content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Are you losing money when tuning controllers?
Copying and distributing are prohibited without permission of the publisher
Are you losing money when tuning controllers?
Here are 10 rules, if followed, that will result in poor process performance
From published literature, there is a wide range of pitfalls into which ... | 4 | [
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Volume using shell method--help?!
April 14th 2010, 12:58 AM
kdl00
Volume using shell method--help?!
Hey guys, i was wondering if you can help me out with this problem...
Use the shell method to find the volume generated by rotating the region bounded by the given curves about the y-axis.
1. $y=x^2,$$y=... | 4 | [
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Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
May 21st 2013, 01:27 AM #1
Junior Member
Joined
Mar 2013
From
Australia
Posts
52
Trigonometry Double Angles - 4tan(x) = 6tan(2x): Solve for x?
4tan(x) = 6 [ 2tan(x)/1 - tan^2(x) ]
Let tan(x) = a
4a (1 - a^2) = 12a
1 - a^2 = 1... | 4 | [
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Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales
International Journal of Differential Equations
VolumeΒ 2011Β (2011), Article IDΒ 863801, 15 pages
http://dx.doi.org/10.1155/2011/863801
Research Article
Oscillation of Second-Order Nonlinear Delay Dynamic Equations on Time Scales
Departmen... | 5 | [
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solutions to an equation question
September 19th 2008, 05:01 PM #1
Junior Member
Joined
Sep 2007
Posts
55
solutions to an equation question
(x-3)^(1/2) - (x)^(1/2) = -3
How many solutions, if any are in this equation? I can't seem to be able to factor this :S Any suggestions are greatly appreciated!... | 4 | [
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... | 31,004 | 31004 | |
probability
October 17th 2012, 08:18 AM #1
Newbie
Joined
Oct 2012
From
india
Posts
1
probability
Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?
A. 1/18
B. 64/4032
C. 63/64
D. 1/9
Re: probability
Answer – (A)
So... | 4 | [
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Finding dimensions
March 23rd 2008, 05:13 PM #1
Newbie
Joined
Feb 2008
Posts
17
Finding dimensions
I'm supposed to find the dimensions of a rectangular region with a maximum area that can be enclosed by 80 feet of fencing. this is what I have so far...
2x+ 2y=80
-2x -2x
2y=80-2x
y= 80... | 4 | [
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Homework Help
Posted by Gabby! on Wednesday, February 22, 2012 at 11:25am.
solve the equation m^6 -64=0
• algebra 2 - renee, Wednesday, February 22, 2012 at 4:54pm
M^6-64=0
M^6=64
take 6root of M^6 to get M
take 6root of 64 which =+or-2
so,M=+-2
• algebra 2 - Steve, Wednesday, February 22, 2... | 4 | [
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Treatise On Analysis Vol-Ii
15 WEAK TOPOLOGIES 73
15. WEAK TOPOLOGIES
(12.15.1) Let (Ea)ae i be a family of locally convex spaces, and for each a let
GwKeu be a family of seminorms defining the topology ofEa. Let E = JQ Ea
aeE
be the product vector space, and for each a el and each X e La, put
(12.15.1.... | 4 | [
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Pre-Calc HELP
October 17th 2005, 04:41 PM #1
trinh
Guest
Pre-Calc HELP ASAP! PLEASE!!
The problem asks to solve the following expression for y in terms of x if x is not equal to zero and y is not equal to zero:
1/X + 1/XY =y
THanks
From 1/x +1/(xy) = y, you want to find y in terms of x only.
O... | 4 | [
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No integer solutions to x^10 + px^9 - qx^7 + rx^4 - s = 0
May 8th 2010, 08:03 PM
the undertaker
No integer solutions to x^10 + px^9 - qx^7 + rx^4 - s = 0
Prove that if p,q,r and s are odd integers, then this equation has no integer roots:
x^10 + px^9 - qx^7 + rx^4 - s = 0
May 8th 2010, 09:05 PM
Soroban
... | 4 | [
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Proof by induction question - inductive step clarification?
December 29th 2010, 06:32 AM #1
Newbie
Joined
May 2010
Posts
7
Hi,
I'm doing some revision, and am asked to prove by induction:
$n^n > 2^{n+1} \text{ for all } n \geqslant 3$
The provided solution has the obvious base step (n = 3),... | 4 | [
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Posts by
Total # Posts: 22
Math
c^2 = a^2 + b^2 22.1^2= 16.8^2 + b^2 solve for 'b' using pythag. theorem
physics
time to travel horizontal distance (8.7m) = time to fall vertical distance (3.3m) (a) solve for t in the vertical direction (i) initial speed in vertical direction is 0 m/s (ii) d = (initial speed in
vert... | 4 | [
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Lessons In Electric Circuits -- Volume V
Lessons In Electric Circuits -- Volume V
Chapter 4
ALGEBRA REFERENCE
Note: while division by zero is popularly thought to be equal to infinity, this is not technically true. In some practical applications it may be helpful to think the result of such a fraction
approachi... | 4 | [
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review of algebra 2
September 10th 2005, 03:45 PM
u317d
3 problems on review of algebra 2
Hi, I really need some help on these 3 problems of my algebra 2 review.
They are:
1. Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain an average return of 18% per year, If she can l... | 4 | [
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Who is faster???
June 15th 2006, 09:32 AM
fizsle
Who is faster???
Paul & john leave city A for City B at the same time. After reaching City B, both return to city A immediately. Paul travels from A to B @ 56kmph and returns @ 64kmph. John travels @ 60kmph both
ways. Who gets back to A first?
(i) Paul
... | 4 | [
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the encyclopedic entry of groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid is a simultaneous generalisation of a group, a setoid (a set equipped with an equivalence relation), and a $G$-set (a set
equipped with an action of a group $G$). Groupoids are often used to capture informat... | 4 | [
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Finding Mass
March 14th 2009, 04:56 PM #1
Junior Member
Joined
Nov 2007
Posts
58
Finding Mass
I am having trouble with the following question:
Find the mass of a ball B given by (x^2) + (y^2) + (z^2) <= (a^2) if the density at any point is proportional to its distance from the z-axis.
Any ideas... | 4 | [
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A Staggering Sequence
Happy new year! Inspired by N. J. A. Sloane's “Seven Staggering Sequences”, I started thinking about the Gijswijt sequence, A090822 in the OEIS. What appealed to me was the notion of "word logarithm"
implicit in its definition:
We begin with b(1) = 1. The rule for computing the next term, b(n... | 4 | [
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Null Space of A linear Functional
March 28th 2011, 11:55 PM #1
Member
Joined
Sep 2009
Posts
161
Null Space of A linear Functional
Dear Colleagues,
Could you please help me in solving the problem:
If $Z$ is an $(n-1)-$dimensional subspace of an $n-$dimensional vector space $X$, show that $Z$ is t... | 5 | [
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Two ways to do an integral
June 17th 2013, 06:12 PM
minneola24
Two ways to do an integral
Hi,
I did this integral this way but the book didn't Convert the left side into arcsin. Am I still right?Attachment 28639Attachment 28640
June 17th 2013, 07:07 PM
hollywood
Re: Two ways to do an integral
No, I d... | 4 | [
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[SOLVED] Limit points
November 8th 2009, 08:53 AM #1
[SOLVED] Limit points
This is a small part of a much larger question to do with optimization but is the only part I cant get!
Apply Newton's method (without linesearch) to minimize the univariate function,
$f(x) = \frac{11}{546}x^6 - \frac{38}{364}x^4... | 4 | [
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Solving an abstract system of equations.
February 24th 2011, 04:18 PM #1
Junior Member
Joined
Aug 2009
Posts
28
Solving an abstract system of equations.
$\text{Given }x=cy+bz,y=az+cx,z=bx+ay\text{ where } x,y,z$
$\text{ are not all zero, prove that }a^2+b^2+c^2+2abc=1.$
Our professor hinted that... | 4 | [
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Space Generation Model & the Large Numbers Coincidences
GravitationLab.comwhose e
ff
ect on a given length is
r
a
r
0
exp@
¡
t
A
;
(4)where
r
0
is some initial cosmic distance,
r
is
r
0
’s expandedlength (the change of which could only be directly perceivedby an imaginary being wh... | 4 | [
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-0.0625,
-0.110351... | 31,023 | 31023 | |
solving triangles- please check my answers!
February 14th 2008, 05:15 PM
iheartthemusic29
solving triangles- please check my answers!
1. How many solutions exist for the triangle where a=3.8, b=14.4, and A=157 degrees?
Answer: No triangles
2. Use the given measurements to solve triangle ABC: a=12, b=20,... | 4 | [
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0.09375,
0.0004787445068359375,
-0.0244140625,... | 31,024 | 31024 | |
Proposition 11
To draw a straight line at right angles to a given straight line from a given point on it.
Let AB be the given straight line, and C the given point on it.
It is required to draw a straight line at right angles to the straight line AB from the point C.
Take an arbitrary point D on AC. Make CE equal to... | 4 | [
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Ferris Wheel
Date: 08/11/97 at 18:37:50
From: Rhiannon
Subject: Finding how high in the air you are
Al and Betty are on a ferris wheel. The wheel there has a radius of
15 feet and its center is 20 feet above ground level. You can describe
various positions on the wheel as if the wheel was a clock.
How far off the... | 4 | [
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Second Derivative Value via Implicit Differentiation
August 3rd 2011, 09:06 PM #1
Second Derivative Value via Implicit Differentiation
Hi guys, I haven't posted in a while but I was tutoring someone and ran into a problem that I thought had got right but blackboard said was incorrect.
The problem is
$\f... | 5 | [
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How Much Ink Do You Need? | ScreenWeb | screenweb.com
(April 2000) posted on Wed Jun 14, 2000
Learn how to calculate the total amount of ink needed for any job based on mesh parameters and run length.
Determining Image Area Knowing the height of the ink layer that a particular mesh will deposit only represents one pi... | 4 | [
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Polynomial functions
Expand and simplify. Express equations in standard form. 1. f(x) = -2(x-1)(x+4)(x+1)(x-3) 2. f(x) = (x+2)(x+1)(x+4) 3.f(x) = x(x-6)
I'm not sure what you have to do... They seem in a pretty simple form. Maybe you want something like the following.. 3.f(x) = x(x-6) x(x-6) = $x^2$-6x = $x^2$-6x+9-9 ... | 4 | [
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0.08251... | 31,029 | 31029 | |
need help putting into words
January 8th 2007, 06:24 AM
math619
need help putting into words
I need to show which of the two expressions is larger and explian why. I know which is the larger number,but can not put it into words to explain. Anyone have any ideas?
a) (1/2)'2 or (1/3)'3
b)(1/3)'-2 or (1/3... | 4 | [
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0.... | 31,030 | 31030 | |
Green's Theorem and converting to polar co-ords
May 6th 2009, 11:24 AM #1
[SOLVED] Green's Theorem and converting to polar co-ords
The question goes...
Use Green's Theorem to evaluate $\oint_{\Gamma}(y^3dx-x^3dy)$, where $\Gamma$, mapped counter-clockwise, is the circle $x^2+y^2=4$. [Hint: you may find it co... | 5 | [
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proof about ....
September 27th 2009, 03:52 PM
koukou8617
proof about ....
the notation a≡b (mod n) to mean that a and b are both represented by
the same element of Zn (under addition (mod n)). Show that a≡b (mod n) if and only if n divide (b-a)
September 28th 2009, 05:13 AM
Defunkt
Assume $a \equiv b... | 4 | [
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... | 31,032 | 31032 | |
Maximising profit
September 13th 2008, 09:00 PM #1
Member
Joined
Jul 2008
Posts
212
Maximising profit
A company operates two cafes. The total daily cost of running the two cafes is
TC = 6000 + 180x + 140y
where x is the number of patrons in cafe one and y the number in cafe two. The total daily r... | 4 | [
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Details
Casio fx-4000P
Datasheet legend
Ab/c: Fractions calculation
AC: Alternating current
BaseN: Number base calculations
Card: Magnetic card storage
... | 4 | [
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Homework Help
Posted by Chelsea on Tuesday, January 31, 2012 at 7:22pm.
A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can
be enclosed? (Note: The side along the barn will ... | 4 | [
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... | 31,035 | 31035 | |
A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 836901, 15 pages
http://dx.doi.org/10.1155/2012/836901
Research Article
A Family of Derivative-Free Methods with High Order of Convergence and Its ... | 5 | [
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Equivalence Relations
September 30th 2009, 12:11 PM #1
Equivalence Relations
Let T be the set of all ordered pairs (x,y) of positive integers. For (m1,m2) in T and (n1,n2) in T define (m1,m2) ~ (n1,n2). Show that ~ is an equivalence relation.
EDIT: [CONTAINS MISSING RELATION, LATER STATED in post 5]
Las... | 5 | [
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How do you determine the number of inflection points
May 4th 2009, 09:06 PM
swatpup32
How do you determine the number of inflection points
for the function $y=2x+cos(x^2)$ on the interval of $0\leq x \leq 5$
$f\prime\prime = -2x(2xcosx^2)- 2sinx^2$
I don't need to find the inflection values. Just the nu... | 5 | [
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Total Surface Area problem.
April 7th 2011, 05:38 AM #1
Newbie
Joined
Apr 2011
Posts
10
Total Surface Area problem.
The question follows like this:
Show that the formula for the T.S.A, A (in square meters) of the box is A=-6x^2 + 12x
The information that was given is:
8x + 4y=12
also
... | 4 | [
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... | 31,039 | 31039 | |
Big Problem
October 23rd 2006, 10:47 PM #1
Bertie
Guest
Big Problem
Can anyone help me do the following problem. Have been trying for ages but cant prove the answer.
let z=re^ih (where h is not fixed)
show that if 0<h<(Pi/2) then mod of cosz tends to infinity as r tends to infinity.
what is the beh... | 5 | [
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Calculus of variations help needed
June 2nd 2009, 05:48 AM #1
Newbie
Joined
Jun 2009
Posts
10
Calculus of variations help needed
I'm attempting to derive the maximum volume enclosed by a given surface area in a volume of revolution. I know the answer is a sphere!
As this is isoperimetric, I used lag... | 5 | [
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Factorials - adding and subtracting
October 30th 2008, 07:54 AM
scott.b89
Factorials - adding and subtracting
Hey,
Kinda struggling with Factorials, more precisely the process of adding and subtracting them. The question is 5! + 4!. Now, the back of the book says the answer is 6x4!, I just don't understand
... | 4 | [
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Math Help
September 25th 2010, 04:47 PM #1
Newbie
Joined
Aug 2010
Posts
13
Series
Show by integrating the series for 1/(1 + x), that if |x| < 1, then
$\ln (1 + x)$ = ${\Sigma_{n=1}^{\infty}}\frac {-1^{(n+1)}}{n} x^n$
isn't that use Taylor expansion series?
Consider the suggested series an... | 5 | [
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0.03125,
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Geometric Sequence Problem
March 8th 2012, 05:45 PM #1
Newbie
Joined
Jun 2011
Posts
12
Geometric Sequence Problem
"The sum of the first 2 terms of a geometric sequence is four times the sum of the next 2 terms, and the sum to infinity is 3. Determine 'r' and write down the sequences."
I don't know h... | 4 | [
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Rhombus Coordinate Geometry
January 17th 2011, 09:32 PM #1
Rhombus Coordinate Geometry
Find the coordinates of C and D, such that ABCD is a rhombus. (see attached diagram)
I went ahead with simultaneous derived from distance formulas and perpendiular gradients and then solved that with Pythagoras theorem to ... | 4 | [
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Integratin by Partial Fractions
September 29th 2008, 01:51 PM #1
Newbie
Joined
Sep 2008
Posts
7
Integratin by Partial Fractions
Here is what I've done so far...
$(x^3-4x^2-16)/((x^2)(x-4))=A/x+B/x^2+C/(x-4)$
so
$x^3-4x^2-16=A(x^2)(x-4)+B(x)(x-4)+C(x)(x^2)$
= $A(x^3-4x^2)+B(x^2-4x... | 5 | [
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sin4x=cos3x
How do I find all the solutions to sin4x=cos3x, [0, 2pi[ ?
Hello, weasley74! Find solutions to: . $\sin4x\:=\:\cos3x\;\;\text{on }[0,\,2\pi]$ Code: * * * * 3x* c * * * * a * * * 4x * * * * * * * * * b We see that: . $\sin4x \:=\:\frac{a}{c} \:=\:\cos3x$ . .
and that $4x$ and $3x$ are complementary. In gene... | 4 | [
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Inverse Trig Func: Integration
April 27th 2013, 07:47 AM #1
Member
Joined
Oct 2011
Posts
153
Inverse Trig Func: Integration
Hi, I’m a bit confused on how to solve a problem like this.
My friend helped me a bit, but didn’t explain very clearly, so I was wondering if you guys could help me understand t... | 5 | [
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help with differentiation and limits
September 6th 2009, 04:53 AM
flyinhigh123
help with differentiation and limits
Differentiate y = logx3 (base is x) ie. y^3 = x
Evaluate lim xsin1/x using u=1/x
x=>∞
lim (√x - √5)/(x-5)
x=>5
thankyou so much to anyone who can help me with these quest... | 5 | [
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Wiley Europe
::
Protein Bioinformatics: An Algorithmic Approach to Sequence and Structure Analysis
Preface.
Acknowledgements.
Part I: SEQUENCE ANALYSIS.
1. Pairwise Global Alignment of Sequences.
1.1 Alignment and Evolution.
1.2 What is an Alignment?
1.3 A Scoring Scheme for the Model.
1.4 Finding Highest-Scorin... | 4 | [
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... | 31,050 | 31050 | |
What is the difference between Langrangian, Hamiltonian and Newtonian Mechanics?
Alexc475
What is the main difference between Langrangian, Hamiltonian, and Netwonian Mechanics in physics, and what are the most important uses of them?
I'm currently a high school senior, with knowledge in calculus based physics, what... | 5 | [
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Rocket Equation
June 11th 2011, 04:31 PM #1
Newbie
Joined
May 2011
Posts
1
Rocket Equation
Hey all
Wasn't really sure where to post this, this thread seemed like a good start.
I've got a side project going on building a hybrid rocket engine for abit of fun, have been working from a few books I h... | 4 | [
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Integration
\begin{align*}\log(e^{2t}+5) & = \log \left[ 5 \left( \dfrac{ e^{2t} }{5} + 1 \right) \right] \\ & = \log(5) + \log\left( \dfrac{ e^{2t} }{5} + 1 \right)\end{align*} So, $\int_2^x \log(e^{2t}+5)dt =
(x-2)\log(5) + \int_2^x \left( \sum_{n\ge 1} (-1)^{n+1}\dfrac{e^{2nt}}{n5^n} \right)dt$ Note: I replaced $\lo... | 5 | [
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Plutonium Decay Problem
January 12th 2010, 01:12 PM #1
Plutonium Decay Problem
Plutonium,
239Pu, has a half-life of 24,100 years. What percent of a given amount remains after 100,000 years?
Is this done correctly?
$1/24100ln(1/2)$
k=0.00002876
$e^(0.00002876(100000))$
= 56.35% a... | 5 | [
0.031494140625,
0.052001953125,
0.00958251953125,
-0.00927734375,
-0.0279541015625,
-0.115234375,
-0.058349609375,
0.1103515625,
-0.006683349609375,
0.10595703125,
0.0810546875,
-0.0830078125,
0.037109375,
0.052734375,
0.050537109375,
0.006103515625,
-0.109375,
-0.050537109375,
-... | 31,054 | 31054 | |
Differentiate with respect to vector
November 10th 2010, 05:18 PM #1
Newbie
Joined
Nov 2010
Posts
3
I have this problem:
$L=\frac{\mathbf{a}^T\mathbf{w}\mathbf{w}^T\mathbf{ a}}{\mathbf{w}^T(\mathbf{B}\mathbf{w}+\mathbf{C}\m athbf{w})}$
Here, $\mathbf{a}$ is a known d-by-1 vector, $\mathbf{w}$ is... | 5 | [
-0.058837890625,
-0.06982421875,
0.00191497802734375,
-0.049072265625,
0.0224609375,
-0.005706787109375,
-0.0279541015625,
-0.0172119140625,
-0.00933837890625,
0.1298828125,
-0.0269775390625,
0.1103515625,
-0.043212890625,
0.0118408203125,
-0.048583984375,
0.1552734375,
0.02795410156... | 31,055 | 31055 | |
Latin American applied research
Servicios Personalizados
Articulo
Indicadores
Links relacionados
Bookmark
versión impresa ISSN 0327-0793
Lat. Am. appl. res. v.34 n.4 Bahía Blanca oct./dic. 2004
Cosserat continua-based micro plane modelling. Theory and numerical analysis
G. Etse^1 and M. Nieto^2
^1 CONICET a... | 4 | [
-0.0299072265625,
-0.03759765625,
-0.01068115234375,
-0.040283203125,
0.00885009765625,
0.0068359375,
0.0030517578125,
0.09619140625,
0.0145263671875,
-0.0089111328125,
0.04638671875,
-0.016357421875,
-0.0179443359375,
0.044921875,
-0.004180908203125,
-0.0439453125,
-0.0341796875,
... | 31,056 | 31056 | |
Realistic two-box parameters and heat capacity choices for Earth's climate system
This will probably be my final post on this question - however I may append updates if other issues come up. In particular this post will look first at whether the fitted parameter values for
two-time-constant fits to temperature vs forc... | 4 | [
-0.038330078125,
-0.01171875,
0.0849609375,
0.07421875,
-0.0003299713134765625,
-0.0234375,
-0.10693359375,
0.004058837890625,
-0.0576171875,
0.0069580078125,
-0.06396484375,
-0.1396484375,
0.032470703125,
-0.055419921875,
0.08935546875,
-0.0277099609375,
-0.0064697265625,
-0.06396... | 31,057 | 31057 | |
Sequences of Functions
March 10th 2013, 08:47 PM #1
Member
Joined
Sep 2012
From
india
Posts
78
Sequences of Functions
I have been studying pointwise and uniform convergence of sequences of functions and i am stuck with this question,
Show that lim(Arctan nx) = (pi/2)sgnx for x in R.
I belie... | 5 | [
-0.04443359375,
-0.07958984375,
0.072265625,
-0.01324462890625,
0.0419921875,
0.0289306640625,
0.042236328125,
0.10009765625,
-0.052490234375,
-0.0703125,
0.06103515625,
-0.06103515625,
0.0830078125,
-0.046142578125,
0.005523681640625,
-0.0966796875,
0.06103515625,
-0.08154296875,
... | 31,058 | 31058 | |
COmplex number uestion
November 19th 2012, 11:45 PM #1
Member
Joined
Nov 2012
From
Singapore
Posts
180
COmplex number uestion
Hi again,
I need help with this question,
Find the complex number z that satisfies the equation 50/z* - 10/z = 2 + 9i given | z | = 2sqrt(10).
I had put 50 and ... | 5 | [
-0.0947265625,
0.08837890625,
0.022216796875,
0.046142578125,
0.0299072265625,
-0.001007080078125,
0.02294921875,
0.09619140625,
-0.1005859375,
-0.044677734375,
0.07763671875,
-0.017578125,
0.08203125,
0.123046875,
-0.0186767578125,
0.01080322265625,
-0.0283203125,
0.015869140625,
... | 31,059 | 31059 | |
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 275134, 9 pages
http://dx.doi.org/10.1155/2013/275134
Research Article
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Busin... | 4 | [
-0.07861328125,
-0.06591796875,
-0.0034027099609375,
0.0172119140625,
-0.031982421875,
-0.022216796875,
-0.06396484375,
-0.036376953125,
0.07763671875,
0.04296875,
0.020263671875,
-0.0223388671875,
-0.00677490234375,
-0.0017547607421875,
-0.050537109375,
0.01123046875,
0.018188476562... | 31,060 | 31060 | |
U-Substitution
I need help with the u-substituion. The first one is.... (2cosx)/(1-cos^2x)
Notice that if $u = \sin{x}$ then $du = \cos{x}\,dx$. So $\int{\frac{2\cos{x}}{\sin^2{x}}\,dx} = 2\int{u^{-2}\,du}$ $= -2u^{-1} + C$ $= -\frac{2}{\sin{x}}+ C$ $= -2\csc{x} + C$.
You can also let $u = 1-\cos^2{x}$, then $\dfrac{... | 5 | [
-0.038330078125,
0.01806640625,
0.0262451171875,
0.12060546875,
0.037841796875,
-0.0068359375,
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-0.0084228515625,
-0.054931640625,
-0.0181884765625,
0.01409912109375,
-0.09716796875,
-0.0177001953125,
-0.054931640625,
-0.03955078125,
-0.04931640625,
0.10595703125,
-0.0... | 31,061 | 31061 | |
What is this called?
$2y^2-2x^2+0=0$ evaluate y' at given point (-2,-2) What is this called? How would I do it?
The relation $y^{2} - x^{2}=0$ defines in implicit form a function $y= f(x)$ and its derivative in a point $(y_{0},x_{0})$ can be obtained from a well known explicit formula... Kind regards $\chi$$\
sigma$
... | 5 | [
-0.0284423828125,
-0.06640625,
-0.0128173828125,
0.043701171875,
-0.00038909912109375,
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-0.0030059814453125,
0.060302734375,
0.03076171875,
0.024658203125,
0.16015625,
0.004302978515625,
-0.038330078125,
-0.005706787109375,
0.0458984375,
0.06494140625,
-0.052001953125... | 31,062 | 31062 | |
Quadrilaterals and Pythagoras Theorem
June 4th 2007, 12:17 AM #1
Newbie
Joined
Jun 2007
Posts
3
Hi, new to this,
The diagonals AC and BD, of a quadrilateral ABCD, are perpendicular. Find the length of AB, if BC=5cm, DC=4cm and AD=3cm. Let the intersection of the diagonals be E.
Now I'm thinking ... | 4 | [
0.006866455078125,
0.07177734375,
0.0240478515625,
-0.09912109375,
-0.056640625,
0.0849609375,
-0.0218505859375,
0.0263671875,
-0.0218505859375,
0.004913330078125,
0.07958984375,
-0.043212890625,
0.01129150390625,
-0.0023040771484375,
-0.013671875,
0.041015625,
-0.04296875,
0.06933... | 31,063 | 31063 | |
Linear transformations and matrices
April 26th 2005, 12:57 AM #1
Newbie
Joined
Apr 2005
Posts
12
Linear transformations and matrices
Hi
I got a question regarding the matrix of linear transformation.
If a linear transformation T: R^3 -> R^2 implies that T(1,2-1) = (1,4) ; T(-1,2,1) = (5,9) and ... | 5 | [
-0.0135498046875,
-0.015869140625,
-0.0908203125,
-0.060302734375,
-0.0078125,
-0.055908203125,
-0.0233154296875,
-0.01025390625,
0.01019287109375,
0.010986328125,
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-0.00579833984375,
-0.052734375,
0.006591796875,
-0.00823974609375,
... | 31,064 | 31064 | |
Trgnometric integrals
October 24th 2009, 05:40 PM
radioheadfan
Trgnometric integrals
How would you evaluate this indefinite integral?
tan^4x dx
I began with Seperating it into two tans. Both to the 2nd power.
Then I got lost. How do I get to my answer?
October 24th 2009, 05:43 PM
Prove It
Qu... | 5 | [
0.057373046875,
0.016357421875,
0.07958984375,
0.033203125,
-0.01129150390625,
-0.0556640625,
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-0.031982421875,
0.01025390625,
-0.037841796875,
0.057373046875,
0.0302734375,
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0.058837890625,
0.0179443359375,
0.0439453125,
0.040283203125,
0.010498046... | 31,065 | 31065 | |
PDE's - Finding a certain solution to Laplace's equation on a circle
September 2nd 2008, 02:44 PM #1
Junior Member
Joined
Nov 2006
Posts
59
PDE's - Finding a certain solution to Laplace's equation on a circle
Find a solution of Laplace's equation $u_{xx} + u_{yy} = 0$ of the form $u(x,y) = Ax^2 + Bxy + C... | 5 | [
-0.0625,
-0.0126953125,
-0.000762939453125,
0.00433349609375,
0.02978515625,
0.03125,
-0.0203857421875,
-0.043212890625,
0.0159912109375,
-0.0849609375,
0.058349609375,
-0.0224609375,
-0.041259765625,
-0.027099609375,
0.01361083984375,
0.027587890625,
-0.07666015625,
-0.0771484375,... | 31,066 | 31066 | |
Which are the digits that never appear in any units' digit of any square number?
November 30th 2013, 02:23 AM #1
Senior Member
Joined
Apr 2006
Posts
290
Which are the digits that never appear in any units' digit of any square number?
He's a maths problem I am stuck with... Thanks for your help in advance... | 4 | [
0.006805419921875,
0.020751953125,
-0.035888671875,
-0.015869140625,
-0.035888671875,
0.11474609375,
-0.00604248046875,
-0.0308837890625,
0.00213623046875,
-0.078125,
0.0167236328125,
0.09814453125,
0.044921875,
0.035888671875,
-0.078125,
-0.055419921875,
-0.07470703125,
0.0390625,... | 31,067 | 31067 | |
Basic linear
April 1st 2010, 03:14 AM #1
Member
Joined
Dec 2009
Posts
180
Basic linear
Hi!
I´m having some issues solving this equation system.
$x_1+x_2+2x_3 = 3$
$x_1-x_2+8x_3 = -1$
$2x_1+3x_2+x_3 = 8$
Nomatter what I do I cant eliminate the 2 terms to get one of the unknows alone... | 5 | [
-0.0869140625,
-0.023193359375,
0.004119873046875,
-0.03857421875,
0.044189453125,
-0.055908203125,
0.004058837890625,
-0.02978515625,
-0.0021514892578125,
0.031982421875,
0.10400390625,
-0.0625,
0.06640625,
-0.0625,
-0.0225830078125,
0.061279296875,
-0.039306640625,
-0.00396728515... | 31,068 | 31068 | |
how to solve this complex number question..
November 20th 2008, 09:08 AM #1
MHF Contributor
Joined
Nov 2008
Posts
1,401
how to solve this complex number question..
http://img353.imageshack.us/img353/672/85253506or3.gif
in normal equation i equalize the "Real" part with the real part
and the "Im"... | 5 | [
-0.087890625,
0.0390625,
-0.0022125244140625,
0.04150390625,
-0.0057373046875,
-0.0458984375,
0.03076171875,
0.0537109375,
0.007293701171875,
-0.07275390625,
0.036865234375,
-0.0322265625,
0.0927734375,
0.08251953125,
-0.07958984375,
0.0023040771484375,
0.04736328125,
-0.1015625,
... | 31,069 | 31069 | |
Rockbox mail archive
From: Jacob <jacob01_at_gmx.net> Date: 2005-08-17
Hi,
just to add my 5c and just because I spent several hours digging again into
digital filter design 2 nights ago, here are the results. I've used
floats even in the filter, but changing it to int (32bit) shouldn't be a
big issue.
You get an app... | 4 | [
-0.034423828125,
0.01324462890625,
0.016845703125,
-0.045166015625,
0.003997802734375,
-0.13671875,
-0.00701904296875,
-0.0537109375,
-0.126953125,
-0.02783203125,
-0.076171875,
-0.05712890625,
-0.0380859375,
-0.0250244140625,
-0.00714111328125,
0.040283203125,
-0.05224609375,
0.07... | 31,070 | 31070 | |
CBSE Class 10 Mathematics Solved Question Paper (1999)
Mathematics
Question Paper
1999
Question 1)
Evaluate without using trigonometric table: cos 75
^o
/sin 15
^o
+ sin 12
^o
/cos 78
^o
– cos 18
^o
/sin 72
^o
(Marks 2)
Question 2)
Evaluate (sec2A – 1)(1 – cosec2A ) (Marks 2)
Question 3)
If tan A =... | 4 | [
-0.00775146484375,
0.109375,
-0.052978515625,
-0.087890625,
-0.005889892578125,
0.047607421875,
-0.00604248046875,
0.13671875,
0.02685546875,
0.064453125,
0.072265625,
-0.021484375,
0.02587890625,
0.002655029296875,
0.0250244140625,
-0.02099609375,
-0.0283203125,
-0.011474609375,
... | 31,071 | 31071 | |
Please help me figure this out!
March 9th 2010, 09:28 PM #1
Newbie
Joined
Mar 2010
Posts
2
Please help me figure this out!
It's been driving me up the wall and this is the fastest math forum I've found on google.
Here's the problem.
8x^2-12X-6XY+9
How to factor???
Thank you in advanc... | 4 | [
0.0400390625,
0.0218505859375,
0.01043701171875,
0.03564453125,
0.06884765625,
0.095703125,
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0.0189208984375,
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-0.0634765625,
0.06884765625,
0.023193359375,
0.05322265625,
0.046875,
-0.0159912109375,
0.076171875,
-0.01434326171875,
0.00994873046875,
... | 31,072 | 31072 | |
Maclaurin series
Find a Maclaurin series expansion for each function. f(x) = cos x f(x) = 1/(1-x) f(x) = x sin x
These are pretty standard but if the intent is to "discover" these on your own, just directly apply the formula for the Maclaurin series (a taylor series centred around a = 0): $f(x) = f(a) + f'(a)
(x-a) + ... | 5 | [
-0.06982421875,
-0.0634765625,
-0.0047607421875,
0.0771484375,
-0.026611328125,
0.05078125,
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-0.046142578125,
0.062255859375,
0.0380859375,
0.07421875,
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-0.04248046875,
-0.039794921875,
0.01190185546875,
-0.035400390625,
-0.056884765625,
-0.046142578125... | 31,073 | 31073 | |
question about radical problem
October 2nd 2009, 09:59 AM #1
Junior Member
Joined
Jul 2009
Posts
36
question about radical problem
can someone tell me how 2x3+ 3squared + 2x3squared + 1 is 7+3x3squared? the only part i dont understand is where my book got the 3 from i thought it should be 7+2x3squared?
... | 4 | [
-0.01531982421875,
-0.0223388671875,
-0.017578125,
0.09375,
-0.02783203125,
0.0181884765625,
0.025390625,
-0.041259765625,
0.0390625,
0.025634765625,
0.0189208984375,
-0.0050048828125,
0.0859375,
-0.003814697265625,
-0.0098876953125,
0.0263671875,
-0.10693359375,
0.01220703125,
-... | 31,074 | 31074 | |
Newton-Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems
Journal of Mathematics
Volume 2013 (2013), Article ID 439316, 9 pages
http://dx.doi.org/10.1155/2013/439316
Research Article
Newton-Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems
Department of Mathematical a... | 5 | [
-0.10400390625,
0.00038909912109375,
0.09716796875,
-0.057373046875,
-0.0179443359375,
0.02587890625,
0.0235595703125,
-0.00390625,
-0.0947265625,
0.0185546875,
0.0634765625,
0.0172119140625,
-0.005523681640625,
-0.037109375,
-0.0634765625,
-0.0035858154296875,
-0.021484375,
-0.059... | 31,075 | 31075 | |
Analysis of Approximation by Linear Operators on Variable
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 454375, 10 pages
http://dx.doi.org/10.1155/2014/454375
Research Article
Analysis of Approximation by Linear Operators on Variable Spaces and Applications in Learning Theory
^1Department of Mathemat... | 5 | [
-0.014404296875,
-0.00982666015625,
0.047119140625,
0.046630859375,
-0.00982666015625,
0.06298828125,
0.11669921875,
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0.0164794921875,
0.035400390625,
0.041015625,
0.0927734375,
0.064453125,
0.028076171875,
-0.038818359375,
-0.06005859375,
0.02783203125,
0.0048522949218... | 31,076 | 31076 | |
Generalized Linear Models
Generalized linear models are fit using the glm( ) function. The form of the glm function is
glm(formula, family=familytype(link=linkfunction), data=)
Family Default Link Function
binomial (link = "logit")
gaussian (link = "identity")
Gamma (link = "inve... | 4 | [
-0.023193359375,
-0.1376953125,
-0.01171875,
0.000014424324035644531,
-0.019775390625,
-0.0291748046875,
-0.01025390625,
0.04345703125,
0.01104736328125,
-0.007293701171875,
0.142578125,
-0.0247802734375,
-0.0595703125,
0.08056640625,
0.0164794921875,
-0.05029296875,
0.05908203125,
... | 31,077 | 31077 | |
Division With Polynomials
May 31st 2008, 04:09 AM #1
Newbie
Joined
May 2008
Posts
7
Division With Polynomials
x 4 + 81 / x - 3
x 4 - 81 / x - 3
5x 3 - 12x 2 - 36x -16 /x + 2
x 5 - 8x 3 + 24x 2 + 12x + 40 / x + 4
x 4 - 3x 3 + 3x 2 - 3x + 6 /x - 2
I try to Dividing them but i all wa... | 4 | [
-0.04150390625,
0.03955078125,
0.0240478515625,
0.01123046875,
0.03369140625,
-0.0263671875,
-0.0244140625,
-0.05126953125,
-0.01080322265625,
-0.026611328125,
0.0284423828125,
-0.04541015625,
0.0341796875,
0.027099609375,
-0.056884765625,
0.0264892578125,
-0.017822265625,
0.040283... | 31,078 | 31078 | |
Lomax {Renext}
Description
Density function, distribution function, quantile function and random generation for the Lomax distribution.
Usage
dlomax(x, scale = 1.0, shape = 4.0, log = FALSE)
plomax(q, scale = 1.0, shape = 4.0, lower.tail = FALSE)
qlomax(p, scale = 1.0, shape = 4.0)
rlomax(n, scale = 1.0, s... | 5 | [
0.00933837890625,
-0.039794921875,
0.017333984375,
-0.0771484375,
-0.0162353515625,
-0.05224609375,
0.01519775390625,
0.107421875,
0.0546875,
0.00171661376953125,
0.0004730224609375,
-0.0086669921875,
0.0185546875,
0.017578125,
0.00799560546875,
-0.0023956298828125,
0.000724792480468... | 31,079 | 31079 | |
Taylor Poly's and l'Hop
May 6th 2008, 12:41 AM #1
Taylor Poly's and l'Hop
Could somebody help me with this problem?
Find the Taylor polynomials the 2nd Taylor polynomial \begin{aligned} T_{f,0}^{(2)} (x)\end{aligned} around 0 for the following function
f(x) = (1)/(1+x)
and this nasty question...
... | 5 | [
0.028076171875,
-0.027099609375,
0.0272216796875,
0.0037384033203125,
0.07666015625,
-0.0478515625,
0.02294921875,
-0.010498046875,
0.017822265625,
0.0888671875,
0.12158203125,
-0.029052734375,
-0.0245361328125,
-0.021484375,
-0.0166015625,
0.034423828125,
-0.0576171875,
-0.0805664... | 31,080 | 31080 | |
Normality and rational singularities via Hilbert series
up vote 3 down vote favorite
3
Let $A$ be a finitely generated ${\mathbb Z}_{\geq 0}$-graded algebra over a field without zero divisors; assume that all graded components are finite-dimensional and that $Spec(A)$ is smooth outside
of a subscheme of codimension 2.... | 4 | [
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-0.... | 31,081 | 31081 | |
Quotient of complex numbers in polar form?
April 28th 2011, 02:56 PM #1
Senior Member
Joined
Dec 2010
From
CPT
Posts
302
Quotient of complex numbers in polar form?
Can anyone help me with this problem?
Use polar form find the quotient express the result in rectangular form
(-4\sqrt{2} + ... | 5 | [
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0... | 31,082 | 31082 | |
Integral Application
Consider the function In this problem you will calculate The summation inside the brackets is Calculate I need to find
right endpoint method: $x_{i}=a+k{\Delta}x$ ${\Delta}x=\frac{3-0}{n}=\frac{3}{n}$ $x_{i}=\frac{3k}{n}$ $f(x_{i}){\Delta}x=\left[\frac{(\frac{3k}{n})^{2}}{4}-9\right]\cdot\frac{3}{... | 5 | [
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... | 31,083 | 31083 | |
vertical motion mechanics problem
March 24th 2010, 01:07 AM
furor celtica
vertical motion mechanics problem
a lift starting from rest moves downward with constant acceleration. It covers a distance s in time t, where s = (1/6)(g)(t^2). A box of mass m is on the floor of the lift. find, in terms of m
and g, a... | 4 | [
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-... | 31,084 | 31084 | |
[SOLVED] Difficult limit
February 15th 2008, 11:13 AM
spammanon
[SOLVED] Difficult limit
Lim [(x+h)²ln(x+h) - x²ln(x)] / h
h→0
Of course this is finding the derivative of the obvious function, but I would like to know if anyone can evluate this WITHOUT using L'Hospital.
Thanks.
February 15th 2008,... | 5 | [
0.00994873046875,
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... | 31,085 | 31085 | |
Brazilian Journal of Chemical Engineering
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Article
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Print version ISSN 0104-6632
Braz. J. Chem. Eng. vol.24 no.3 São Paulo July/Sept. 2007
http://dx.doi.org/10.1590/S0104-66322007000300005
... | 4 | [
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... | 31,086 | 31086 | |
differential equation problem
November 7th 2010, 08:11 AM #1
Newbie
Joined
Oct 2010
Posts
2
Hi, sorry this is quite a long question, but struggling to think where to even start!
Thanks!
To help determine a possible strategy for future whaling the population is modelled
mathematically.
(a)... | 4 | [
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Complex numbers: equation
November 9th 2007, 02:23 PM #1
Newbie
Joined
Nov 2007
Posts
3
Complex numbers: equation
Could enyone solve this for me:
Equation system:
(−2 + 2i)z1 + (3 + 3i)z2 = 6 + 2i
(3 + 4i)z1 + (8 − 6i)z2 = −6 + 17i
Im(z1)
Re(z1)
Im(z2)
Re(z2)
(-2 +... | 5 | [
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Conjugacy Classes in Groups
December 10th 2011, 06:01 PM #1
Conjugacy Classes in Groups
I am a math hobbyist working by myself. I am currently reading Beachy and Blair: "Abstract Algebra" on conjugacy in groups. I wish to ensure I have understood the notion of conjugacy classes. To
do this I am considering th... | 5 | [
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0.023193359375,
0.02270507... | 31,089 | 31089 | |
Rules for p-Series Convergence
December 1st 2006, 12:45 PM #1
Newbie
Joined
Sep 2006
Posts
7
Rules for p-Series Convergence
in a p-Series does the numerator have to equal 1, or can it be other constants?
ie does sum 6/(n^3) converge?
Thank You.
You can take the 6 outside the sum:
$6... | 5 | [
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-0.0854492... | 31,090 | 31090 | |
Homework Help
Posted by math on Wednesday, December 28, 2011 at 12:33am.
can u help
this the qustion is :
A circle passes through the points (1,4)&(5,0) and its centre lies on the line x+y-3=0.Find
(i) the equation of the circle and it parametric equations .
(ii) the centre,diameter and area of the circle .
(iii)... | 4 | [
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Find minimum using Hessian matrix
April 6th 2011, 06:54 AM #1
Find minimum using Hessian matrix
$f(x,y)=\frac{1}{4}x^4+x^2y+y^2$
Find the minimum point of $f$ using the Hessian matrix $H$.
My working:
$f_x=x^3+2xy=0 \implies x(x^2+2y)=0$
$f_y=x^2+2y=0$
The critical points of $f$ lie on th... | 4 | [
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Summation to infinity
In your previous thread we have found that, $\sum_{r=1}^{n}(\frac{1}{4r^2-8r+3})=\frac{1}{2}\left(-1-\frac{1}{2n-1}\right)$ Here we have to find, $\sum_{r = 0}^{n}\frac{1}{4r^2-8r+3}=\frac{1}{3}+\
sum_{r = 1}^{n}\frac{1}{4r^2-8r+3}$ Therefore taking the limit as n tend to infinity, $\sum_{r = 0}^{... | 5 | [
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0.068359375,
-0.06689453125... | 31,093 | 31093 | |
Help for solving the differential equation!!
September 24th 2009, 05:56 AM
wsun
Help for solving the differential equation!!
The Qs is to solve the differential equation:
$\frac{dy}{dx} = \frac{(x+y)}{(x-y)}$ with y(1) = 1
I have tried to use Homogeneous differential equation rules:
$\frac{dy}{dx} = ... | 5 | [
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help finding x-coordinates of points of intersection
December 1st 2008, 02:57 PM #1
Newbie
Joined
Aug 2008
Posts
20
help finding x-coordinates of points of intersection
I need help with the following problem:
Let S be the region bounded between f(x)=16-x^2 and g(x)=2x+1
Find the x-coordinates of... | 4 | [
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Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 190768, 25 pages
http://dx.doi.org/10.1155/2012/190768
Research Article
Multigrid Discretization and Iterative Algorithm for Mixed... | 4 | [
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Rational Number
September 30th 2006, 03:14 PM #1
Newbie
Joined
Sep 2006
Posts
16
Rational Number
I have the following problem:
Prove that the sqrt(2+sqrt(2)) is irrational.
I did the problem similarly to how one of my TAs showed in a tutorial.
Let the sqrt(2+sqrt(2)) = a. Square both sides.... | 4 | [
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permutation
August 9th 2009, 12:04 AM #1
Newbie
Joined
Aug 2009
Posts
14
permutation
24 card are put a pile in numerical order with 1 on the top and 24 on the bottom. they are first of all given a riffle shuffle so that the bottom card remains where it is, and then divided into
four quarters. th... | 5 | [
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Several maths questions
June 18th 2009, 01:44 PM #1
Newbie
Joined
Oct 2008
Posts
21
Several maths questions
Alright, at uni they make us sit a skills test of stuff we did back at school. Problem is i can't remember half of it! Struggling big time, goign to see a tutor on Monday and got till august to
... | 4 | [
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