,
-0.02380371093... | 33,961 | 33961 | |
Riemann's Hypothesis
December 22nd 2009, 03:53 PM
Vitruvian
Riemann's Hypothesis
Today I was speaking to a friend of mine, and he brought up something called Riemann's Hypothesis. He told me that it was a concept relating to the distribution of primes and has yet to be
proven, and is evidently somehow relate... | 4 | [
-0.0693359375,
-0.01129150390625,
0.0291748046875,
0.06787109375,
0.07080078125,
0.0201416015625,
0.0186767578125,
0.13671875,
0.0174560546875,
-0.0220947265625,
-0.039306640625,
0.0400390625,
0.07080078125,
-0.07861328125,
-0.021484375,
-0.11328125,
0.002197265625,
-0.06298828125,... | 33,962 | 33962 | |
Find number of periods from annuity formula
August 22nd 2011, 05:20 AM #1
Member
Joined
Jan 2009
From
Punjab, Pakistan
Posts
88
Find number of periods from annuity formula
I have attempted to separate the number of periods (n) from the following equation
pv (1 + i)^n + pmt (1 + i * type) [{(1 + ... | 4 | [
-0.036376953125,
0.08740234375,
0.003448486328125,
0.039794921875,
0.01043701171875,
-0.083984375,
0.07666015625,
0.0625,
0.06396484375,
0.04248046875,
-0.0000049173831939697266,
-0.04345703125,
-0.0026397705078125,
0.076171875,
0.0286865234375,
-0.020751953125,
-0.1103515625,
-0.0... | 33,963 | 33963 | |
Calculator for confidence intervals
Calculator for confidence intervals of relative risk This calculator works off-line. (IE4)
Programme written by DJR Hutchon. Enter data into the boxes "A","B","C",and "D"
┌───────┬──────────────────────┬─────────────────────┐
│ │ │Group characteristic │
... | 4 | [
0.02197265625,
0.053955078125,
-0.0615234375,
0.0128173828125,
-0.02001953125,
0.054931640625,
-0.07958984375,
0.09716796875,
-0.052001953125,
0.005035400390625,
0.06689453125,
-0.07470703125,
0.0771484375,
-0.052978515625,
-0.035888671875,
0.0242919921875,
-0.0283203125,
0.0317382... | 33,964 | 33964 | |
Implicit Line Finding?
June 14th 2009, 10:50 AM #1
Implicit Line Finding?
Find the equation of the line(s) tangent to the curve $x^3+2xy-y^2=-2$ at the point(s) where $x=1$.
My answer is
$y=-\frac{3}{4}x+\frac{15}{4}$
and
$y=-\frac{5}{4}x+\frac{1}{4}$.
Is this correct?
It would be be... | 5 | [
-0.12255859375,
-0.005279541015625,
-0.018310546875,
-0.013427734375,
0.0230712890625,
0.028076171875,
-0.007110595703125,
0.06884765625,
0.01519775390625,
-0.038330078125,
0.11279296875,
-0.044189453125,
0.050048828125,
-0.0162353515625,
-0.019287109375,
0.09033203125,
-0.0593261718... | 33,965 | 33965 | |
problem solving on function!
August 27th 2009, 12:02 PM #1
Newbie
Joined
Aug 2009
Posts
9
Pollution control has become a very important concern in all countries. If controls are not put in place, it has been predicted that the function P=10000t^5/4 + 14000 will describe the average
pollution, in parti... | 4 | [
-0.0052490234375,
0.08642578125,
0.09912109375,
0.048095703125,
0.01171875,
0.059814453125,
0.0172119140625,
0.06298828125,
-0.0830078125,
0.06982421875,
0.064453125,
-0.09912109375,
0.06982421875,
0.0576171875,
-0.0306396484375,
0.06591796875,
-0.11279296875,
-0.023193359375,
-0... | 33,966 | 33966 | |
Some simple logarithm questions
May 29th 2009, 01:03 PM #1
Junior Member
Joined
Oct 2007
Posts
55
Some simple logarithm questions
the book simply says find the exact value of each expression. without a calculator. using properties of logarithms.( which it lists, but I can't see where they apply)
1. l... | 4 | [
0.052734375,
0.0260009765625,
-0.034912109375,
-0.005584716796875,
-0.0027618408203125,
-0.0556640625,
0.0025177001953125,
0.0250244140625,
0.01519775390625,
0.038818359375,
-0.0028533935546875,
-0.107421875,
-0.00848388671875,
0.01531982421875,
0.0751953125,
0.0791015625,
-0.1503906... | 33,967 | 33967 | |
finding a specific operator
January 13th 2012, 07:21 PM
Zeke
finding a specific operator
Hi! I am kinda going mad trying to find the following operator. Here goes the problem: Let $(z_n)$ be a complex seq. such that $\lim z_n=0$ and let $(x_n)$ be a seq. of pos. numbers such that $\
lim x_n=\infty$. Show tha... | 5 | [
-0.1513671875,
-0.002593994140625,
-0.02783203125,
0.0240478515625,
-0.0255126953125,
0.004913330078125,
0.0537109375,
0.03076171875,
-0.0126953125,
-0.09912109375,
0.056396484375,
0.09912109375,
-0.0439453125,
-0.05517578125,
-0.02587890625,
0.0224609375,
0.01239013671875,
-0.0458... | 33,968 | 33968 | |
calculus ab word problem
January 8th 2009, 01:31 PM #1
Junior Member
Joined
Dec 2008
Posts
37
At time t, t is greater than or equal to 0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t=0, the radius of the sphere is 1 and at t=15 he
radius is 2 (the v... | 5 | [
0.0014190673828125,
0.051513671875,
-0.006317138671875,
-0.01336669921875,
-0.01544189453125,
-0.010498046875,
-0.0537109375,
0.042724609375,
0.06640625,
0.0732421875,
0.01953125,
-0.0194091796875,
0.036865234375,
0.10302734375,
-0.01055908203125,
-0.041259765625,
0.0255126953125,
... | 33,969 | 33969 | |
parametric equation on line in 3d
February 20th 2007, 08:16 PM #1
Junior Member
Joined
Feb 2007
Posts
44
parametric equation on line in 3d
find parametric equation for the line with the following properties. the lines passes through the origin, it is contained in the plane 2x+3y-z=0. and is orthogonal to... | 4 | [
-0.11572265625,
0.01312255859375,
-0.08251953125,
-0.07861328125,
-0.03271484375,
0.026123046875,
0.00799560546875,
0.032470703125,
-0.05126953125,
0.00531005859375,
-0.031982421875,
-0.03125,
0.0556640625,
-0.01416015625,
-0.06201171875,
0.060302734375,
-0.10205078125,
-0.08154296... | 33,970 | 33970 | |
Homework Help
Posted by K on Friday, November 30, 2007 at 1:36am.
Initial info:
The atoms of crystalline solid pack together into a three-dimensional array of many small repeating units called unit cells. The simplest of the unit cells are those that have cubic symmetry, with
atoms positioned at the corners of a cube... | 4 | [
0.04052734375,
-0.0751953125,
-0.035888671875,
0.07275390625,
-0.0296630859375,
-0.03515625,
0.046142578125,
-0.027099609375,
-0.0361328125,
-0.05615234375,
0.025390625,
-0.044677734375,
-0.0103759765625,
0.09814453125,
-0.00537109375,
-0.06689453125,
-0.00653076171875,
0.010437011... | 33,971 | 33971 | |
Please help with Using Period to Evaluate Sin and Cosine
July 3rd 2005, 07:14 PM #1
Junior Member
Joined
Jun 2005
Posts
43
Please help with Using Period to Evaluate Sin and Cosine
Hi, I am trying to follow the logic of tis problem and the solution.
cos (- 7pi/2) = cos(-4pi + pi/2) = cos pi/2 = 0.
... | 4 | [
-0.09423828125,
0.0262451171875,
0.0615234375,
0.083984375,
-0.0294189453125,
0.006134033203125,
-0.03271484375,
0.0218505859375,
0.058349609375,
0.003936767578125,
0.107421875,
-0.07373046875,
0.044921875,
0.06591796875,
0.0419921875,
-0.07861328125,
-0.10205078125,
0.001274108886... | 33,972 | 33972 | |
Posts by
Total # Posts: 26,863
math
first day he ran 1.5 2nd day he ran 1.5(1.1) 3rd day he ran 1.5(1.1)(1.1) = 1.5(1.1)^2 .. on the 7th day he ran 1.5(1.1)^6 so we have: 1.5 + 1.5(1.1)+ 1.5(1.1^2 + ... + 1.5(1.1)^6 which is a
geometric series whose sum is 1.5( 1.1^7 - 1)/(1.1 - 1) = 1.5(.9487171)/.1 = 14.230756...
... | 5 | [
-0.006011962890625,
0.0274658203125,
-0.0029754638671875,
0.051513671875,
-0.037353515625,
-0.126953125,
-0.0084228515625,
0.06884765625,
0.046875,
0.06982421875,
-0.052490234375,
-0.00555419921875,
0.00927734375,
0.1123046875,
-0.041259765625,
-0.032958984375,
-0.10107421875,
-0.0... | 33,973 | 33973 | |
An Asymmetric Proximal Decomposition Method for Convex Programming with Linearly Coupling Constraints
Advances in Operations Research
Volume 2012 (2012), Article ID 281396, 20 pages
http://dx.doi.org/10.1155/2012/281396
Research Article
An Asymmetric Proximal Decomposition Method for Convex Programming with Linearly... | 4 | [
-0.024169921875,
0.01025390625,
-0.03173828125,
-0.057861328125,
0.017578125,
0.025390625,
0.0341796875,
-0.018798828125,
-0.0390625,
0.004608154296875,
-0.0216064453125,
0.05712890625,
0.08837890625,
0.06103515625,
-0.000858306884765625,
0.041748046875,
0.08984375,
-0.0419921875,
... | 33,974 | 33974 | |
Rigid Body Trajectories in Different 6D Spaces
ISRN Mathematical Physics
VolumeΒ 2012Β (2012), Article IDΒ 467520, 21 pages
http://dx.doi.org/10.5402/2012/467520
Research Article
Rigid Body Trajectories in Different 6D Spaces
^1School of Systems Engineering, University of Reading, Reading RG6 6AY, UK
^2Department of... | 4 | [
0.0311279296875,
-0.06884765625,
-0.03271484375,
-0.072265625,
0.00958251953125,
0.04345703125,
-0.0113525390625,
-0.047607421875,
0.06494140625,
-0.0172119140625,
0.140625,
0.06298828125,
-0.087890625,
-0.033447265625,
-0.0037841796875,
-0.06396484375,
-0.038818359375,
0.047607421... | 33,975 | 33975 | |
Product of Linear Operators - A basic quesiton
October 10th 2009, 11:53 PM
aman_cc
Product of Linear Operators - A basic quesiton
Let $T_1, T_2,....T_n$ be linear operators on a vector space V.
Let $v\in V$ such that one of $T_1(v),T_2(v),..,T_n(v)$ is 0.
Is it ok to say $T_1T_2....T_n(V)=0$?
October ... | 5 | [
-0.03466796875,
-0.0257568359375,
-0.021240234375,
-0.028564453125,
-0.04736328125,
-0.007415771484375,
0.0238037109375,
-0.05029296875,
-0.01483154296875,
-0.0908203125,
0.03857421875,
-0.01312255859375,
-0.015625,
0.027099609375,
0.01385498046875,
0.0030517578125,
-0.030029296875,
... | 33,976 | 33976 | |
5. The Ellipse
Why study ellipses?
Orbiting satellites (including the earth and the moon) trace out elliptical paths.
Many buildings and bridges use the ellipse as a pleasing (and strong) shape.
One property of ellipses is that a sound (or any radiation) beginning in one focus of the ellipse will be reflected so it... | 4 | [
0.0247802734375,
-0.08154296875,
-0.0283203125,
-0.04296875,
-0.00347900390625,
-0.05078125,
0.01385498046875,
-0.005584716796875,
0.1279296875,
-0.046875,
0.0791015625,
-0.006011962890625,
-0.04248046875,
-0.07763671875,
-0.0205078125,
0.025146484375,
-0.01409912109375,
0.02441406... | 33,977 | 33977 | |
Summations help!
February 15th 2011, 07:15 AM
collegestudent321
Summations help!
Hello,
I am trying to solve a summation but i keep getting the wrong answer:
summation of 2^i from i=0 to i=h/2
I have tried using the geometric series equation and have gotten:(2^((h/2)+1) - 1) / (2-1) which simplifie... | 4 | [
-0.0245361328125,
0.08251953125,
0.0067138671875,
0.04248046875,
0.018798828125,
-0.07958984375,
0.045654296875,
0.029541015625,
0.0218505859375,
-0.0036468505859375,
-0.0869140625,
-0.138671875,
0.051513671875,
0.0023040771484375,
-0.06396484375,
0.08740234375,
-0.0301513671875,
-... | 33,978 | 33978 | |
Shtetl-Optimized
Monday, June 30th, 2008
This post will be longer and more technical than most — but what can I say? Sometimes you need to get something technical off your chest. The topic is something my student, Andy Drucker, and I (along
with several interested others) have been thinking about on and off for months... | 4 | [
-0.0947265625,
0.0634765625,
0.011474609375,
-0.0020294189453125,
0.0400390625,
-0.00162506103515625,
-0.032470703125,
0.000324249267578125,
-0.000690460205078125,
0.0791015625,
-0.080078125,
0.016357421875,
0.01708984375,
0.056884765625,
0.0228271484375,
-0.03369140625,
-0.003036499... | 33,979 | 33979 | |
Differential equation system (Please HELP)
May 26th 2010, 02:43 PM #1
Newbie
Joined
May 2010
Posts
3
Differential equation system (Please HELP)
Hi
In few hours I got an exam in Differential equations
1 really need help with these to differential equation systems (I am not sure how to solve them... | 4 | [
-0.115234375,
-0.06591796875,
0.0167236328125,
-0.0400390625,
0.0859375,
0.0308837890625,
-0.034912109375,
0.053466796875,
-0.01708984375,
-0.00171661376953125,
0.119140625,
-0.09130859375,
0.07080078125,
-0.056396484375,
-0.037353515625,
-0.00628662109375,
-0.061279296875,
-0.0279... | 33,980 | 33980 | |
Normal Subgroups and Factor Groups
April 22nd 2009, 03:44 PM #1
Junior Member
Joined
Apr 2009
Posts
26
Normal Subgroups and Factor Groups
Let G = GL(2,R) and let K be a subgroup of R*. Prove that H = {A ∈ G| det A ∈ K} is a normal subgroup of G.
Normal
A subgroup $H\leq G$ is said to be normal iff ... | 5 | [
-0.05029296875,
-0.0400390625,
0.0595703125,
0.0034332275390625,
0.014404296875,
-0.09375,
0.04736328125,
-0.07275390625,
-0.0167236328125,
-0.024658203125,
0.0751953125,
-0.006622314453125,
0.025390625,
-0.06982421875,
-0.026123046875,
-0.01324462890625,
0.045166015625,
-0.0144042... | 33,981 | 33981 | |
trig problem
April 15th 2013, 03:53 PM
mcleod86
trig problem
Hi, i have just started a tafe course and have come across this problem. I have not taken trig in along time, any guidance would be appreciated.
question.
6. How do you find the length of the baseline AD when it is interrupted by an obstacle?... | 4 | [
-0.06884765625,
0.045166015625,
-0.0152587890625,
-0.04638671875,
-0.0303955078125,
0.022705078125,
-0.044921875,
0.06298828125,
-0.06787109375,
0.00286865234375,
0.0303955078125,
-0.05615234375,
-0.04931640625,
0.01422119140625,
0.024169921875,
0.03076171875,
-0.0751953125,
0.0027... | 33,982 | 33982 | |
Topology question: continuous maps and homeomorphisms
April 18th 2011, 12:26 AM #1
Junior Member
Joined
Aug 2009
Posts
36
Topology question: continuous maps and homeomorphisms
Let R denote the real numbers.
Let S^2 denote the unit sphere in R^3
Let f: S^2 -> R^4 be defined by f(x,y,z)=(x^2-y^2,xy... | 5 | [
0.05615234375,
0.0712890625,
-0.00506591796875,
0.009765625,
0.0123291015625,
0.142578125,
0.035400390625,
-0.038818359375,
-0.0079345703125,
0.009521484375,
0.05224609375,
0.048828125,
-0.0286865234375,
0.032470703125,
0.0291748046875,
-0.04443359375,
-0.0123291015625,
-0.01818847... | 33,983 | 33983 | |
Cauchy sequences
October 26th 2008, 01:34 AM
terr13
Cauchy sequences
Suppose $x_n$ is a Cauchy sequence in a metric spare X, and some subsequence $x_k$ converges to a point $p \in X$. Show the full series converges to p.
Is this correct?
First prove convergence of $x_n$. Find an integer N such that $\f... | 5 | [
-0.0712890625,
-0.0164794921875,
0.052001953125,
-0.12353515625,
-0.0634765625,
0.08056640625,
0.08642578125,
0.036865234375,
0.031005859375,
-0.03125,
0.000339508056640625,
-0.00238037109375,
-0.03466796875,
0.04052734375,
0.06396484375,
0.01446533203125,
0.0205078125,
-0.01312255... | 33,984 | 33984 | |
yet another trig substitution
February 12th 2009, 07:48 PM
mollymcf2009
yet another trig substitution
Last one on this homework!!!
$\int \frac{\sqrt{x^2-100}}{x^3}dx$
Here is where I have gotten to:
*I left out the first 10 steps I did, let me know if you wanna see all those.
$\frac{1}{100} \i... | 4 | [
-0.06396484375,
0.0089111328125,
0.060302734375,
-0.0308837890625,
0.004913330078125,
-0.0211181640625,
-0.037841796875,
-0.000598907470703125,
-0.0147705078125,
0.035400390625,
0.091796875,
0.0294189453125,
-0.04736328125,
0.10498046875,
0.018310546875,
0.055419921875,
0.04467773437... | 33,985 | 33985 | |
Conditional probability.
March 31st 2011, 11:59 PM #1
Newbie
Joined
Mar 2011
Posts
3
Conditional probability.
Hey guys, I'm having trouble with figuring this out:
What is P(V) given the following information?
P(F|V) = 0.02, P(F^c|V) = 0.98 P(F|V^c) = 0.4, P(F) = 0.2, P(F^c) = 0.8
Where I'v... | 4 | [
0.103515625,
0.0849609375,
0.0257568359375,
0.046875,
0.08251953125,
-0.003021240234375,
0.000370025634765625,
0.021484375,
0.0244140625,
0.076171875,
0.037841796875,
-0.08154296875,
-0.0296630859375,
0.1396484375,
0.004730224609375,
0.006256103515625,
-0.080078125,
-0.03271484375,... | 33,986 | 33986 | |
Stuck on finding an Integral
Hi all, I am stuck on trying to find $\int sin(2x+\frac{\pi}{4})cos(2x+\frac{\pi}{4})dx$
Have you considered $\sin(2x) = 2\cdot\sin(x)\cos(x)$? Mustn't forget one's trigonometry.
Try u substitution, with $u=sin(2x+\pi/4)$. Then $du=2cos(2x+\pi/4)$, and the rest is easy.
Not sure how I wo... | 4 | [
0.005889892578125,
0.01507568359375,
0.04541015625,
0.043212890625,
0.00421142578125,
0.0400390625,
-0.01422119140625,
0.00457763671875,
-0.0400390625,
-0.007476806640625,
0.0250244140625,
-0.07763671875,
-0.0301513671875,
0.044921875,
-0.0179443359375,
-0.033935546875,
0.08447265625... | 33,987 | 33987 | |
Prey/Predator Model (need help asap please)
November 2nd 2008, 03:10 PM #1
Junior Member
Joined
Mar 2007
Posts
33
Prey/Predator Model (need help asap please)
Hey I need help with a question regarding a prey/predator model. The question is in 2 parts (paraphrasing them). (i) if there are no predators, wha... | 5 | [
-0.0595703125,
0.00634765625,
0.02001953125,
-0.04541015625,
0.041259765625,
-0.07666015625,
-0.019775390625,
0.00372314453125,
0.001129150390625,
0.043701171875,
0.1533203125,
-0.09521484375,
0.0732421875,
0.0537109375,
0.032958984375,
0.07275390625,
-0.0091552734375,
-0.019897460... | 33,988 | 33988 | |
Algebraic Division
October 20th 2008, 01:04 PM
db5vry
Algebraic Division
I need serious help with this, I can't understand it at all:
If I had, for example, x³ + 4x² + 5x + 2 and had to divide it by (x+2)
How would I do it?
Can you please go through a method with me to solve this? It would be grea... | 4 | [
-0.07763671875,
0.0028228759765625,
0.03662109375,
0.044189453125,
0.08642578125,
-0.04736328125,
-0.04931640625,
-0.048583984375,
-0.035400390625,
-0.01318359375,
0.03369140625,
-0.045654296875,
0.00390625,
-0.00750732421875,
-0.046630859375,
0.0042724609375,
-0.031494140625,
0.02... | 33,989 | 33989 | |
Set y = 0?
October 2nd 2009, 06:29 AM
tsmith
Set y = 0?
The question first tells me to graph the function to determine any x-intercepts.
y = 20(2/X+1 - 3/x)
When I put it in my calculator, I got x-intercept = (1,0)
Now it tells me to set y = 0 to confirm this result.
So,
0 = 20(2/X+1 - 3/x)
... | 4 | [
-0.036376953125,
-0.032470703125,
-0.060791015625,
0.0166015625,
-0.001708984375,
-0.0206298828125,
-0.00164031982421875,
-0.006622314453125,
-0.023193359375,
-0.0118408203125,
0.07861328125,
-0.09765625,
0.0191650390625,
0.05859375,
0.054931640625,
0.0576171875,
-0.08642578125,
-0... | 33,990 | 33990 | |
Find the center the length of the axes and eccentricity of ellipse.
Find the center the length of the axes and eccentricity of ellipse. $2x^2+3y^2-4x-12y+13=0$
Hi - Complete the square for x: $2x^2 - 4x = 2(x^2 - 2x)$ $=2((x-1)^2-1)$ $=2(x-1)^2-2$ and for y: $3y^2-12y =3(y^2-4y)$ $=3((y-2)^2-4)$ $=3(y-2)^2-12$ So the ... | 4 | [
0.0703125,
0.013427734375,
-0.10546875,
-0.09130859375,
0.07373046875,
0.0267333984375,
-0.040771484375,
0.05810546875,
0.046142578125,
-0.015625,
0.11572265625,
0.0400390625,
-0.06884765625,
-0.0576171875,
-0.049560546875,
-0.00101470947265625,
-0.0849609375,
-0.0301513671875,
0... | 33,991 | 33991 | |
A probability exercise on the Bernoulli distribution
July 18, 2009
By Todos Logos
What is the probability, flipping a coin 8 times, to obtain the sequence HHTTTHTT? (H = head; T= tail)
The theory teaches us that to solve this question, we can simply use the following formula:
$$f(x)=P(X=x)=B(n,p)=\begin{pmatrix}n\... | 5 | [
-0.0242919921875,
0.040283203125,
0.03173828125,
-0.031494140625,
-0.021484375,
0.040283203125,
0.09130859375,
0.039306640625,
0.038330078125,
0.038330078125,
0.044677734375,
-0.0126953125,
0.0159912109375,
0.01422119140625,
0.004638671875,
0.052490234375,
-0.038330078125,
-0.08593... | 33,992 | 33992 | |
An Introduction to Tuning and Temperament
In this post, I will explain some different tuning systems and their advantages and disadvantages. First, let’s see what the basic goals are of tuning systems.
1. There should be 12 notes per octave, in half-step intervals.
2. An octave (12 half steps) should be at a ratio o... | 4 | [
-0.0213623046875,
0.064453125,
-0.099609375,
-0.06396484375,
-0.14453125,
-0.027099609375,
-0.0289306640625,
0.031494140625,
0.0159912109375,
0.042724609375,
-0.09375,
-0.01434326171875,
0.00775146484375,
-0.053466796875,
0.03125,
-0.0235595703125,
-0.03125,
0.02099609375,
-0.050... | 33,993 | 33993 | |
Easy integral?
$(e^{\cos(x)} \sin( \sin(x) ))'=-\sin x \,e^{\cos x}\sin(\sin x)+e^{\cos x}\cos(\sin x) \cos x$$=e^{\cos x}\left(\cos(\sin x)\cos x-\sin x\,\sin(\sin x)\right)=$... $e^{\cos x}\cos(x+\sin x)$ !! Oh,
dear hollie mollie: yes, it is! A question: how did you come up with it? Some program or some insight? Ton... | 5 | [
-0.08056640625,
0.05810546875,
-0.037353515625,
0.027099609375,
0.04638671875,
0.03466796875,
0.031494140625,
-0.04443359375,
-0.04296875,
0.042724609375,
0.12890625,
-0.041015625,
0.02978515625,
-0.0242919921875,
0.0791015625,
-0.0986328125,
0.01708984375,
0.057861328125,
-0.044... | 33,994 | 33994 | |
Are hollow pipes less likely to bend under weight
enigma
What you may have heard is this, Nicholas:
Between a solid pipe and a hollow pipe of the same weight, the hollow pipe will be more resistant to bending. It will also have a much larger radius.
From the equations already presented above, the maximum bending m... | 4 | [
0.01519775390625,
0.0250244140625,
0.020751953125,
0.01312255859375,
-0.05908203125,
-0.1396484375,
-0.02294921875,
0.1533203125,
0.00653076171875,
-0.043701171875,
-0.0859375,
-0.021728515625,
-0.022216796875,
0.0027008056640625,
-0.06396484375,
0.0052490234375,
0.005523681640625,
... | 33,995 | 33995 | |
temperature problem
August 3rd 2011, 03:09 PM #1
temperature problem
Problem Statement
The temperature, $T$, of a cooling fin of a finite length, $L$, satisfies
$\frac{d^2T}{dx^2} = -k^2\left( T_L-T \right),\quad 0\leq x\leqL,\quad T(0) = 0,\quad T(L) = T_L$
where $k$, $T_0$, and $T_L$ are constants
... | 5 | [
-0.06396484375,
0.04443359375,
0.07763671875,
-0.00262451171875,
0.00738525390625,
0.078125,
0.021240234375,
0.0228271484375,
0.0091552734375,
0.042724609375,
0.09326171875,
-0.1044921875,
0.031005859375,
-0.0157470703125,
-0.01611328125,
-0.0172119140625,
-0.044189453125,
-0.08740... | 33,996 | 33996 | |
Quick trig problem
February 14th 2010, 07:09 AM #1
Newbie
Joined
Feb 2010
Posts
23
Quick trig problem
Truth is, I haven't simplified trig problems in a while. I was wondering if you guys could help me out.
Here's the problem:
Write the trigonometric expression in terms of sine and cosine, and t... | 4 | [
-0.0294189453125,
0.0157470703125,
0.064453125,
0.033447265625,
-0.01544189453125,
-0.006805419921875,
0.00970458984375,
0.0245361328125,
-0.01397705078125,
0.018798828125,
0.1025390625,
-0.048095703125,
0.004547119140625,
0.06298828125,
0.0595703125,
-0.036865234375,
0.044921875,
... | 33,997 | 33997 | |
12. The Binomial Probability Distribution
A binomial experiment is one that possesses the following properties:
Later, on this page...
1. The experiment consists of n repeated trials;
2. Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial);
3. The probabil... | 4 | [
0.061767578125,
-0.0286865234375,
0.01116943359375,
0.0419921875,
-0.0751953125,
0.041259765625,
0.11962890625,
0.034912109375,
0.10888671875,
0.0654296875,
0.056640625,
0.036376953125,
0.06396484375,
-0.006561279296875,
0.004241943359375,
0.000286102294921875,
-0.0233154296875,
-0... | 33,998 | 33998 | |
Bernoulli's Equation
September 5th 2011, 06:33 AM #1
Junior Member
Joined
Jul 2009
Posts
59
Bernoulli's Equation
What did I do wrong here?
$\frac{dy}{dx} + \frac{2}{x}y = y^2$
$\Rightarrow (-1)y'y^{-2}+(-1)y^{-1}$
$\Rightarrow (-1)y^{-2}y'+(-1)y^{-1}=-1$
$\Rightarrow y^{-2}y'+y^{-1}=1... | 5 | [
-0.0986328125,
-0.005950927734375,
0.1005859375,
0.07470703125,
0.068359375,
-0.0986328125,
-0.0025787353515625,
0.00836181640625,
-0.03662109375,
-0.018798828125,
0.0341796875,
0.00537109375,
0.080078125,
0.0272216796875,
-0.09765625,
0.000652313232421875,
-0.0849609375,
-0.079101... | 33,999 | 33999 |