content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Circle Geometry
August 23rd 2007, 04:18 AM #1
Newbie
Joined
Aug 2007
Posts
6
Circle Geometry
This last question on my homework is really annoying. I'm pretty sure the answer is laughing right in my face, but I just can't do it.
The question is:
Ab and CD are two intersecting chords of a circle ... | 4 | [
-0.058837890625,
0.050537109375,
-0.046875,
-0.038330078125,
-0.04638671875,
-0.00225830078125,
0.0220947265625,
0.06494140625,
0.11181640625,
0.04296875,
0.031494140625,
-0.051025390625,
0.09033203125,
-0.00020599365234375,
-0.00191497802734375,
0.01275634765625,
-0.047119140625,
... | 8,800 | 8800 | |
Quadratic Equation Part 4
October 28th 2009, 05:19 AM #1
Member
Joined
Jun 2009
Posts
78
Quadratic Equation Part 4
1. Solve $(\frac{3-i}{2+i})z=\frac{5+5i}{-1+2i}$. Give your answer in form a+bi
a. Show z on an Argand diagram, find the modulus and argument of z
2. Find the set of values of x suc... | 5 | [
-0.0341796875,
0.0078125,
0.008544921875,
0.02001953125,
-0.049560546875,
0.01214599609375,
0.0263671875,
0.0159912109375,
0.03369140625,
-0.0034942626953125,
0.0289306640625,
-0.07373046875,
0.055419921875,
0.034912109375,
-0.03515625,
0.035888671875,
0.043701171875,
-0.0590820312... | 8,801 | 8801 | |
Floor function proof (probably easy)
August 26th 2013, 04:13 PM #1
Newbie
Joined
Jan 2013
From
Pennsylvania
Posts
23
Floor function proof (probably easy)
I want to know if my attempt is anywhere near being correct...
I'm supposed to prove that floor(n + m) = n + floor(m) where n is an integer a... | 4 | [
0.00732421875,
0.07958984375,
-0.0164794921875,
0.03271484375,
-0.0098876953125,
-0.026611328125,
0.0286865234375,
0.049560546875,
-0.0296630859375,
-0.03515625,
-0.07470703125,
0.003997802734375,
0.059326171875,
0.0262451171875,
0.038330078125,
0.032470703125,
0.09423828125,
0.063... | 8,802 | 8802 | |
Proving Lucas Numbers and Fibonacci Numbers
March 18th 2008, 07:10 AM
hockey777
Proving Lucas Numbers and Fibonacci Numbers
The Lucas numbers $l_{0}, l_{1}, l_{2},...,l_{n}...$ are defined on the same recurrence relation defining the Fibonacci numbers, but the Lucas numbers posses different initial conditions.
... | 4 | [
-0.03759765625,
-0.0201416015625,
-0.00390625,
-0.060546875,
0.055908203125,
0.0478515625,
-0.0166015625,
0.07080078125,
0.0257568359375,
0.0341796875,
-0.00787353515625,
-0.006591796875,
-0.07763671875,
-0.034423828125,
-0.034423828125,
-0.05517578125,
-0.08642578125,
-0.059570312... | 8,803 | 8803 | |
Synthetic Division
January 1st 2006, 12:40 PM
aussiekid90
Concept Help PLEASE!!!
Alright, i have to discuss how synthetic division can be used with any linear factor of the form ax+b. for example, any polynomial divided synthetically by ax+b. I didn't know that it was
possible i thought you could only do x+b... | 4 | [
-0.095703125,
0.018310546875,
-0.08203125,
0.0419921875,
0.01806640625,
0.0267333984375,
-0.034912109375,
-0.06982421875,
-0.04052734375,
-0.00799560546875,
0.0021514892578125,
-0.0390625,
0.01953125,
0.0517578125,
-0.02490234375,
0.0086669921875,
-0.060546875,
0.0654296875,
-0.0... | 8,804 | 8804 | |
Odds of 1 to 6 straight
What are the odds of rolling 1,2,3,4,5,6 (any order) with one throw of six standard dice?
Re: Odds of 1 to 6 straight
are you tossing the die six times?
I didn't understand the one throw comment.
$6!/6^6$
Re: Odds of 1 to 6 straight
6 dice are thrown once?
1/6*1/6*1/... | 4 | [
0.00958251953125,
-0.11376953125,
0.002899169921875,
0.03369140625,
-0.02294921875,
0.0031890869140625,
0.0279541015625,
-0.035400390625,
0.053955078125,
0.0186767578125,
-0.047119140625,
-0.0185546875,
0.0068359375,
-0.0634765625,
-0.009033203125,
0.027587890625,
-0.09423828125,
0... | 8,805 | 8805 | |
uniform convergence
February 18th 2011, 12:58 PM #1
Member
Joined
Nov 2010
Posts
94
uniform convergence
(a) Fn(x) = nxe^(-nx), x>= 0. Prove that the convergence is uniform for x>= @, where @ is any positive number. Why is the convergence not uniform on the interval 0<= x<= @??
(b) Fn(x) = (tan^-1)nx... | 4 | [
-0.02880859375,
0.02294921875,
0.0693359375,
-0.0125732421875,
-0.056640625,
0.041015625,
0.10595703125,
0.01220703125,
-0.00714111328125,
-0.001251220703125,
0.027587890625,
0.0272216796875,
0.038330078125,
0.021728515625,
0.041259765625,
-0.13671875,
0.04443359375,
-0.1455078125,... | 8,806 | 8806 | |
Math Forum Discussions - Re: How to combine an If statement with Statistics
Date: Jul 18, 2013 2:44 AM
Author: Bob Hanlon
Subject: Re: How to combine an If statement with Statistics
off = 140;(*Expected Number of Off Counts*)
=E1 = .3;(*Ratio of On/Off Counts*)
Non = RandomVariate[PoissonDistribution[=E1*off], 100000... | 4 | [
0.02734375,
0.038330078125,
-0.005615234375,
0.01446533203125,
0.06005859375,
0.028564453125,
0.035888671875,
0.037353515625,
0.00848388671875,
-0.007781982421875,
0.13671875,
-0.051025390625,
0.0732421875,
0.01953125,
0.07470703125,
-0.031005859375,
0.05029296875,
-0.052734375,
... | 8,807 | 8807 | |
Nilpotent Linear Transformation
February 3rd 2011, 07:03 PM #1
Junior Member
Joined
Nov 2008
Posts
53
Nilpotent Linear Transformation
A linear transformation T: V -> V is called nilpotent of order p if T^p = 0 and T^(p-1) is not equal to 0. If T is nilpotent, show that 1 - T is an isomorphism, where 1 de... | 5 | [
-0.042724609375,
0.058349609375,
0.031494140625,
-0.0186767578125,
-0.0220947265625,
-0.0478515625,
0.055908203125,
-0.0595703125,
0.0302734375,
-0.09521484375,
0.02978515625,
0.0211181640625,
-0.080078125,
0.025146484375,
-0.042724609375,
0.017578125,
-0.044921875,
-0.041259765625... | 8,808 | 8808 | |
matrix problem
September 24th 2010, 05:48 AM #1
Newbie
Joined
Mar 2010
Posts
6
An airline company offers daily flights among Budapest, Frankfurt, Tunis, and Windsor
The number of daily direct flights is as follow:
From Windsor - 2 flights to Tunis, one flight to Budapest and one flight to Frankfu... | 4 | [
0.064453125,
-0.05517578125,
-0.1259765625,
0.0546875,
-0.050048828125,
0.049560546875,
-0.016357421875,
-0.02294921875,
-0.0693359375,
0.018798828125,
-0.0218505859375,
-0.0003871917724609375,
-0.037353515625,
0.06787109375,
0.0079345703125,
0.078125,
-0.031494140625,
-0.081542968... | 8,809 | 8809 | |
modulus and argument
June 14th 2009, 06:43 AM
z1llch
modulus and argument
find the modulus and arguments of the complex number $(1+\sqrt 3i)^3$.
my solution;
$(1+\sqrt 3i)(1+\sqrt 3i)(1+\sqrt 3i)$
$= 1+2\sqrt3i+3i^2(1+\sqrt 3i)$
$= -2+2\sqrt3i(1+\sqrt 3i)$
$= -2-2\sqrt3i+2\sqrt3i+2(3)i^2$
... | 4 | [
-0.04931640625,
-0.01611328125,
-0.061767578125,
0.047607421875,
-0.059326171875,
-0.02978515625,
0.047119140625,
0.052978515625,
0.04345703125,
-0.0732421875,
0.0537109375,
-0.037353515625,
0.052734375,
0.049072265625,
-0.005706787109375,
-0.037109375,
-0.01904296875,
-0.059570312... | 8,810 | 8810 | |
Joint probability!
March 29th 2011, 08:21 AM
jabba1
Joint probability!
A steel manufacturer is testing a new additive for manufacturing an allow of steel. The joint probability mass function of tensile streanth and additive concentrative is
concentration additive tensile strength 100 150 200
.02 .05 .06... | 5 | [
0.0027008056640625,
0.00628662109375,
-0.01507568359375,
-0.0478515625,
-0.0034942626953125,
-0.04345703125,
0.0908203125,
0.0286865234375,
-0.0206298828125,
0.0284423828125,
0.06689453125,
-0.03271484375,
0.10302734375,
0.0595703125,
0.0155029296875,
0.052978515625,
0.0400390625,
... | 8,811 | 8811 | |
Cerebral Mastication
Mandelbrot Set in R
After writing the previous entry about Taleb and Mandelbrot I was thinking, “hey, I should be able to create the Mandelbrot set using R.” I’ve never actually tried to code the Mandelbrot set, but it
seems easy enough. Well I messed with it for 2 maybe 3 seconds and then Googled... | 4 | [
-0.039306640625,
-0.019287109375,
-0.09326171875,
-0.0155029296875,
-0.045654296875,
0.006500244140625,
0.03515625,
0.03857421875,
-0.0216064453125,
-0.00116729736328125,
-0.0067138671875,
-0.03466796875,
0.0167236328125,
0.044677734375,
-0.0174560546875,
-0.054443359375,
-0.03564453... | 8,812 | 8812 | |
Help me on all these problems
August 19th 2009, 11:08 AM #1
Newbie
Joined
Jun 2009
Posts
22
Help me on all these problems
Find the points that are symmetric to given point (a) across the x axis, (b) across the y axis, and (c) across the origin
1. (1,4)
2. (2,-3)
3. Find equations for the ve... | 4 | [
-0.06201171875,
-0.045166015625,
0.03466796875,
-0.134765625,
0.0189208984375,
0.039794921875,
-0.035888671875,
0.07275390625,
-0.0152587890625,
0.038818359375,
0.0908203125,
-0.01031494140625,
0.01422119140625,
-0.003692626953125,
0.0247802734375,
0.1025390625,
-0.138671875,
-0.08... | 8,813 | 8813 | |
Pre-test 6b Help Hurry
Hey Brookester: Let's do #4. The bacteria. What you need to do is use the given data and solve for k. Once you know k, you can use that to solve the problem. Given: $125=50e^{3k}$ Solve for k: $\frac
{5}{2}=e^{3k}$ $ln(\frac{5}{2})=3k$ $k=\frac{ln(\frac{5}{2})}{3}$ Now use that in the problem to ... | 4 | [
-0.0322265625,
0.04736328125,
0.00628662109375,
-0.0576171875,
-0.09619140625,
-0.046630859375,
0.0048828125,
0.0301513671875,
-0.0625,
0.1494140625,
0.12158203125,
-0.162109375,
0.0247802734375,
0.033203125,
-0.004486083984375,
0.0211181640625,
-0.06982421875,
-0.01312255859375,
... | 8,814 | 8814 | |
ing
To make a listing or a test that applies to all variables, constraints, or objectives, AMPL now also offers "generic" names for these components. New built-in sets and functions let AMPL also access
additional information about model components, such as their names and dimensions.
The xref command: displaying mo... | 4 | [
-0.037841796875,
-0.1015625,
0.0128173828125,
0.0140380859375,
0.0223388671875,
0.01556396484375,
0.054443359375,
0.040283203125,
-0.007476806640625,
-0.0279541015625,
0.033935546875,
-0.1005859375,
0.053466796875,
0.0634765625,
-0.000675201416015625,
0.0081787109375,
0.0098876953125... | 8,815 | 8815 | |
Math Help
November 5th 2009, 03:38 PM #1
Member
Joined
Oct 2009
Posts
86
help needed
A boat is being pulled into a dock by a means of a rope attached to a pulley on the dock which is 5 meters above the level of the boat. The rope is being pulled in at a rate of 10 meters per
minutes. How fast is the... | 4 | [
-0.1044921875,
0.0849609375,
0.026611328125,
-0.033203125,
0.01043701171875,
-0.0252685546875,
-0.06591796875,
0.06494140625,
-0.11962890625,
0.00677490234375,
0.08349609375,
0.01171875,
0.0098876953125,
0.09521484375,
-0.0703125,
0.1513671875,
-0.01519775390625,
0.0751953125,
-0... | 8,816 | 8816 | |
please please help! i have finals tomorrow!
January 28th 2009, 07:47 PM #1
Newbie
Joined
Jan 2009
Posts
1
please please help! i have finals tomorrow!
well my question is how to calculate the area of the circle when its in a triangle and i only have the units for the triangle and not the circle.
here ... | 4 | [
0.005218505859375,
0.10205078125,
-0.036376953125,
0.027587890625,
-0.00075531005859375,
-0.083984375,
-0.035400390625,
0.1005859375,
-0.0247802734375,
-0.041259765625,
-0.004547119140625,
-0.047607421875,
0.032958984375,
0.025390625,
0.0400390625,
0.01055908203125,
-0.0703125,
0.0... | 8,817 | 8817 | |
Polar Coordinate Integration
August 14th 2006, 05:36 PM #1
Newbie
Joined
Aug 2006
Posts
23
Polar Coordinate Integration
Hello,
Having problems setting integration limits due to symmetry.
I have two questions:
One asks to find the volume of the solid formed by the interior of the circle
... | 5 | [
-0.0017852783203125,
0.0322265625,
-0.02197265625,
-0.052001953125,
0.0419921875,
-0.048828125,
0.01226806640625,
0.1201171875,
0.00823974609375,
-0.01202392578125,
-0.033203125,
0.03271484375,
0.037353515625,
0.09521484375,
0.033203125,
-0.030029296875,
0.01116943359375,
-0.042968... | 8,818 | 8818 | |
Green's Theorem
February 2nd 2011, 11:37 AM #1
Junior Member
Joined
Apr 2010
Posts
59
Green's Theorem
Hey,
I have a tutorial question that is starting to bug me.
I know the formula is:
A = $\frac{1}{2}\oint_{C}(x\,\mathrm{d}y + y\, \mathrm{d}x)$
I have the problem:
Using Green's the... | 5 | [
0.01251220703125,
0.00439453125,
0.04296875,
-0.0030975341796875,
0.057861328125,
-0.049560546875,
0.0230712890625,
0.07861328125,
0.03955078125,
0.05615234375,
0.031982421875,
0.0517578125,
-0.0234375,
0.072265625,
0.0869140625,
0.028564453125,
-0.057861328125,
-0.0030975341796875... | 8,819 | 8819 | |
Last two digits...
May 28th 2010, 05:12 PM #1
Newbie
Joined
Oct 2009
Posts
20
Last two digits...
I have to find the last two digits of 222227^2010.
So I know that this gets reduced to 27^2010 mod 100
But I don't know how to solve 27^x = 1(mod 100) to get this process going. Or am I going about ... | 5 | [
0.0157470703125,
0.07470703125,
0.00872802734375,
-0.00836181640625,
0.021484375,
0.034912109375,
0.046142578125,
0.11083984375,
-0.080078125,
0.01141357421875,
0.04833984375,
0.00115203857421875,
0.055419921875,
0.056640625,
0.0021209716796875,
-0.01116943359375,
-0.123046875,
0.0... | 8,820 | 8820 | |
find the value if money flow compounded continuously...
December 12th 2008, 11:52 PM #1
Newbie
Joined
Nov 2008
Posts
22
How do I solve this question?
I'd like to know how to make a formula!
An investment is expected to produce a uniform continuous rate of money flow of $500 per year for 10 years.... | 5 | [
0.06640625,
0.0308837890625,
-0.028564453125,
-0.049072265625,
0.0142822265625,
0.00811767578125,
-0.01806640625,
0.06884765625,
-0.015625,
0.033447265625,
0.01544189453125,
-0.005157470703125,
-0.039794921875,
0.051025390625,
-0.01373291015625,
0.01055908203125,
-0.033447265625,
0... | 8,821 | 8821 | |
Solve differnetial eqation laplace transforms
July 13th 2009, 09:31 PM #1
Solve differnetial eqation laplace transforms
Question is Solve using laplace transform i need someone to clarify the notation i dont get the liimits
y'' − y' − 6y = 0 for {0 < t < 2 ; e^t for t > 2}, y(0) = 3, y0(0) = 4
i dont ge... | 5 | [
-0.04052734375,
0.027099609375,
0.0252685546875,
-0.1083984375,
0.0537109375,
0.0162353515625,
-0.07568359375,
0.039306640625,
-0.029052734375,
0.02294921875,
0.039306640625,
-0.031494140625,
-0.033447265625,
-0.10107421875,
0.060302734375,
0.010986328125,
-0.07373046875,
0.0010604... | 8,822 | 8822 | |
2-colorings of the reals
up vote 12 down vote favorite
4
It's easy to prove that, if $\mathbb{R}$ is well-orderable, then there is a 2-coloring of pairs of reals with no uncountable homogeneous set, i.e., there is an $m: [\mathbb{R}]^2\rightarrow 2$ such
that for all uncountable sets $U\subseteq\mathbb{R}$, there are ... | 5 | [
-0.0067138671875,
-0.00860595703125,
0.041015625,
0.0299072265625,
0.02978515625,
0.0888671875,
0.03759765625,
-0.11083984375,
-0.01611328125,
0.0380859375,
0.008056640625,
0.00098419189453125,
0.078125,
0.05810546875,
0.01251220703125,
0.031982421875,
0.006011962890625,
-0.0659179... | 8,823 | 8823 | |
separation axioms
GIVE AN EXAMPLE : X:normal Y:normal BUT X X Y : not normal normal is not productive
The classic example (given in Kelley's General Topology, and attributed by him to Dieudonné and Morse, independently) uses ordinal spaces. Let $\Omega_0$ be the set of all ordinal numbers less than
the first uncountab... | 4 | [
0.04833984375,
-0.0546875,
0.01043701171875,
-0.041015625,
0.0255126953125,
0.0517578125,
-0.016845703125,
-0.04833984375,
0.0155029296875,
-0.00982666015625,
0.0211181640625,
0.028076171875,
0.034912109375,
0.04052734375,
0.059814453125,
0.07275390625,
0.00008106231689453125,
-0.0... | 8,824 | 8824 | |
Estimators...
August 20th 2009, 12:28 PM
Moo
Estimators...
Hello,
Okay, I don't know at all if I did these questions correctly...
Let $f(x;\theta)=\begin{cases} 1-\theta & \text{ if } -1\leq x\leq 0 \\ 2\theta (1-x) & \text{ if } 0<x\leq 1 \\ 0 & \text{ if } x>1 \end{cases}$
and where $0<\theta<1$... | 5 | [
-0.0869140625,
-0.012451171875,
0.03515625,
-0.045654296875,
0.07275390625,
-0.0654296875,
0.0439453125,
-0.00897216796875,
-0.024169921875,
0.03955078125,
-0.0654296875,
0.0072021484375,
0.05908203125,
-0.0240478515625,
-0.07421875,
0.021728515625,
0.007110595703125,
-0.083984375,... | 8,825 | 8825 | |
integrability
let f and g be integrable functions on [a,b]. Show that $|\int_{a}^{b} fg| \leq {({\int_{a}^{b}} f^{2})^{1/2} {({\int_{a}^{b}} g^{2})^{1/2}$
Last edited by rondo09; August 7th 2010 at 11:08 PM.
First, there's a (rather huge and important) mistake: it must be $|\int_{a}^{b} fg| \leq {({\int_{a}^{b}} f^2)... | 5 | [
0.0703125,
-0.05126953125,
0.0245361328125,
-0.02734375,
-0.031982421875,
-0.0089111328125,
-0.007354736328125,
0.034423828125,
-0.037841796875,
0.01177978515625,
-0.06982421875,
0.12451171875,
0.04296875,
-0.04736328125,
-0.0247802734375,
-0.00726318359375,
0.06884765625,
-0.00126... | 8,826 | 8826 | |
Swinburne’s Test Method For Testing DC shunt motor
For a d.c shunt motor change of speed from no load to full load is quite small. Therefore, mechanical loss can be assumed to remain same from no load to full load. Also if field current is held
constant during loading, the core loss too can be assumed to remain s... | 4 | [
-0.03125,
0.0859375,
0.0257568359375,
0.0196533203125,
0.032470703125,
-0.0269775390625,
-0.018798828125,
0.047119140625,
0.059814453125,
-0.01336669921875,
-0.00139617919921875,
-0.021484375,
0.06982421875,
-0.044677734375,
-0.0712890625,
0.012451171875,
-0.0458984375,
0.079101562... | 8,827 | 8827 | |
Polynomials and x+i
July 6th 2009, 12:51 AM #1
Junior Member
Joined
Jan 2009
Posts
26
Polynomials and x+i
I could use some help with this:
Find a polynomial of degree three with real number coefficients and zeros of 3 + i and -7.
Kind of having trouble with the real number coefficients, and how ... | 4 | [
-0.0947265625,
0.05908203125,
-0.05615234375,
0.1015625,
-0.055419921875,
0.0380859375,
0.07666015625,
-0.006256103515625,
-0.022216796875,
-0.0184326171875,
-0.01348876953125,
-0.1044921875,
0.0634765625,
0.054443359375,
0.03759765625,
-0.0101318359375,
-0.06689453125,
0.08203125,... | 8,828 | 8828 | |
[SOLVED] Need help on this proof
May 5th 2008, 11:23 AM #1
Newbie
Joined
May 2008
Posts
3
Prove that a[n]=x*2^n+y*3^n is a solution to the equation
a[n] = 5*a[n-1] - 6*a[n-2] when n>=2 ,x and y are integers and numbers in [] s are subscripts and ^ denotes power .
To prove $a_n = x2^n+y3^n$ i... | 4 | [
-0.1318359375,
0.00689697265625,
-0.0172119140625,
0.0040283203125,
0.025390625,
0.047119140625,
0.0264892578125,
-0.036865234375,
-0.026611328125,
-0.00799560546875,
0.0062255859375,
-0.0101318359375,
-0.0235595703125,
-0.0296630859375,
-0.0086669921875,
0.09423828125,
-0.0825195312... | 8,829 | 8829 | |
Dimension of Affine Bundles on Projective Space
up vote 3 down vote favorite
2
Let $X \to \mathbb P^n$ be a fiber bundle of algebraic varieties with $X$ an affine variety. What is the smallest dimension that $X$ can be?
An obvious lower bound is $n+1$.
An upper bound is $2n$, given by taking the complement of a gene... | 5 | [
-0.0693359375,
-0.0341796875,
0.0654296875,
-0.0103759765625,
0.0123291015625,
-0.055419921875,
0.0712890625,
0.06591796875,
-0.044677734375,
-0.095703125,
0.04296875,
-0.0224609375,
-0.06494140625,
-0.0177001953125,
-0.03271484375,
0.037109375,
0.0400390625,
-0.04736328125,
-0.0... | 8,830 | 8830 | |
Prove continuouty of 1/x (delta-epsilon)
October 19th 2009, 12:33 PM #1
Newbie
Joined
Mar 2009
Posts
16
Prove continuouty of 1/x (delta-epsilon)
Hi guys, I've been trying to do this for a while but I'm not really getting anywhere. Hints would be much appreciated!
The problem
Prove that the fun... | 5 | [
-0.0234375,
-0.0203857421875,
0.01129150390625,
-0.023681640625,
-0.0361328125,
0.0076904296875,
0.1015625,
-0.042724609375,
-0.041748046875,
-0.0306396484375,
0.064453125,
-0.0556640625,
0.0186767578125,
0.03515625,
0.05859375,
0.007598876953125,
0.1357421875,
-0.03857421875,
-0... | 8,831 | 8831 | |
Integration
January 19th 2010, 06:53 PM #1
Member
Joined
Nov 2009
Posts
92
Integration
1. Evaluate integral(e^(7x)cos(2x)dx)
I let u =e^(7x) and so du = 7e^(7x)dx. dv is cos(2x) so V= 1/2sin(2x). I did the procedure, but i cant get the answer. Please show me some intermediate steps please!
2. E... | 5 | [
-0.0150146484375,
0.0751953125,
0.07080078125,
0.035888671875,
0.09228515625,
0.0211181640625,
-0.06787109375,
-0.002349853515625,
-0.048095703125,
0.0306396484375,
0.041748046875,
-0.09375,
-0.07861328125,
0.00823974609375,
0.03662109375,
-0.0810546875,
0.000606536865234375,
0.065... | 8,832 | 8832 | |
Distances (in general)
September 21st 2008, 05:26 PM #1
Junior Member
Joined
Sep 2008
Posts
28
Distances (in general)
I've asked several of my friends about this question, but nobody knows where to start with it, and unfortunately, neither do I. Here it is:
Given point A(x1,y1) and the line ax+by+c=... | 5 | [
-0.0211181640625,
0.04052734375,
-0.051025390625,
-0.07958984375,
-0.05810546875,
0.09228515625,
-0.023681640625,
0.0380859375,
0.0859375,
0.03076171875,
0.09326171875,
0.00836181640625,
0.003631591796875,
0.07275390625,
-0.1474609375,
0.07568359375,
0.006195068359375,
-0.056884765... | 8,833 | 8833 | |
2.7The Modified z-Transform
. The Modified z-Transform 39 Note that delaying a causal sequence always results in an initial zero value. To avoid inappropriate initial values, we rewrite the delay as T d = T - mT , 0 m < 1 m = 1
- T d T (2.33) For example, a time delay of 0.2 s with a sampling period T of 1 s correspond... | 4 | [
-0.1796875,
0.03955078125,
0.07568359375,
0.0089111328125,
0.052001953125,
-0.00518798828125,
0.01904296875,
-0.02587890625,
0.034423828125,
0.0146484375,
0.039306640625,
0.011474609375,
0.037109375,
-0.064453125,
-0.0072021484375,
-0.04150390625,
-0.07080078125,
-0.031494140625,
... | 8,834 | 8834 | |
Reacting gas volume ratios moles reactants products Gay-Lussac's Law combining volumes gcse/igcse/O level chemistry calculations igcse KS4 science A level GCE AS A2 O Level practice questions exercises
10. Reacting gas volume ratios of reactants or products (Avogadr... | 4 | [
0.0167236328125,
-0.07861328125,
-0.042236328125,
0.043212890625,
0.03857421875,
-0.05810546875,
0.0263671875,
0.07080078125,
0.0986328125,
0.00408935546875,
-0.052001953125,
0.01171875,
-0.01043701171875,
0.02197265625,
-0.019775390625,
-0.0279541015625,
-0.04052734375,
0.07910156... | 8,835 | 8835 | |
Probability Questions
October 21st 2008, 01:30 PM #1
Newbie
Joined
Oct 2008
Posts
1
Probability Questions
Wasn't sure how to categorize these.
3. Calculate the probability of selecting a college student at random and finding out they have an IQ less than 60 if (a) the probability distribution of the... | 5 | [
0.0308837890625,
0.039794921875,
0.0751953125,
-0.051025390625,
-0.01513671875,
-0.02197265625,
0.050537109375,
0.047607421875,
-0.03173828125,
0.0625,
0.05078125,
-0.02197265625,
0.030029296875,
0.03662109375,
-0.0260009765625,
0.045166015625,
-0.0390625,
-0.1318359375,
-0.06884... | 8,836 | 8836 | |
The Benefits of Introducing Assignment
Next: The Costs of Introducing Up: Assignment and Local State Previous: Local State Variables
The Benefits of Introducing Assignment
As we shall see, introducing assignment into our programming language leads us into a thicket of difficult conceptual issues. Nevertheless,... | 4 | [
-0.11279296875,
0.0011444091796875,
-0.01434326171875,
-0.039794921875,
0.01007080078125,
-0.032958984375,
0.0654296875,
-0.061767578125,
0.07958984375,
0.02783203125,
-0.033203125,
0.034912109375,
0.0634765625,
0.004913330078125,
0.0164794921875,
-0.052978515625,
0.0869140625,
0.0... | 8,837 | 8837 | |
optimzation problem # 22
August 13th 2009, 09:34 AM
skeske1234
optimzation problem # 22
The manager of a 120 unit apartment complex knows from experience that all units will be occupied if the rent is 400 dollars a month. A market survey suggests that, on the average, one additional
unit will remain vacant f... | 4 | [
-0.0296630859375,
-0.0152587890625,
-0.0419921875,
-0.056884765625,
-0.06689453125,
0.0302734375,
0.03564453125,
0.05810546875,
-0.06396484375,
0.08203125,
0.0101318359375,
0.037109375,
0.0927734375,
0.07373046875,
0.04150390625,
0.08447265625,
0.01416015625,
0.023681640625,
-0.0... | 8,838 | 8838 | |
The Probability Density Operator for the Klein - Gordon Equation
The Probability Density Operator for the K- G Equation
P.S.C. Bruskiewich
Mathematical-physics, University of British Columbia, Vancouver, BC
Dr. Maurice Pryce
Quantum-Physics, University of British Columbia, Vancouver, BC
This paper was written in 198... | 4 | [
-0.0712890625,
0.02490234375,
0.046630859375,
0.111328125,
-0.0157470703125,
0.06787109375,
0.08203125,
-0.0303955078125,
0.0242919921875,
0.044189453125,
0.0301513671875,
-0.062255859375,
-0.07177734375,
0.006072998046875,
-0.0172119140625,
-0.0087890625,
0.01116943359375,
0.03613... | 8,839 | 8839 | |
Help setting up two line integrals
July 28th 2012, 07:02 AM
NickE
Help setting up two line integrals
How do I set up these line integrals?
First problem:
Line integral of y^3dx + x^2dy where C is the arc of the parabola x=1-y^2 from (0,-1) to (0,1).
Second problem:
Line integral of ydx + (x+y... | 5 | [
-0.012939453125,
0.0052490234375,
0.0625,
-0.02197265625,
0.032958984375,
0.0322265625,
-0.0111083984375,
0.0908203125,
-0.051025390625,
-0.026123046875,
0.041259765625,
-0.000873565673828125,
0.034423828125,
-0.045166015625,
-0.01171875,
0.1162109375,
-0.07275390625,
-0.0202636718... | 8,840 | 8840 | |
Torque time
If you're just getting into motors and drives, here's some advice that will help you get off to a fast start.
Horsepower is useful in determining the total amount of work that must be accomplished in a given span of time. But torque is what brings machinery to life, turning feed screws, cutting tools, and
... | 4 | [
-0.07421875,
-0.0198974609375,
0.00933837890625,
0.02392578125,
-0.08544921875,
-0.0235595703125,
-0.0267333984375,
-0.01043701171875,
0.07470703125,
-0.000530242919921875,
-0.025390625,
0.0019378662109375,
0.00482177734375,
0.0036773681640625,
-0.047607421875,
-0.037353515625,
0.012... | 8,841 | 8841 | |
Tips on Solving Differential Equations
Date: 10/27/2003 at 07:19:52
From: David
Subject: Differential equations
I'm teaching myself differential equations with a great book
(Differential Equations - With Applications and Historical Notes,
George F. Simmons). Although the book is great, the questions often go
beyond t... | 4 | [
-0.09912109375,
-0.0264892578125,
0.06494140625,
0.0142822265625,
0.099609375,
-0.0291748046875,
-0.0302734375,
-0.033203125,
-0.095703125,
-0.0242919921875,
0.09765625,
0.0277099609375,
-0.0218505859375,
0.061767578125,
0.02685546875,
0.00830078125,
-0.09375,
0.07666015625,
-0.0... | 8,842 | 8842 | |
abstract algebra
April 17th 2014, 01:18 PM #1
Newbie
Joined
Feb 2014
From
Colombia
Posts
20
Thanks
1
abstract algebra
given the function f: X --> R+ that is bounded above, proove that sup(f^2)=sup^2(f)
I did the proof when given two functions f and g, we have that sup(f*g) is less then or eq... | 5 | [
-0.0211181640625,
0.0205078125,
0.041259765625,
0.017822265625,
-0.0037689208984375,
0.05419921875,
0.0008544921875,
0.057861328125,
-0.027587890625,
-0.024658203125,
-0.0159912109375,
0.09619140625,
0.01336669921875,
-0.052734375,
0.0174560546875,
0.005767822265625,
0.038330078125,
... | 8,843 | 8843 | |
Math Forum Discussions
Math Forum
Ask Dr. Math
Discussions
Internet Newsletter
MathTools
Teacher2Teacher
Teacher Exchange
Workshops
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: fzero f(x) vs. fminbnd f(x)^2
Replies: 2 Last Post... | 5 | [
-0.0654296875,
-0.07470703125,
0.0751953125,
0.06689453125,
0.04052734375,
0.0206298828125,
-0.01953125,
0.06787109375,
0.005401611328125,
0.080078125,
0.03271484375,
-0.017578125,
-0.0279541015625,
0.138671875,
-0.01123046875,
0.0252685546875,
-0.047119140625,
-0.0155029296875,
... | 8,844 | 8844 | |
A Quick Introduction to Monte-Carlo and Quasi-Monte Carlo Integration
In a surprising range of circumstances, it is necessary to calculate the area or volume of a region. When the region is a simple shape, such as a rectangle or triangle, and its exact dimensions are
known, this is easily accomplished through standard ... | 5 | [
0.029296875,
0.032958984375,
-0.01141357421875,
0.030029296875,
0.00921630859375,
-0.130859375,
-0.0107421875,
-0.00171661376953125,
0.0274658203125,
-0.0233154296875,
-0.10400390625,
-0.004669189453125,
0.048583984375,
-0.014892578125,
0.052734375,
-0.12451171875,
0.06982421875,
0... | 8,845 | 8845 | |
Exterior powers of the tangent bundle are a chain complex?
up vote 1 down vote favorite
Cartan's formula says: $\mathcal{L}_X \omega = (di_X + i_Xd) \omega $
For a 1-form, this is equivalent to:
$d\omega(X,Y) = X(\omega(Y)) - Y(\omega(X)) - \omega([X,Y]) $
For a 2-form, you can get:
$d\omega(X,Y,Z) = X(\omega(Y,Z)... | 4 | [
-0.150390625,
0.012939453125,
0.07421875,
0.0194091796875,
0.01422119140625,
-0.0145263671875,
0.051025390625,
-0.015625,
-0.037353515625,
-0.052001953125,
0.03564453125,
-0.023193359375,
-0.03955078125,
-0.04736328125,
0.0869140625,
0.09521484375,
-0.09716796875,
-0.00686645507812... | 8,846 | 8846 | |
divisibility proof
January 20th 2009, 02:24 PM
JediBlob
divisibility proof
I am really having trouble answering this question that i've been set
Prove that 2^(3^n) + 1 is divisible by 3^(n+1)
i have tried a few numbers and it definately is true, however i have no idea how to prove it, any help would be... | 5 | [
-0.07373046875,
-0.004486083984375,
-0.0654296875,
0.021728515625,
0.064453125,
0.0172119140625,
0.049560546875,
0.033447265625,
-0.0277099609375,
-0.046630859375,
-0.1123046875,
-0.0791015625,
0.0693359375,
0.0167236328125,
0.02880859375,
-0.015380859375,
-0.0400390625,
0.02661132... | 8,847 | 8847 | |
Analyzing Range of Function with and without Calculus
Date: 08/19/2007 at 10:24:03
From: Kieh
Subject: Show (x^2+x+1)/(x+1) does not lie between -3 and 1.
Show that for all real values of x, (x^2+x+1)/(x+1) does not lie
between -3 and 1 on the y-axis.
I really do not know how to start it! I think that only plotting... | 4 | [
-0.046630859375,
0.01470947265625,
0.0033416748046875,
0.0024871826171875,
-0.0184326171875,
0.034912109375,
-0.0498046875,
-0.0167236328125,
0.051025390625,
-0.10888671875,
0.060302734375,
-0.046630859375,
0.041015625,
0.12060546875,
-0.032958984375,
-0.08349609375,
-0.0089111328125... | 8,848 | 8848 | |
Diophantine Equation
I was looking for some help solving the equation 15 625x + 8404 = 1024y thank you
You have $5^6x+2^2\cdot 11\cdot 191=2^{10}y$$\Longrightarrow 5^6x-2^{10}y=-2^2\cdot 11\cdot 191$ . Since $(5^6,2^{10})=1$ , the above equation has solution in the integers, and as $5^6\cdot 313+2^
{10}\cdot (-4776)=1... | 5 | [
-0.0673828125,
0.01458740234375,
-0.042724609375,
-0.0284423828125,
0.06396484375,
-0.051513671875,
0.01953125,
0.046142578125,
-0.1015625,
-0.0228271484375,
0.040283203125,
0.051513671875,
0.024169921875,
0.016845703125,
-0.04052734375,
0.0546875,
-0.03369140625,
-0.042236328125,
... | 8,849 | 8849 | |
Law of cosines
From Math Images
(Difference between revisions)
(→example triangulation) Next diff →
← Previous diff
Line 35: Line 35:
==Example Triangulation== ==Example Triangulation==
Complete the triangle using the law o... | 4 | [
-0.0947265625,
0.1572265625,
-0.014404296875,
-0.05810546875,
0.03662109375,
-0.051025390625,
-0.0712890625,
0.054931640625,
-0.018798828125,
0.091796875,
0.09619140625,
-0.0286865234375,
-0.00701904296875,
0.02685546875,
0.020263671875,
-0.0791015625,
-0.08935546875,
-0.0183105468... | 8,850 | 8850 | |
Indeterminate Forms
Date: 04/23/2001 at 18:18:22
From: Brian Jennings
Subject: Indeterminate Forms
Concerning the indeterminate forms such as 0/0 and infinity/infinity,
why is one to the infinite power considered an indeterminate form?
Date: 04/23/2001 at 18:42:14
From: Doctor Schwa
Subject: Re: Indeterminate Form... | 4 | [
-0.00885009765625,
0.0250244140625,
-0.0218505859375,
0.10986328125,
-0.0020294189453125,
-0.05029296875,
-0.023681640625,
0.0223388671875,
0.1357421875,
0.036376953125,
0.015625,
-0.040771484375,
0.01416015625,
0.04736328125,
-0.02880859375,
-0.0230712890625,
-0.034423828125,
-0.0... | 8,851 | 8851 | |
image of the moon
December 2nd 2008, 08:28 PM #1
Junior Member
Joined
Feb 2008
From
NWT, Canada
Posts
51
image of the moon
You wish to form an image of the moon, diameter 3500 km, a distance of 380 000 km away, with a reflecting telescope. If the image needs to be 4.5 cm in diameter, find the require... | 4 | [
0.050537109375,
0.05615234375,
0.04248046875,
-0.06640625,
-0.0303955078125,
-0.08251953125,
-0.028076171875,
0.126953125,
-0.09033203125,
0.032470703125,
0.03857421875,
-0.08837890625,
0.0208740234375,
0.006683349609375,
-0.033447265625,
0.0361328125,
-0.010986328125,
0.0354003906... | 8,852 | 8852 | |
Why does this integral equal zero
November 24th 2010, 01:55 AM #1
Junior Member
Joined
May 2010
Posts
28
Why does this integral equal zero
Why does it equal to zero? I know it has something to do with sine being an odd function, but why does the integral of an odd function equal 0 ? (if it does)
... | 4 | [
-0.05126953125,
-0.03173828125,
0.053955078125,
0.041259765625,
0.126953125,
0.0380859375,
0.0159912109375,
0.0966796875,
-0.04931640625,
0.04931640625,
0.0498046875,
-0.02099609375,
0.006256103515625,
0.0250244140625,
-0.033935546875,
-0.0047607421875,
-0.0380859375,
-0.1000976562... | 8,853 | 8853 | |
Complete the Square
February 13th 2006, 02:09 AM
phgao
Complete the Square
1. x^2 + 2x + k
2. kx^2 + 2x + k
3. x^2 - 3kx + 1
For the first I get: -1+- root(1+k)
Second : [-1+- root(1-k)]/k
But I'm told im wrong. Help!
February 13th 2006, 02:16 AM
jacs
are you supposed to just find k?... | 4 | [
-0.0260009765625,
0.0439453125,
0.055908203125,
0.076171875,
-0.05224609375,
-0.035888671875,
0.030517578125,
-0.0250244140625,
0.03515625,
0.032958984375,
0.04150390625,
-0.06005859375,
0.0113525390625,
0.01300048828125,
-0.07861328125,
0.0106201171875,
-0.06103515625,
-0.01599121... | 8,854 | 8854 | |
What is the number of excess electrons on each sphere in the following case?Two small spheres spaced 35 cm apart have... - Homework Help - eNotes.com
What is the number of excess electrons on each sphere in the following case?
Two small spheres spaced 35 cm apart have an equal charge. How many excess electrons must be... | 5 | [
0.0634765625,
0.10791015625,
-0.0289306640625,
0.0155029296875,
-0.009521484375,
0.025634765625,
-0.00042724609375,
0.0693359375,
-0.01300048828125,
0.06982421875,
0.033447265625,
-0.11181640625,
0.043212890625,
0.09765625,
0.00311279296875,
-0.03173828125,
0.023193359375,
-0.03088... | 8,855 | 8855 | |
Use Lagrange multipliers to find the maximum and minimum
February 23rd 2010, 05:25 PM #1
Newbie
Joined
Feb 2010
Posts
6
Use Lagrange multipliers to find the maximum and minimum
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If a value do... | 4 | [
-0.013671875,
-0.022705078125,
-0.0947265625,
-0.037841796875,
-0.00066375732421875,
0.045654296875,
0.0015716552734375,
-0.021728515625,
-0.046875,
-0.024169921875,
-0.002166748046875,
0.01416015625,
0.06787109375,
-0.006988525390625,
-0.0206298828125,
0.023193359375,
-0.04663085937... | 8,856 | 8856 | |
Two's Complement
Date: 07/13/99 at 18:48:26
From: Thomas F. Corbin
Subject: Computer programming
What is two's complement and how is it used?
Date: 07/14/99 at 12:03:05
From: Doctor Peterson
Subject: Re: Computer programming
Hi Tom,
Basically, two's complement numbers are a way to encode negative
numbers into or... | 4 | [
-0.032470703125,
0.05517578125,
0.0302734375,
-0.038818359375,
-0.0693359375,
-0.02685546875,
0.018798828125,
0.0830078125,
-0.0013427734375,
-0.0205078125,
-0.0189208984375,
-0.04150390625,
0.06298828125,
-0.068359375,
-0.050048828125,
-0.0172119140625,
0.006683349609375,
-0.05664... | 8,857 | 8857 | |
change in variable question
October 16th 2010, 03:41 PM #1
Senior Member
Joined
Sep 2009
Posts
299
Y=sin(x)
let X~uniform[0,pi/2]
compute density of fy(y) for Y.
my attempt
------------
arcsin(Y) = X
fx(arcsinY)
-------------- = sqrt(1-y^2) * fx(arcsinY)
(1/sqrt(1-y^2))
... | 5 | [
-0.00634765625,
-0.04638671875,
-0.0230712890625,
-0.032470703125,
-0.00579833984375,
-0.0966796875,
0.0289306640625,
-0.03564453125,
-0.1015625,
-0.0216064453125,
-0.0031280517578125,
-0.0031280517578125,
0.0230712890625,
0.09130859375,
-0.0147705078125,
-0.0693359375,
0.02758789062... | 8,858 | 8858 | |
Urgent physics help (rotating vertical bar)
October 10th 2008, 01:13 PM #1
Newbie
Joined
Oct 2008
Posts
2
Urgent physics help (rotating vertical bar)
I found this problem very recently on the forum but mine seems to have a 4th and fifth part to it
The diagram shows a small ball of mass m=0.280kg th... | 5 | [
0.041015625,
0.018310546875,
-0.0283203125,
-0.1337890625,
-0.035400390625,
0.0218505859375,
-0.057861328125,
0.1298828125,
0.035400390625,
0.04541015625,
0.04736328125,
0.0255126953125,
0.02099609375,
-0.045166015625,
-0.06396484375,
0.0966796875,
-0.019775390625,
-0.062255859375,... | 8,859 | 8859 | |
Iterated Function Systems
Technical Description
The description given here is based on the extended mathematical development given in Barnsley's 1988 work, Fractals Everywhere, which is highly recommended to anyone with an interest in fractals and
a modest mathematical background.
The AFFINE TRANSFORMATIONS referred... | 4 | [
-0.05615234375,
-0.0281982421875,
-0.05810546875,
-0.06201171875,
-0.050537109375,
0.0299072265625,
0.00439453125,
0.0019683837890625,
0.1357421875,
-0.052490234375,
0.01434326171875,
-0.030029296875,
0.00640869140625,
0.0093994140625,
0.000514984130859375,
-0.0322265625,
-0.04321289... | 8,860 | 8860 | |
Math Help
May 6th 2009, 03:38 AM #1
Member
Joined
Apr 2008
Posts
191
Proving
(a) Show that if P is a non-singular nxn matrix then $\lambda$ is an eigenvalue of A if and only if, $\lambda$ is an eigenvalue of $PAP^{-1}$.
(b) Show that if P is a non-singular nxn matrix such that $A^3=o_{n}$. Show tha... | 4 | [
-0.0751953125,
0.0303955078125,
-0.0005645751953125,
-0.02294921875,
-0.01025390625,
0.01806640625,
0.0986328125,
-0.0634765625,
-0.003936767578125,
-0.0301513671875,
0.0732421875,
0.021728515625,
-0.048828125,
-0.01251220703125,
0.005706787109375,
0.04248046875,
0.025390625,
0.003... | 8,861 | 8861 | |
general question
October 20th 2010, 03:07 AM
akshay1995
general question
Q. For any acute triangle, all its angles have measure in integral degree. The smallest angle has measure 1/5 of the measure of the greatest angle. Find the measure of the angles of the triangle?
October 20th 2010, 05:05 PM
emakarov
... | 4 | [
-0.07421875,
0.0712890625,
0.056884765625,
-0.0120849609375,
0.01483154296875,
0.01556396484375,
0.05810546875,
0.046875,
-0.04296875,
0.01171875,
-0.052978515625,
-0.0341796875,
0.02197265625,
0.06396484375,
0.056884765625,
-0.06494140625,
0.0135498046875,
-0.0252685546875,
-0.1... | 8,862 | 8862 | |
WebDiarios de Motocicleta
Consider a doubly-ended queue with 1000 elements. Alice and Bob take turns to remove an element from either end of the queue. The player who removes a larger sum wins.
Who wins the game?
This problem appeared in
IOI
1996 in Hungary, but it's a well-known puzzle by now.
Prelude: A while ... | 5 | [
-0.01165771484375,
0.0028228759765625,
-0.0025482177734375,
-0.0693359375,
-0.06787109375,
-0.058837890625,
0.103515625,
-0.051513671875,
0.0179443359375,
0.0208740234375,
-0.119140625,
0.0517578125,
0.015380859375,
-0.035400390625,
-0.00128173828125,
-0.0128173828125,
0.16015625,
... | 8,863 | 8863 | |
integration by substitution
December 23rd 2010, 12:36 PM #1
integration by substitution
Question: evaluate the indefinite integral by using substitution
$\int \frac{e^x+1}{e^x}$
The answer key has $x-e^{-x}+C$
I tried the substitutions
1. $u=e^x\Rightarrow du=e^x dx$
2. $u=e^x+1\Rightarrow... | 5 | [
-0.05859375,
0.041015625,
0.1025390625,
0.0184326171875,
0.07080078125,
-0.046142578125,
0.0022125244140625,
-0.028564453125,
-0.03955078125,
-0.0152587890625,
0.08154296875,
-0.1484375,
-0.03857421875,
0.068359375,
-0.0208740234375,
-0.08935546875,
0.026611328125,
0.0164794921875,... | 8,864 | 8864 | |
First Order Derivative II
February 18th 2009, 11:40 AM #1
First Order Derivative II
$\frac{\mathrm{d}y}{\mathrm{d}x} = y - 2, \ \ \ y(0)=1$
Is this solveable to get $y(x)=...$. When I used seperation of variable I got $c=\ln (-1)$ which isn't possible. Can someone solve it? Thanks in advance.
Last edite... | 5 | [
-0.06689453125,
-0.07958984375,
0.07177734375,
0.03515625,
0.058349609375,
-0.0205078125,
-0.051025390625,
0.01373291015625,
-0.046142578125,
0.017578125,
0.10205078125,
-0.0458984375,
-0.02392578125,
0.048583984375,
-0.0537109375,
0.003509521484375,
-0.07080078125,
-0.048095703125... | 8,865 | 8865 | |
Finding points on a parabola (involving normal lines)
October 15th 2009, 01:17 PM #1
Junior Member
Joined
Sep 2009
Posts
37
Finding points on a parabola (involving normal lines)
"Find the point(s) on the parabola $f(x) = x^2 - 4x + 3$ at which the normal line passes through the point (2,0). Illustrate by... | 4 | [
-0.01043701171875,
-0.0341796875,
0.0198974609375,
-0.0191650390625,
0.041748046875,
0.0107421875,
-0.06005859375,
0.061767578125,
0.0634765625,
0.036376953125,
0.091796875,
-0.0255126953125,
0.09912109375,
0.037353515625,
-0.01336669921875,
0.0888671875,
-0.013671875,
-0.102050781... | 8,866 | 8866 | |
Complex Oblique Asymptote problem
January 17th 2009, 01:36 PM
Kipper
Complex Oblique Asymptote problem
Hello,
I'm currently taking Grade 12 advance functions math and our teacher assigned an interesting question for us to work through over the weekend.
I have to graph the following equation which inclu... | 4 | [
-0.051513671875,
-0.00007343292236328125,
-0.00775146484375,
0.1064453125,
0.0211181640625,
-0.03125,
-0.10302734375,
0.055419921875,
0.035400390625,
-0.08154296875,
0.0732421875,
-0.07421875,
0.0234375,
0.009033203125,
0.056396484375,
0.0211181640625,
-0.023681640625,
-0.0234375,
... | 8,867 | 8867 | |
Quadratic Formula: Solve for b
Date: 08/15/2001 at 11:29:02
From: Shawn
Subject: Quadratic Formula
How do you solve for b in the quadratic formula?
Date: 08/15/2001 at 12:48:28
From: Doctor Ian
Subject: Re: Quadratic Formula
Hi Shawn,
I'm not entirely sure why you'd _want_ to solve for b, since it's
normally a c... | 4 | [
-0.0712890625,
0.04248046875,
0.05908203125,
0.02734375,
-0.038818359375,
0.0693359375,
-0.1083984375,
0.0625,
0.033203125,
0.00628662109375,
0.0927734375,
-0.02197265625,
-0.0267333984375,
0.056640625,
0.0011444091796875,
0.1123046875,
0.017333984375,
-0.00083160400390625,
0.031... | 8,868 | 8868 | |
Following series convergent/divergent
June 10th 2009, 07:24 PM #1
Following series convergent/divergent
Here are the 2 series where their nth terms are shown:
$<br /> c_n = (-1)^n \frac{(n+1)^n}{n^n}<br />$
$<br /> d_n = \frac{(n+1)^n}{n^{n + 1}}<br />$
Attempted solution:
So I know about all t... | 5 | [
-0.06396484375,
-0.041015625,
-0.00011014938354492188,
0.06494140625,
-0.03076171875,
-0.06298828125,
-0.1181640625,
0.026611328125,
0.002655029296875,
-0.033935546875,
-0.0888671875,
-0.0830078125,
-0.005615234375,
0.01409912109375,
-0.041015625,
-0.035888671875,
0.0198974609375,
... | 8,869 | 8869 | |
Find All of X
Find all of x for which x^3-x^2-x+1 ----------------- = 0 x^3-x^2+x-1
So long as the denominator isn't 0 for a particular value of x this equation may as well read x^3 - x^2 - x + 1 = 0 (Just multiply both sides by x^3 - x^2 + x - 1) Just for reference when does x^3 -
x^2 + x - 1 = 0? Let's apply the Rat... | 4 | [
-0.09619140625,
0.053466796875,
-0.042724609375,
0.0869140625,
-0.007354736328125,
-0.0172119140625,
0.0283203125,
-0.045654296875,
0.083984375,
-0.134765625,
0.005767822265625,
-0.052734375,
0.04736328125,
0.08251953125,
-0.0272216796875,
0.0181884765625,
-0.06298828125,
-0.015380... | 8,870 | 8870 | |
Hasse Diagram confusion
March 24th 2013, 04:15 PM
personofblah
Hasse Diagram confusion
So the homework problem I was doing is as follows:
Answer these questions for the partial order represented by this Hasse diagram.
a) Find the maximal elements.
b) Find the minimal elements.
c) Is there a great... | 4 | [
0.06787109375,
0.07666015625,
0.08544921875,
-0.08642578125,
-0.006591796875,
0.041259765625,
-0.0400390625,
0.0966796875,
-0.042236328125,
0.0269775390625,
-0.08251953125,
0.0225830078125,
0.0242919921875,
-0.0751953125,
0.00019073486328125,
0.050537109375,
0.0159912109375,
-0.067... | 8,871 | 8871 | |
DE Tutorial - Part II: Nonhomogenous Second Order Equations and Their Applications
May 24th 2008, 07:24 PM
Chris L T521
DE Tutorial - Part II: Nonhomogenous Second Order Equations and Their Applications
The DE Tutorial is currently being split up into different threads to make editing these posts easier.
Se... | 5 | [
-0.10595703125,
-0.01220703125,
0.0703125,
0.0361328125,
0.0238037109375,
0.0673828125,
-0.0712890625,
-0.0849609375,
0.0201416015625,
0.02734375,
0.06982421875,
-0.028076171875,
-0.0047607421875,
0.01116943359375,
-0.005157470703125,
0.056884765625,
-0.0126953125,
0.053466796875,
... | 8,872 | 8872 | |
roblems
IMOK Key Fob Problems
What are the key fob problems?
Each year since 2005 the United Kingdom Mathematics Trust has produced a key fob, given to participants in the IMOK competition. The key fob contains a mathematical problem at an appropriate level.
2014 problem
Hints
Find a way to express the number of c... | 5 | [
-0.01068115234375,
0.0771484375,
-0.08203125,
-0.0281982421875,
-0.049072265625,
0.0281982421875,
0.00726318359375,
0.08837890625,
-0.0673828125,
-0.01263427734375,
-0.0361328125,
-0.05029296875,
-0.0146484375,
0.0027618408203125,
0.02880859375,
0.02880859375,
-0.05078125,
-0.02490... | 8,873 | 8873 | |
Basic Trig Question
11-11-2010 #1
Registered /usr
Join Date
Aug 2001
Location
Newport, South Wales, UK
Posts
1,260
Hello,
Sorry about this but my trig's been firing blanks lately:-
If I know the area of a triangle and its internal angles, can I work out the length of its sides?
Yes, tho... | 4 | [
0.002288818359375,
0.04150390625,
-0.025634765625,
-0.01202392578125,
0.01470947265625,
-0.052001953125,
-0.072265625,
0.01025390625,
-0.076171875,
-0.004852294921875,
-0.0211181640625,
-0.06982421875,
-0.0186767578125,
0.08203125,
0.0810546875,
0.0242919921875,
-0.0625,
0.01770019... | 8,874 | 8874 | |
Calculating the length of trench where 1.5m depth is exceeded
July 11th 2012, 05:39 AM
peteryoull
Calculating the length of trench where 1.5m depth is exceeded
Hi all,
I am trying to write a formula in excel to calculate the length of a trench (as in to lay a pipe in the ground). Where the trench is over 1.... | 4 | [
-0.019287109375,
0.0224609375,
0.08935546875,
-0.0240478515625,
-0.03466796875,
-0.107421875,
-0.13671875,
0.126953125,
-0.00439453125,
0.0634765625,
-0.07568359375,
-0.06201171875,
-0.046875,
0.07080078125,
0.01275634765625,
0.138671875,
-0.06396484375,
-0.010986328125,
-0.08496... | 8,875 | 8875 | |
How to cancel out decimal exponents
July 10th 2012, 08:42 PM #1
Member
Joined
Sep 2009
Posts
104
Thanks
1
How to cancel out decimal exponents
How would I state this:
10L^0.2(2.25L)^0.3
in terms of L^1 or L?
In previous exercises in my textbook, I've only dealt with a case where L is to... | 4 | [
0.053466796875,
-0.00732421875,
-0.02392578125,
0.011962890625,
0.026123046875,
-0.045166015625,
0.0264892578125,
-0.00384521484375,
0.03271484375,
0.051513671875,
0.0400390625,
-0.0284423828125,
-0.0018157958984375,
0.0673828125,
0.0228271484375,
0.055908203125,
-0.10693359375,
0.... | 8,876 | 8876 | |
Math Final Tomorrow! :S Probability Question.
June 16th 2009, 06:41 PM #1
Newbie
Joined
Oct 2007
Posts
8
okay so I have my math final tomorrow and he said that this question was on the test, I've tried all the approaches I could come up with but still haven't gotten the answer.
The question is:
... | 4 | [
-0.0101318359375,
0.0546875,
-0.048828125,
-0.00640869140625,
0.054443359375,
0.007293701171875,
0.0517578125,
0.01275634765625,
0.115234375,
0.0771484375,
-0.03857421875,
0.0068359375,
-0.01214599609375,
0.052001953125,
-0.02001953125,
-0.059326171875,
-0.07958984375,
-0.031738281... | 8,877 | 8877 | |
differential equations
Hi, I'm having a little trouble with this question: (x + y)dy/dx = y^2/(x + 4y)
\displaystyle \begin{align*} \left(x + y\right)\frac{dy}{dx} &= \frac{y^2}{x + 4y} \\ \frac{dy}{dx} &= \frac{y^2}{(x + y)(x + 4y)} \\ \frac{dy}{dx} &= \frac{y^2}{x^2 + 5x\,y + 4y^2} \\ \frac{dy}{dx}
&= \frac{\left(\f... | 5 | [
-0.023193359375,
-0.038818359375,
0.050048828125,
-0.0174560546875,
0.02587890625,
-0.023681640625,
-0.0380859375,
-0.031982421875,
0.0228271484375,
-0.044677734375,
0.08740234375,
-0.0225830078125,
-0.095703125,
0.0771484375,
-0.035400390625,
0.05908203125,
-0.037841796875,
0.0236... | 8,878 | 8878 | |
K-12 Math Problems
The domain of a function in x refers to all the possible values of x for which the function is defined. That is, it consist of all the values that make the function exist. Unless otherwise stated,
the possible values for the domain is from the set of real numbers. Usually, your teacher will only ask ... | 4 | [
-0.0230712890625,
0.0308837890625,
-0.02099609375,
-0.05615234375,
-0.10693359375,
-0.037353515625,
0.00433349609375,
-0.06103515625,
0.0751953125,
0.03515625,
0.06884765625,
-0.053955078125,
0.0162353515625,
0.020751953125,
0.01904296875,
0.003875732421875,
-0.0211181640625,
-0.01... | 8,879 | 8879 | |
Love of Logic [Science Tattoo]
Melissa writes,
I have a mathematical tattoo on my left forearm. It’s in Frege’s notation (from “Grundgesetze der Arithmetik”), which was one of the first modern logical notations. If it were written on a flat
surface, it would start with the short vertical line, which is the ass... | 4 | [
0.04150390625,
0.03466796875,
0.015625,
0.0306396484375,
-0.006744384765625,
-0.033935546875,
0.030517578125,
0.0537109375,
0.1435546875,
0.0169677734375,
-0.10302734375,
0.0198974609375,
0.02783203125,
-0.00872802734375,
-0.01068115234375,
-0.059814453125,
-0.0693359375,
-0.042236... | 8,880 | 8880 | |
Azimuthal Projections
Benjamin Høyer: Cartography
Previous chapter Contents Next chapter
(Mathematical foreword) (Cylindrical Projections )
Azimuthal Project... | 4 | [
-0.052490234375,
0.10595703125,
0.02685546875,
-0.10107421875,
0.0283203125,
-0.052490234375,
-0.01416015625,
0.0244140625,
0.057861328125,
0.030517578125,
0.0040283203125,
-0.0029449462890625,
0.056640625,
-0.06640625,
-0.0458984375,
-0.07421875,
-0.07861328125,
0.033935546875,
... | 8,881 | 8881 | |
The Proof for the Current Derivative for Powers is False by Miles Mathis
return to homepage
return to updates
... | 5 | [
-0.07958984375,
0.032958984375,
0.055419921875,
0.115234375,
0.05810546875,
-0.06298828125,
-0.029541015625,
-0.0380859375,
0.004669189453125,
0.01165771484375,
0.0255126953125,
0.076171875,
0.0196533203125,
0.019287109375,
-0.055908203125,
0.04296875,
-0.058837890625,
0.0268554687... | 8,882 | 8882 | |
Calculating limits - general question
September 26th 2010, 08:26 AM #1
Member
Joined
Sep 2009
Posts
83
Calculating limits - general question
Hey!
I encountered a question in my homework that was: "Evaluate the limit, if it exists".
$limit as x approaches 2 \frac{x^2 - x + 6}{x-2}$
It is not p... | 4 | [
-0.051513671875,
-0.02880859375,
-0.00982666015625,
0.03173828125,
0.08447265625,
0.05224609375,
-0.0732421875,
-0.006072998046875,
0.050048828125,
-0.0634765625,
0.07861328125,
-0.07666015625,
-0.00012493133544921875,
0.03662109375,
0.0025482177734375,
0.031982421875,
0.003997802734... | 8,883 | 8883 | |
HARD Integration
November 30th 2008, 05:06 AM #1
hey, last week we had a homework with f**** 26 Integration problems, i killed my self and couldnt solve this 9, can anyone help with any ?sort of teach how to do
1. tan ^ 3 x sec x dx
2. sec ^ 4 x dx
3. [ dx / 2 - sin ^ 2 x ] dx
4. [ sin ^ 3 x / roo... | 5 | [
-0.000545501708984375,
-0.01336669921875,
0.0419921875,
0.041748046875,
0.00775146484375,
-0.03662109375,
0.02197265625,
-0.0189208984375,
-0.0087890625,
0.016357421875,
0.0908203125,
-0.0189208984375,
-0.045654296875,
0.04345703125,
0.0269775390625,
-0.048583984375,
0.00086975097656... | 8,884 | 8884 | |
Finding the length of a side of a triangle:
May 17th 2007, 10:52 PM
thumpin_termis
Finding the length of a side of a triangle:
http://i118.photobucket.com/albums/o...s/triangle.jpg
In the above triangle ABC, line segment AD is 6, and I'm supposed to find the length of side BC.
I know I'm missing some ba... | 4 | [
-0.0498046875,
0.06787109375,
0.005096435546875,
-0.037109375,
-0.055908203125,
-0.002288818359375,
-0.0279541015625,
0.0322265625,
-0.01483154296875,
-0.02685546875,
0.01953125,
-0.107421875,
-0.0281982421875,
-0.0205078125,
0.040771484375,
0.047119140625,
-0.07080078125,
-0.01281... | 8,885 | 8885 | |
Ordered Field definition/description
April 21st 2011, 12:37 PM #1
Ordered Field definition/description
Hello,
What does it mean to be an ordered field? I can't find a definition in my Abstract Algebra book, nor in Wolfram.
Thanks,
Yvonne
a (linearly or totally) ordered field is a field F with an... | 4 | [
-0.0089111328125,
0.0498046875,
0.03759765625,
-0.0218505859375,
-0.10302734375,
0.06103515625,
-0.040771484375,
-0.04833984375,
0.076171875,
0.0086669921875,
0.00946044921875,
0.0498046875,
0.0267333984375,
-0.0140380859375,
0.0003814697265625,
0.044921875,
-0.0233154296875,
-0.04... | 8,886 | 8886 | |
Converting Decimals (Non-ending + Repeating) to Fractions
December 21st 2010, 04:29 PM
BIOS
Converting Decimals (Non-ending + Repeating) to Fractions
Just wondering what is the best way of converting a non ending repeating decimal number into a fraction.
Ex:
Convert 0.0315 into a fraction (315 is repea... | 4 | [
-0.05859375,
0.058349609375,
-0.00970458984375,
-0.02978515625,
0.01171875,
-0.044189453125,
-0.0023956298828125,
0.018798828125,
0.004913330078125,
0.00628662109375,
-0.0164794921875,
-0.1162109375,
-0.0079345703125,
0.06494140625,
-0.044921875,
0.0084228515625,
-0.0478515625,
0.0... | 8,887 | 8887 | |
A Question on Auto-Adjoint functors
up vote 3 down vote favorite
1
Let $F: \mathscr{C}\to \mathscr{C}^{op}$, with an adjoint $G$, and $\eta: 1_\mathscr{C} \Rightarrow G\circ F $ and $\varepsilon: F\circ G\Rightarrow 1_{\mathscr{C}^{op}}$ with components (in $\
mathscr{C}$):
$\eta_M: M\to G(F(M))$ and $\varepsilon^{op... | 5 | [
-0.060546875,
-0.0185546875,
0.10595703125,
0.03759765625,
-0.00787353515625,
0.0634765625,
0.08984375,
-0.023193359375,
-0.0093994140625,
-0.0400390625,
0.0498046875,
-0.034423828125,
-0.0198974609375,
-0.02197265625,
0.035400390625,
0.08642578125,
0.018310546875,
0.043212890625,
... | 8,888 | 8888 | |
find r .... exponents
September 12th 2010, 10:00 AM #3
Super Member
September 12th 2010, 09:02 AM #2
September 12th 2010, 08:58 AM #1
Newbie
$\displaystyle \frac{3x^3-2x^2+2x-2}{x-4} = ax^2+bx+c+\frac{r}{x-4}$
$\displaystyle \Rightarrow 3x^3-2x^2+2x-2 = (x-4)(ax^2+bx+c)+r$
$\displaystyle \Rightarrow 3... | 4 | [
-0.041015625,
0.031982421875,
-0.07666015625,
0.05126953125,
0.0244140625,
0.1357421875,
-0.02197265625,
0.0289306640625,
-0.054443359375,
-0.0732421875,
0.03271484375,
-0.08642578125,
0.03662109375,
0.025390625,
-0.01141357421875,
0.0194091796875,
-0.037353515625,
-0.017333984375,... | 8,889 | 8889 | |
Integrals!
December 17th 2007, 07:09 AM #1
Newbie
Joined
Dec 2007
Posts
2
Integrals!
Hi people!
I can't solve these ones, they're tough!
Solve $\int {\frac{{\sqrt {\sqrt {x^4 + 1} - x^2 } }}<br /> {{x^4 + 1}}\,dx}$
Evaluate $\int_0^1 {x\ln x\,dx}$
Thanks!
for the second one do in... | 5 | [
0.035888671875,
-0.0172119140625,
0.08544921875,
-0.0263671875,
-0.00006151199340820312,
-0.09765625,
-0.0625,
0.037109375,
-0.01409912109375,
-0.04736328125,
-0.02392578125,
-0.0111083984375,
0.0179443359375,
0.08837890625,
-0.11572265625,
0.054931640625,
0.041259765625,
-0.012145... | 8,890 | 8890 | |
[SOLVED] Price demand exquation
June 26th 2009, 09:16 AM #1
Newbie
Joined
Jun 2009
Posts
3
[SOLVED] Price demand exquation
I am having problems with the following problem that relates p(price) and demand (x) with the equation:
$<br /> x^2+2xp+25p^2=74,500<br />$
1. If the price is increasing at... | 5 | [
-0.0289306640625,
0.00193023681640625,
0.05859375,
-0.048095703125,
-0.00167083740234375,
0.00701904296875,
0.00927734375,
0.06298828125,
0.01519775390625,
0.0966796875,
0.08837890625,
-0.07568359375,
0.036376953125,
0.019775390625,
0.056640625,
0.03515625,
-0.050537109375,
0.02233... | 8,891 | 8891 | |
Fourier Decomposition Optimization
Next: Beyond Local Optimization: Annealing Up: Optimization Examples Previous: Optimization Examples
Let us now consider an arbitrary function represented by its Fourier decomposition. This function, denoted F(x), is a linear combination of sinusoids as in Equation 6.22.
Sin... | 4 | [
-0.080078125,
0.060302734375,
-0.012451171875,
-0.001220703125,
-0.00067138671875,
0.00421142578125,
0.0303955078125,
0.039306640625,
-0.06982421875,
0.044921875,
-0.0238037109375,
-0.0145263671875,
0.0286865234375,
-0.07080078125,
-0.00604248046875,
0.053955078125,
-0.00509643554687... | 8,892 | 8892 | |
i
Difference Equations
To solve difference equations, you have to load the package solve_rec.mac. You do this with the following command:
batch(solve_rec);
The function to solve a difference equation is solve_rec, it is called with two or more arguments. The first argument is a difference equation, and the second ar... | 5 | [
-0.09814453125,
0.0301513671875,
-0.027099609375,
-0.039794921875,
-0.06787109375,
-0.068359375,
-0.03369140625,
-0.00848388671875,
-0.046875,
-0.000476837158203125,
0.032958984375,
-0.039306640625,
-0.023193359375,
-0.1025390625,
0.0016021728515625,
0.0177001953125,
-0.0615234375,
... | 8,893 | 8893 | |
A nonparametric Bayesian approach for clustering bisulfate-based DNA methylation profiles
Abstract
Background
DNA methylation occurs in the context of a CpG dinucleotide. It is an important epigenetic modification, which can be inherited through cell division. The two major types of methylation include
hypomethylatio... | 4 | [
0.0035858154296875,
0.00897216796875,
-0.054931640625,
-0.0703125,
-0.00179290771484375,
-0.042724609375,
-0.03662109375,
0.007415771484375,
-0.0306396484375,
-0.09716796875,
0.0693359375,
-0.03759765625,
0.040283203125,
-0.0189208984375,
-0.08740234375,
0.04345703125,
-0.07958984375... | 8,894 | 8894 | |
[Numpy-discussion] [ANN] ALGOPY 0.21, algorithmic differentiation in Python
[Numpy-discussion] [ANN] ALGOPY 0.21, algorithmic differentiation in Python
Sebastian Walter sebastian.walter@gmail....
Sun Aug 1 07:05:58 CDT 2010
I'm happy to announce the first official release of ALGOPY in version 0.2.1.
Rationale:
~~~~~... | 5 | [
-0.1494140625,
-0.050537109375,
0.01055908203125,
-0.004180908203125,
0.0089111328125,
-0.1240234375,
-0.053466796875,
-0.01409912109375,
-0.04296875,
0.05224609375,
0.0007171630859375,
0.025146484375,
0.013427734375,
0.0096435546875,
-0.0181884765625,
0.0830078125,
-0.03759765625,
... | 8,895 | 8895 | |
Probability of getting every result after n tries
July 19th 2012, 08:13 AM
brokenlugs
Probability of getting every result after n tries
Hello,
I need to determine a probability for some work related to my Master Thesis. It may seem really easy but I've been trying for the last two days and I couldn't get an... | 5 | [
-0.0260009765625,
-0.004669189453125,
-0.060302734375,
-0.0537109375,
-0.05419921875,
0.02001953125,
-0.0027618408203125,
0.0174560546875,
0.037841796875,
0.03466796875,
-0.06396484375,
0.03466796875,
-0.06787109375,
-0.015625,
0.0289306640625,
0.0133056640625,
-0.058349609375,
0.0... | 8,896 | 8896 | |
Line Integrals
March 11th 2009, 11:22 AM #1
Junior Member
Joined
Jan 2009
Posts
58
Line Integrals
I don't understand how to go about solving a problem of this form;
Integrate f(x,y,z)=x+ sqrt(y) - z^2 over the path C from (0,0,0) to (1,1,1) given by C=C1nC2uC3, where
C1: r(t)=tk , 0<t<1
C2:... | 5 | [
-0.050048828125,
-0.01043701171875,
-0.061767578125,
-0.056884765625,
-0.0537109375,
0.02099609375,
-0.01043701171875,
0.01287841796875,
-0.054931640625,
0.072265625,
-0.0830078125,
0.04443359375,
0.046875,
0.0140380859375,
-0.1005859375,
0.0301513671875,
-0.046142578125,
0.0085449... | 8,897 | 8897 | |
Bergman space of holomorphic functions on unit disc is closed in L^2 (unit disc)
February 8th 2011, 10:54 AM #1
Junior Member
Joined
Dec 2009
Posts
32
Bergman space of holomorphic functions on unit disc is closed in L^2 (unit disc)
Hello!
Could you please help with the following question:
Let $... | 4 | [
0.01220703125,
-0.0010528564453125,
-0.0036163330078125,
0.010986328125,
0.030517578125,
0.10791015625,
-0.00032806396484375,
0.059326171875,
0.04443359375,
0.0791015625,
0.018798828125,
0.0159912109375,
0.049560546875,
-0.01495361328125,
-0.0281982421875,
-0.05224609375,
-0.02880859... | 8,898 | 8898 | |
Separable Equations
March 6th 2011, 02:59 PM #1
Junior Member
Joined
Aug 2009
Posts
38
Separable Equations
1. Solve
$dP/dt = P(a-bP)$ where a and b are constants
$dP/[P(a-bP)] = dt$
rewrote the integral as
$-dP/[P(bP-a)] = dt$
then used this list of integrals [HTML]http://en.wikipedia... | 5 | [
-0.08984375,
-0.008056640625,
0.06787109375,
-0.0205078125,
0.0040283203125,
0.050537109375,
0.045654296875,
-0.005462646484375,
0.01531982421875,
0.01708984375,
0.083984375,
-0.029541015625,
0.004119873046875,
0.09228515625,
0.01806640625,
0.01519775390625,
-0.052978515625,
-0.048... | 8,899 | 8899 |