content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Infinite roots
Prove that a polynomial $f \in K[X,Y]$ has infinite roots in $K^2$ if $K$ is algebraically closed. thanks!
If $f \in K[X,Y]$ is a non-constant polynomial then it factors into $f = \prod_i l_i$ where $l_i = a_iX+b_iY+c_i$ ( $a_i,b_i$ not both zero) are linear polynomials. Thus, it suffices to prove that
... | 5 | [
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0.12890625,
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mechanics question, resultant forces.
February 13th 2008, 09:21 AM #1
Junior Member
Joined
Nov 2007
Posts
33
mechanics question, resultant forces.
Two forces P and Q act on a particle. The force P has magnitude 7N and acts due north. The resultant of P and Q is a force of magnitude 10N acting in a direct... | 4 | [
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-0.09716796875,
0.00201... | 40,701 | 40701 | |
Need help with an alegebra question
November 28th 2008, 11:34 AM #1
Newbie
Joined
Nov 2008
Posts
4
Need help with an alegebra question
Hello, haven't done algebra for a while. Can someone give me step by step help with the following equation:
14.74=3.05+1/(1.1150)^10*[(.76*1+a))/(.1150-a)]
Than... | 4 | [
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0.05517578125,
-0.07373046875,
0.0058898925781... | 40,702 | 40702 | |
Even permutaions and Alternating group help!!
April 8th 2010, 09:01 AM
killercatfish
Even permutaions and Alternating group help!!
I fear I have become stumped with permutations once we hit cycles. I understand cycle notation, and multiplication. I desperately seek help on a few homework problems that I just can... | 5 | [
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... | 40,703 | 40703 | |
Why use the natural log...?
Date: 9 Jan 1995 12:01:38 -0500
From: Gina Chen
Subject: Natural log
Dear Dr. Math,
I am a student at Monta Vista High School and I would like to know:
Why do we have to use the natural log for the antiderivative of 1/x?
Why doesn't the power rule work on the antiderivative of 1/x?
Than... | 5 | [
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... | 40,704 | 40704 | |
Negative sum
July 2nd 2006, 11:19 PM
cmart022
Negative sum
If S = 1 + 2 + 4 + 8 + 16...
S = 1 + (2 + 4 + 8 + 16...)
S = 1 + 2*(1 + 2 + 4 + 8...) — (since S = 1 + 2 + 4 + 8... we multiply it by two)
Then
S = 1 + 2S
S - 2S = 1
-S = 1
S = -1
How can that be?
July 2nd 2006, 11:24 ... | 4 | [
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Algebra story problem. Need Help ASAP
February 17th 2008, 04:27 PM
armath
Algebra story problem. Need Help ASAP
ok...you have some $1 bills, $5 bills, and $10 bills. There are 225 bills total and they are worth $596. If you have seven times as many $1 as you do $10, how many of each bill do you have?????
i ... | 4 | [
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Nth term for diagonals/sides
April 29th 2010, 12:10 PM
Mukilab
Nth term for diagonals/sides
Find the nth term formula for the number of sides in a shape against how many diagonals this shape has.
I have the answer but is there I need workings because I do not know how to approach this.
April 29th 2010, 12:... | 4 | [
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Stable w-length
up vote 11 down vote favorite
3
Let $F$ be a free group, and $w$ an element of $F$. In any group $G$, a $w$-word is the image of $w$ or $w^{-1}$ under a homomorphism from $F$ to $G$. The subgroup of $G$ generated by $w$-words is
denoted $G(w)$.
For any $g \in G(w)$, the $w$-length of $g$, denoted $l(g... | 4 | [
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Help on homework!(Quadratics)
July 24th 2012, 12:40 PM #16
MHF Contributor
Joined
Dec 2007
From
Ottawa, Canada
Posts
3,080
Thanks
66
Re: Help on homework!(Quadratics)
NO. I was attempting to show a "general case" when the "C" = 0 (which is the case with your problem).
Let me do it another wa... | 4 | [
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Find the number of elements in the intersection of 3 sets
October 23rd 2008, 03:07 AM #1
Find the number of elements in the intersection of 3 sets
Let A={ $n \in N$ | 5 divides n}
B={ $n \in N$| both n and $\frac {n}{5}$ contain only odd digits}
and C={ $n \in N$ | both n and $\frac {n}{5}$ contain exactl... | 4 | [
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Filtering Projection in Image Processing_1_
Projection Filtering in Image Processing
Danil N. Kortchagine and Andrey S. Krylov
Faculty of Computational Mathematics and Cybe... | 4 | [
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Integrate problem- need to review for accuracy
February 7th 2010, 10:21 AM #1
Newbie
Joined
Feb 2010
Posts
5
Integrate problem- need to review for accuracy
Please check to see if I correctly solved this problem.
∫ sqrt(4X^2+9X^4)
∫ (x) sqrt(4+9X^2)
let u= 4 + 9x^2
let du= 18x dx
... | 5 | [
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Practical Number?
Author Practical Number?
posted
Greenhorn
Hello i am stuck with the problem of finding the practical numbers between to integers..
Joined: for example if the two integers are 1 and 12 then t... | 4 | [
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... | 40,713 | 40713 | |
Math help Cross-section
May 5th 2009, 08:31 AM
dj41490
Math help Cross-section
The base of each solid below is the region in the xy-plane bounded by the x-axis, the graph x^(1/2) and the line x=3. Fine the volume of the solid. Each cross-section of S4 perpendicular to the
y-axis is an isoscelesles right tria... | 5 | [
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[Aptitude] Permutation Combination made easy without Formulas - Mrunal
If the following questions make you uncomfortable, then read this article.
• In how many ways can 5 member committee be formed out of 20 students? Or
• How many ways can the word “UPSC” be arranged so that “U” is always second from left.
• In... | 4 | [
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Coordinate Geometry Proofs & Area
Ways to Prove a Quadrilateral
Right Triangle
(A triangle is a right angle...)
1.. if it contains one right angle (show slopes are negative reciprocals, therefore perpendicular sides, therefore right angles, therefore right angle)
2...if the lengths of its side satisfy the converse of... | 4 | [
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0.062011... | 40,716 | 40716 | |
Math Help
Prove that between two zeros of $e^x\, \sin(x)=1$ there is a zeros of $e^x\,\cos(x)=-1$ Let: $f(x) = e^x\, \sin(x) - 1$ First observe that: $e^x\,\cos(x)+1=f'(x)-f(x)$, Now if $x_1$ and $x_2$ are
consecutive zeros of $f(x)$ then the signs of $f'(x_1)$ and $f'(x_2)$ would be different (the other possibility t... | 5 | [
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0.00... | 40,717 | 40717 | |
Solve the equation...
June 13th 2008, 07:35 PM #1
Newbie
Joined
Jun 2008
Posts
9
Solve the equation...
3^(x-2) = 4^(2-x)
I know how to do these when the bottom numbers can be divided by each other to get the top equations down to solve, but how can I do this when when the numbers on the bottom are d... | 4 | [
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Notable Properties of Specific Numbers
Notable Properties of Specific Numbers
First page . . . Back to page 11 . . . Forward to page 13 . . . Last page (page 25)
370 = (037 + 073 + 307 + 370 + 703 + 730)/6, which is the average of all possible permutations of... | 4 | [
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0.010803... | 40,719 | 40719 | |
Strang's "Calculus Puzzle"
January 6th 2013, 12:08 PM #1
Junior Member
Joined
Dec 2012
From
Earth
Posts
58
Strang's "Calculus Puzzle"
Found this "puzzle" from Strang's Calculus.
The slope-intercept form of a line (y = mx + b) requires TWO numbers, the point-slope form (y - f(a) = f'(a)(x-a)) req... | 5 | [
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Homework Help
Posted by Ivyl on Tuesday, August 2, 2011 at 6:46am.
One hundred tiles of a certain size are needed to pave a floor. If a tile, which measures 4 cm less on each side, will be used, 225 tiles will be needed. Find the size of the larger tile.
• Geometry - Reiny, Tuesday, August 2, 2011 at 8:20am
Le... | 4 | [
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Independence of being an integer
up vote 24 down vote favorite
6
In this MO question, the OP asked for an example of a statement which was known not to be independent of ZFC, but for which the truth value was unknown. I immediately thought of a question I asked on
math.SE: is $e^{e^{e^{79}}}$ an integer? This is appar... | 4 | [
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0.02270507... | 40,722 | 40722 | |
Simple implicit differentiation, not so simple for me..
November 12th 2009, 02:59 PM
thatonegurl
Simple implicit differentiation, not so simple for me..
I need help with finding dy/dx by implicit differentiation with this problem:
x^2y+y^2x=-2
I am really trying to get this but I am stressing terribly ... | 5 | [
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0.002319335937... | 40,723 | 40723 | |
Weight
Talk2
848pages on
this wiki
Weight
A Brief Definition
A lot of the time, society confuses mass and weight. Mass is a measurement of how much of matter an object has, while weight is a measurement of the force due to graivty exterted downward on that
object. Weight is only one type of force Mass will remain... | 4 | [
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0.1083984375,... | 40,724 | 40724 | |
A generalization of the SET problem
up vote 5 down vote favorite
1
In the lattice point problem, given $n$ and $d$, one seeks to find the least positive integer $f(n,d)$ such that every collection of $f(n,d)$ $d$-tuples of integers contains $n$ whose average is an
integer $d$-tuple (geometrically, the centroid is a la... | 5 | [
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0.05078125,
-0.040771484375... | 40,725 | 40725 | |
Finding exponential growth rate
THe population of Murrayville doubled in 30 years. What was the exponential growth rate?
This question is exactly similar to the last question i answered for you. $n = \frac{ln2}{ln(1 + r/100)}$ where n is the doubling period so n = 30 and r is the rate
An exponential function can alwa... | 4 | [
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0.000736236572265625,
... | 40,726 | 40726 | |
Reference Request: Lax Ends
up vote 5 down vote favorite
2
I've read in a few different places that the standard fact \[ \text{Nat}\,(F,G) \cong \int_x \text{Hom}\,(Fx,Gx) \] can be upgraded to \[ \textbf{LaxNat}\,(F,G) \cong \oint_x\textbf{Hom}\,(Fx,Gx) \]
Where the left hand side is the category of lax natural trans... | 4 | [
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0.047607421875,
-0.021484375,
-0.0576171875,
0.055419921875,
0.014892578125,
-0.08642578125,
-0.022216796875,
0.0869140625,
0.0308837890625,
-0.0020599365234375,
0.08... | 40,727 | 40727 | |
Problem with Diff'ing a rational expression
November 18th 2007, 07:17 AM #1
Newbie
Joined
Nov 2007
Posts
10
Problem with Diff'ing a rational expression
Keep getting all twisted up in the algebra in finding the first and second derivative of the following
x(third)-4x(squared)/(x-2)(squared)
F’(x... | 5 | [
-0.01165771484375,
-0.029541015625,
0.054443359375,
-0.020263671875,
-0.0186767578125,
0.0262451171875,
-0.07470703125,
-0.031982421875,
0.056396484375,
-0.01275634765625,
0.08203125,
-0.06298828125,
0.0693359375,
0.0262451171875,
-0.0164794921875,
0.057373046875,
-0.037353515625,
... | 40,728 | 40728 | |
The law of cosines
July 21st 2008, 12:10 PM #1
Newbie
Joined
Jul 2008
Posts
8
The law of cosines
round each angle measures to the nearest degree and side measures to the nearest tenth.
Triangle ABC, a = 15, b = 19, c = 28
i dont understand what formula to use for this geometry problem and how t... | 4 | [
-0.0712890625,
0.134765625,
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-0.01904296875,
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0.0771484375,
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0.10107421875,
0.0537109375,
0.029296875,
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0.07958984375,
0.0439453125,
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0.0286865234375,
-0.05... | 40,729 | 40729 | |
Is there a way to further reduce this?
I am guessing that the text in the subject line is your question...? What do you mean by "reducing" the equation?
ln(y)=(2/3)*ln(x) = ln(y) = ln(x)^(2/3) Multiplying both sides by e, we end up with: y = x^(2/3)
thanks enjam, that's just what i was confused about. i didn't know t... | 4 | [
0.006866455078125,
-0.0137939453125,
0.047119140625,
0.041015625,
0.037841796875,
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0.0751953125,
0.0517578125,
0.06298828125,
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0.07568359375,
0.1171875,
0.027587890625,
-0.16796875,
0.1337890625,
-0.11... | 40,730 | 40730 | |
Triangular Mesh Generation Method - Patent 4941114
United States Patent: 4941114
( 1 of 1 )
United States Patent
4,941,114
Shigyo
, et al.
July 10, 1990
Triangular mesh generation method
Abstract
A triangular mesh generation apparatus ... | 4 | [
-0.08837890625,
0.07763671875,
-0.1005859375,
-0.07373046875,
-0.04296875,
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-0... | 40,731 | 40731 | |
Gcd/lcm
September 19th 2012, 02:43 PM
franios
Gcd/lcm
For non-zero integers a & b verify the following condition are equivalent.
a) a divides b
b) gcd(a,b)= (Absolute value of a)
c) lcm(a,b)= (Absolute value of b)
September 19th 2012, 03:57 PM
johnsomeone
Re: Gcd/lcm
When you're asked to "... | 5 | [
-0.053466796875,
-0.0205078125,
-0.0849609375,
-0.09521484375,
0.0245361328125,
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0.030517578125,
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0.01361083984375,
0... | 40,732 | 40732 | |
Extended function
January 15th 2009, 01:40 PM #1
Junior Member
Joined
Sep 2008
Posts
30
Extended function
Let F(x) = [(x² + 3x -4) / (x² - 4x + 3)]
Give a formula for the extended function that is continuous at x=1
Notice that
$\frac{x^2 + 3x -4}{x^2 - 4x + 3} = \frac{(x+4)(x-1)}{(x-3)(x-1... | 4 | [
-0.048095703125,
-0.004119873046875,
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0.02490234375,
-0.021728515625,
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-0.041259765625,
-0.036376953125,
-0.011474609375,
-0.00872802734375... | 40,733 | 40733 | |
Nonlinear method for boundary value problems of a constant function.
October 16th 2012, 09:58 AM #1
Newbie
Joined
Oct 2012
From
Philippines
Posts
2
Nonlinear method for boundary value problems of a constant function.
the question Im having a hard time dealing with is this equation
y"(t)=-g where ... | 4 | [
-0.0869140625,
0.0159912109375,
0.03857421875,
-0.0625,
-0.04443359375,
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-0.037109375,
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-0.043701171875,
0.03564453125,
0.0439453125,
0.00653076171875,
0.006988525390625,... | 40,734 | 40734 | |
[SOLVED] Vectors: Work Question(Dot Product)
February 16th 2009, 08:51 AM #1
Junior Member
Joined
Feb 2009
Posts
27
[SOLVED] Vectors: Work Question(Dot Product)
If a 10N force, acting in the direction of the vector (1, 1), moves an object from P(-2, 1) to Q(5, 6), calculate the work done. The distance is... | 4 | [
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0.06298828125,
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-0.08203125,
0.005279541015... | 40,735 | 40735 | |
Multivariable calculus - implicit differentiation
March 6th 2010, 06:46 PM #1
Junior Member
Joined
Jan 2009
Posts
66
Multivariable calculus - implicit differentiation
Guys l just want to know if l am on the right path in this question. The question and attempt to the solution is on the pdf file attached... | 5 | [
-0.0830078125,
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-0.... | 40,736 | 40736 | |
Real Analysis - Uniform Convergence
January 21st 2009, 01:01 AM #1
Member
Joined
Oct 2008
Posts
135
Real Analysis - Uniform Convergence
c. Prove that if there exists an M > 0 such that |fn| <= M and |gn| <= M for all n Є N, then (fn*gn) does converge uniformly.
Any help with this would be greatly ap... | 4 | [
-0.0771484375,
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0.083984375,
0.0322265625... | 40,737 | 40737 | |
Integration Limit
August 16th 2010, 05:16 AM #1
Junior Member
Joined
Dec 2009
Posts
34
Integration Limit
Hi. I was thinking a bit and I tried to use the definition of differentiation to see how the rules were created like the standard "multiply by the power and minus one from the power" for
functions... | 5 | [
-0.0081787109375,
0.0169677734375,
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0.0174560546875... | 40,738 | 40738 | |
Melbourne's Weather and Cross Correlations
During a lunchtime discussion among recent
GCaP class attendees
, the topic of weather came up and I casually mentioned that the weather in Melbourne, Australia, can be very changeable because the continent is so old that there is very little geographical relief
to moderate ... | 4 | [
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... | 40,739 | 40739 | |
Introduction to Machine Learning
Hardcover | $60.00 Short | £30.95 | ISBN: 9780262012430 | 584 pp. | 8 x 9 in | 172 figures, 10 tables| December 2009
Essential Info
Table of Contents
Series Foreword xvii
Figures ... | 4 | [
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0.00872802734... | 40,740 | 40740 | |
quadratic equations in matrix form.
February 12th 2011, 01:30 AM
mgrafton
quadratic equations in matrix form.
Hi
I'm sure this question will seem seem very trivial, but I was wondering if you could help me out.
Although I can see that quadratic equations such as
5x^2 -6xy+5y^2=8 can be shown as th... | 5 | [
-0.07177734375,
-0.0155029296875,
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-0.061279296875,
-0.05517578125,
-0.0... | 40,741 | 40741 | |
solve system
December 13th 2006, 04:37 PM #1
Newbie
Joined
Dec 2006
Posts
2
solve system
I need help understanding how to find solutions to equational systems such as 4x-y+3z=-2
3x+5y-z=15
-2x+y+4z=14
I have no idea how to find the solution, I have read over the examples in the book a thousan... | 5 | [
-0.10595703125,
0.03125,
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0.054443359375,
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0.041015625,
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-0.044677734375,
0.058349609375,
-0.0225830078125,
-0.0... | 40,742 | 40742 | |
Arithmetic Progression
February 28th 2011, 12:29 AM #1
Junior Member
Joined
Feb 2011
Posts
56
Arithmetic Progression
Find the sum of the positive integers which are less than 150 and are not multiples of 5 or 7. Can anyone help me?
This is the sum of the integers less than 150 minus the sum of multi... | 5 | [
-0.01513671875,
0.060546875,
0.05419921875,
-0.08544921875,
-0.0279541015625,
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0.0081787109375,
-0.00634765625,
-0.078125,
0.0213623... | 40,743 | 40743 | |
Calculus with Parametric Curves
March 30th 2009, 06:38 PM
aaronb
Calculus with Parametric Curves
x=2cos(theta)
y=sin(2theta)
I have to find the coordinates of the horizontal and vertical tangents to this problem. I know that the top of the derivative must be 0 for horizontal and 0 on the bottom for the ... | 5 | [
-0.0634765625,
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0.042724609375,
-0.0025177001953125,
0.036376953125,
-0.08300781... | 40,744 | 40744 | |
Triangle PQR...
May 25th 2009, 12:58 PM #1
Junior Member
Joined
May 2009
Posts
68
Triangle PQR...
In triangle PQR, <p = 30 degrees
<Q = 80 degrees
<R = 70 degreees
QH is an altitude and RM is a median and H is on the line PR,
the measure of <MHP is:
a) 15 degrees or 20 degrees or 30 ... | 4 | [
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-0.0693359375,
-0.032958984375,
-0.0123291... | 40,745 | 40745 | |
ELASTICITY
Chapter 9 – Mohr and Fourie
Week 4
Today’s session
Definition of Elasticity
Different types of elasticity
1. Price elasticity of demand
Calculating the price elasticity of
demand (at a point =>
point elastici... | 4 | [
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0.08984375,
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-0.03369140625,
-0.0732421875,
-0.028076171875,
0.0203857421875... | 40,746 | 40746 | |
Polynomial Express
by the remainder theorem, we see that $x = 1$ is a root. thus by the factor theorem, $(x - 1)$ is a factor. dividing our cubic by $x - 1$, we see that: $x^2 - 5x^2 + 8x - 4 = (x - 1)(x^2 - 4x + 4) =
(x - 1)(x - 2)^2 = 0$ thus, we have $x = 1$ or $x = 2$ $x^3-5x^2+8x-4 > 0$ i leave this part to you. w... | 4 | [
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0.0257568359375,
0.038330078125,
-0.07... | 40,747 | 40747 | |
Math Help
February 7th 2013, 07:48 PM #1
Member
Joined
Nov 2012
From
Singapore
Posts
180
Planes
Find the equation of the plane perpendicular to the Z-axis and through (2,-1,4)
I know that this plane will be parallel to the XOY plane. But then how do I find the equation of the plane, how do I kn... | 4 | [
-0.0250244140625,
0.009521484375,
-0.0233154296875,
-0.059326171875,
0.0181884765625,
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0.0233154296875,
-0.037841796875,
0.010498046875,
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0.058837890625,
0.03515625,
-0.09130859375,
0.0556640625,
-0.11962890625,
-0.03466796... | 40,748 | 40748 | |
Is my answer for derivative right
April 27th 2009, 01:35 PM
janedoe
Is my answer for derivative right
Find derivative of y= (x)/(x+y)
I used the quotient rule and then got y' on one side. My final answer is:
[(x+y)² - y] / (-2)
Is that correct?
Thanks!
April 27th 2009, 01:45 PM
derfleurer
... | 5 | [
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0.01318359375,
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0.00250244140625,
0.038818359375,
-0.040771... | 40,749 | 40749 | |
Embedding of a "quotient graph"
up vote 6 down vote favorite
2
Consider the simple undirected graph $G$ with natural equivalence relation $\sim$ on $V(G)$:
$u\sim v$ iff they are similar, i.e. iff there exists $\phi\in Aut(G)$ with $\phi(u)=v$.
Define a "quotient graph" $G_{Aut}$ in the following way:
$V(G_{Aut})=V... | 5 | [
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0.05078125,
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0.0263671875,
0.025634765625,
-0.00... | 40,750 | 40750 | |
re: solve exponential equations
February 26th 2009, 05:29 AM #1
Newbie
Joined
Feb 2009
Posts
16
re: solve exponential equations
Hi:
This is not really so urgent, but I couldn't find anywhere that exponential questions seem to go. Any tips?
Question is to solve the following:
The current, i a... | 4 | [
-0.045166015625,
0.04052734375,
0.1201171875,
0.01165771484375,
-0.0257568359375,
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0.01055908203125,
0.1103515625,
0.0024871826171875,
0.08642578125,
-0.08056640625,
-0.004333... | 40,751 | 40751 | |
Sum of Series Where Exponent is Sum of Arithmetic Progression
up vote 2 down vote favorite
Hi,
How do i get the sum of such a sequence:
$1 + x^{-1} + x^{-3} + x^{-6} + ...$
where the exponents are actually sum of arithmetic progression. i.e.
$x^{-0} + x^{-(0 + 1)} + x^{-(0 + 1 + 2)} + x^{-(0 + 1 + 2 + 3)} + ...$
... | 5 | [
-0.036376953125,
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0.0986328125,
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-0.00162506103515625,
-0.059326171875,
-0.00482177734375,
-0.000652313232... | 40,752 | 40752 | |
Pendulum Problem using derivative of sine/cosine
October 8th 2012, 07:52 AM
mockingjay95
Pendulum Problem using derivative of sine/cosine
Pendulum completes swing (back and forth) each 6s. As it swings, the distance, d, in cm, depends on time t, in seconds. At t=1.3 d is at its max of 110cm. Its min is 50cm. D i... | 5 | [
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0.0830078125,
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0.0223388671875,
0.00823974609375,
0.041259765625,
0.041259765625,
-0.0028076171875,
... | 40,753 | 40753 | |
Math Forum Discussions - Uncountable Diagonal Problem
Date: Dec 30, 2012 3:47 AM
Author: William Elliot
Subject: Uncountable Diagonal Problem
A list of length eta, is a function from the ordinals < beta
to a set of items. Mega-sequence will be used as a synonym for list.
How long does a list without duplicates of in... | 5 | [
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0.006072998046875,
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-0.0272216796875,
0.0439453125,
0.0247802734375,
-0.0859375,
... | 40,754 | 40754 | |
Stoke's Theorem
May 8th 2010, 02:10 PM #1
Stoke's Theorem
In the interest of disclosure, this is a homework problem for which I will
receive a grade.
First the problem,
Let S be a closed surface given by x^4+y^4+z^4=1.
Evaluate
$<br /> \iint\limits_S {(abla \times F)} \bullet nd\sigma <br /... | 4 | [
-0.0194091796875,
0.076171875,
-0.0419921875,
-0.01019287109375,
-0.003021240234375,
0.01953125,
0.03369140625,
0.0654296875,
-0.08447265625,
-0.01226806640625,
-0.09375,
-0.0024261474609375,
0.006500244140625,
0.056884765625,
-0.06494140625,
0.040283203125,
-0.03564453125,
-0.0595... | 40,755 | 40755 | |
Volume of a Spherical Cap
Date: 12/06/2000 at 23:41:51
From: Eric Reid
Subject: deriving the volume formula for spherical caps
I know the volume formula for spherical caps but I do not understand
how it is derived. I believe that the area formula for circles is part
of the formula, but I am not sure of the rest.
Th... | 5 | [
0.047607421875,
0.0252685546875,
0.032958984375,
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0.08056640625,
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0.022216796875,
0.10498046875,
0.056884765625,
0.023193359375,
-0.041748046875,
-0.01336669921875,
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0.07275390625,
-0.01611328125,
-0.10595703125,
-0.0947265625,
0.0... | 40,756 | 40756 | |
anyone know the answers to these?
January 23rd 2008, 04:39 AM
jenko
anyone know the answers to these?
1. A test was carried out on a electrical circuit and the following resaults obtained:
4t1+t2=6
-3t1+5t2=0
the 1s and 2s are lower case dont know how to do it sorry!
solve analytically the abo... | 4 | [
-0.03466796875,
0.027099609375,
0.056396484375,
-0.06298828125,
0.06396484375,
-0.00323486328125,
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0.142578125,
-0.0166015625,
0.00396728515625,
0.11328125,
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0.01220703125,
0.087890625,
-0.0247802734375,
0.07958984375,
-0.06103515625,
-0.03735351562... | 40,757 | 40757 | |
Finding exact area with the Definite Integral
November 14th 2007, 11:18 PM
janvdl
Finding exact area with the Definite Integral
Okay i was busy trying to figure these things out and then i got stuck.
Now using the Riemann notation to calculate the area under the graph $x^2 + 1$ we get the following:
$R... | 5 | [
-0.037353515625,
-0.031982421875,
-0.010986328125,
-0.0576171875,
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-0.037841796875,
0.051513671875,
0.0201416015625,
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-0.047607421875,
-0.0203857421875,
-0.0140380859375,
-0.01220703125,
-0.032470703125,
-0.03466796875,
-0.060791015... | 40,758 | 40758 | |
stuff
July 18th 2009, 11:42 AM
billym
stuff
2 Questions, I think I got the first one:
a) How many solutions exist to the equation x + y + z = 15, where x, y, and z have to be non-negative integers?
C(17,2) = 136 ... correct?
b) How many solutions exist to the equation xyz = 3^6 * 2 ^ 13, where x,... | 4 | [
-0.09228515625,
0.0322265625,
-0.0478515625,
-0.006256103515625,
0.060791015625,
0.035888671875,
0.06591796875,
-0.029296875,
-0.0498046875,
-0.00113677978515625,
0.01483154296875,
-0.042236328125,
-0.00180816650390625,
-0.011962890625,
0.00537109375,
0.06494140625,
-0.0478515625,
... | 40,759 | 40759 | |
Probability mass funcitons
March 26th 2008, 03:41 PM
Andreamet
Probability mass funcitons
a jury of 12 people is randomly selected from a group of 8 red hat, 7 blue hat,3 green hat and 20 yellow hat potential jurors. Let R, B, G and Y be the # of jurors, respectively. Calculate the
joit probability mass func... | 5 | [
0.048095703125,
0.000518798828125,
-0.0289306640625,
-0.043212890625,
0.055419921875,
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0.036865234375,
0.005859375,
0.0654296875,
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0.07421875,
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-0.0087890625,
0.0556640625,
0.078125,
-0.00177001953125,
0.030029296875,
-0.1... | 40,760 | 40760 | |
Impossible integral question
By Murray Bourne, 10 Sep 2010
Scarlett, a reader of the IntMath Newsletter, recently wrote:
Can you help me with this question pls? Thx
Integration from 0 to -1
[x(2x+1)/2(4x+1)^2] dx
this is what i manage to work out
let u = 2x^2+x
(du)^-2 = (4x+1)^-2 dx
1/... | 5 | [
0.01336669921875,
0.003662109375,
0.10986328125,
0.07373046875,
-0.0033416748046875,
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0.00836181640625,
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0.0230712890625,
0.00341796875,
0.004425048828125,
0.07275390625,
-0.09228515625,
0.01025390625,
0.0849609375,
-0... | 40,761 | 40761 | |
GCD = p (prime)
February 17th 2007, 03:53 PM
Ideasman
GCD = p (prime)
Suppose (a, b) = p, which is a prime, then determine EVERY possible value of:
1.) (a^2, b^2)
2.) (a^2, b)
3.) (a^3, b^2)
Note: (a, b) means gcd(a, b).
February 17th 2007, 04:37 PM
Soroban
Hello, Ideasman!
I don'... | 4 | [
0.005859375,
0.0126953125,
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0.04833984375,
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-0.03369140625,
0.09033203125,
0.045654296875,
-0.025634765625,
-0.0512695312... | 40,762 | 40762 | |
dy
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Here's the question you clicked on:
ujuge321 Group Title
calculate the followi... | 5 | [
-0.07080078125,
0.05908203125,
-0.0281982421875,
-0.0517578125,
-0.000774383544921875,
-0.04541015625,
0.0009002685546875,
-0.01007080078125,
0.026611328125,
0.0181884765625,
0.04443359375,
-0.07763671875,
-0.005401611328125,
0.01904296875,
-0.00128936767578125,
-0.03955078125,
-0.00... | 40,763 | 40763 | |
Normal Distribution problem.
November 13th 2010, 09:37 AM
Darkprince
Normal Distribution problem.
Hello again. Here is the problem and my solution, if anyone can tell me if I am correct or cross-check our answers, I will be grateful!
Carrots grown by a particular farmer have weights in grammes approximately... | 5 | [
0.0089111328125,
0.0247802734375,
0.0157470703125,
-0.03564453125,
0.01177978515625,
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0.09033203125,
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0.043701171875,
0.09033203125,
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0.0126953125,
-0.002288818359375,
0.02197265625,
0.10400390625,
-0.00... | 40,764 | 40764 | |
Math Help
December 29th 2012, 12:58 PM #1
Newbie
Joined
Nov 2012
From
London
Posts
6
Calculus 2
f(x,y) = x2 + y2 subject to the constraint xy = 1, find all extrema, if they exist. Where x is in [-10, 10]
The only (x,y) that satisfy the constraint are =+_1 and y=+_1. In both cases f(x) =2. Here i... | 4 | [
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-0.084... | 40,765 | 40765 | |
Limit definition of definite integrals
February 6th 2009, 01:34 PM #1
Member
Joined
Oct 2008
Posts
242
Limit definition of definite integrals
In a practice quiz I'm working on for my calc class I'm asked to evaluate the given definite integral from 3 to 7 of (x^2-3x+5)dx using the limit definition of a d... | 4 | [
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0.033447265625,
... | 40,766 | 40766 | |
An Introduction to Special Relativity (2)
In a last ditch efort to satisfactorily explain the riddle of the null result (from the Michelson-Morley experiment), a fantastic idea was put forward by George F. Fitzgerald in 1890. Using the
analogy of a rubber ball which is deformed upon striking a wall, Fitzgerald conc... | 4 | [
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0.0133056640625,
-0.0196533203125,
0.0366... | 40,767 | 40767 | |
absolute value proof
July 3rd 2008, 09:11 PM #1
Member
Joined
Jun 2008
Posts
170
absolute value proof
Prove $|x| \leq y \Longleftrightarrow -y \leq x \leq y$.
If $x \geq 0$, then $|x| = x$. So $x \leq y$. Then $|x| = x \geq -y$ and so $-y \leq x \leq y$. If $x < 0$, then $|x| = -x$. So $|x| = -x \le... | 4 | [
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0.1337890625,
-0.09375,
0.002197265... | 40,768 | 40768 | |
Special triangles and ratio of areas help?
February 11th 2011, 04:18 PM
picklepie159
Special triangles and ratio of areas help?
Hi Mathforums!
I've been lurking around here for a round a week and found you guys are really helpful. Just today, I've been hit with two hard problems (to me, at least. The class g... | 4 | [
0.020751953125,
0.05126953125,
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-0.01129150390625,
0.0181884765625,
0.0223388671875,
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0.0263671875,
-0.009033203125,
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-0.0322265625,
0.049072265625,
0.0303955078125,
-0.0380859375,
-0.056884765625,
-0.0207519... | 40,769 | 40769 | |
Solving ax + b is less than cx + d
Date: 12/11/2001 at 23:54:35
From: Sara
Subject: Solving ax + b < cx + d
Here is a problem:
6-9x is less than or equal to 5x-1
Please teach me the process in English, as if you were explaining to a
10-year-old.
Date: 12/12/2001 at 08:50:36
From: Doctor Rick
Subject: Re: Solv... | 4 | [
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0.03662109375,
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0.058837890625,
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0.11... | 40,770 | 40770 | |
Antennas and Propagation.L04
Radiation Integrals and Auxiliary Potential
Functions
Ranga Rodrigo
June 23, 2010
Lecture notes are fully based on Balanis [?]. Some diagrams and text are direc... | 4 | [
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0.01544189453125,
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... | 40,771 | 40771 | |
Stem-and-Leaf Plots and Box-and-Whiskers Plot
One way to measure and display data is to use a stem-and-leaf plot. A stem-and-leaf plot is used to visualize data. To set up a stem-and-leaf plot we follow some simple steps.
First we have a set of data. This could for instance be the results from a math test taken by a ... | 4 | [
0.0057373046875,
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0.06591796875,
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-0.00738525390625,
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0.02880859375,
-0.042724609375,
0.00146484375,
-0.09130859375,
0.0... | 40,772 | 40772 | |
Functions of fuel consumption
September 18th 2011, 07:48 PM #1
Functions of fuel consumption
For a truck, its fuel consumption in $\frac{ml}{hr}$ is given by
$f(v)=(v-10)^2+9900$, where $v$ is the speed in $\frac{km}{hr}$. Find the speed that gives the best distance to fuel ratio
No calculus is to be use... | 4 | [
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0.0274658203125,
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0.1708984375,
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0.0289306640625,
0.11376953125,
0.095... | 40,773 | 40773 | |
Need help with Consumer Surplus and the Integration step (easy)
December 10th 2009, 04:51 PM #1
Newbie
Joined
Dec 2009
Posts
3
Need help with Consumer Surplus and the Integration step (easy)
Im doing online homework of consumer surpluses and the example gives a step that is the integration part that I do... | 5 | [
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0.022705078125,
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0.09814453125,
0.037841796875,
0.029541015625,
0.00098419189453125,
0.0017547607421875... | 40,774 | 40774 | |
Factoring (Distributive Property in Reverse)
We can work the distributive property in reverse—we just need to check our rear view mirror first for small children.
When we rewrite ab + ac as a(b + c), what we are actually doing is factoring. A factor in this case is one of two or more expressions multiplied together.... | 4 | [
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0.0654296875,
-0.03369140625,
0.10351562... | 40,775 | 40775 | |
Spherical Geometry and Triangles
Associated Topics || Dr. Math Home || Search Dr. Math
Spherical Geometry and Triangles
... | 5 | [
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-0.0154... | 40,776 | 40776 | |
Surface Normals
From Math Images
Surface Normals
This picture is of plane segments in different rotations in space. They each have an arrow coming out of their front face at exactly $90^{^{\circ}}$ (orthogonal) to the surface.
Basic Description
Several kinds of computation in computer graphics depend on know... | 4 | [
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0.0021... | 40,777 | 40777 | |
2 simple outer measure problems
September 18th 2010, 06:55 AM #1
Newbie
Joined
Sep 2010
Posts
4
2 simple outer measure problems
Hello all.
These are homework problems, so partial solutions / advice would be preferred.
These come from the book Real Analysis (4th ed) by Royden and Fitzpatrick
... | 4 | [
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0.04150390625,
... | 40,778 | 40778 | |
cross products
March 6th 2007, 10:06 PM #1
Senior Member
Joined
Jan 2007
Posts
477
cross products
Find the cross product of the vectors i + j - k and i - j + k
any help with this one please.
This is pretty standard. Do you know the formula for the cross product of two vectors?
Let a = <1, ... | 4 | [
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0.0410... | 40,779 | 40779 | |
Help on a couple basic Trig Questions
January 21st 2011, 05:13 PM
WalaBen86
Help on a couple basic Trig Questions
Hello, I'm new here so advanced apologies if I'm posting improperly. I am in need of some assistance on these two problems. It's been a while since I've done trig and although I know the basics I
... | 4 | [
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-0.07275390625,
-0.02270... | 40,780 | 40780 | |
integrate integral 1/x(ln (x)^1/2)
October 30th 2008, 03:05 AM #1
Member
Joined
Jun 2008
Posts
175
Question asks to evaluate the integral
$<br /> \int\limits_e^{e^4 } {\frac{1}{{x\sqrt {\ln x} }}} dx<br />$
Attempt by substitution, Letting u = ln x
$<br /> = \int\limits_e^{e^4 } {\frac{1}{x}u... | 5 | [
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-0.044921875,
-0.0... | 40,781 | 40781 | |
block matrix question
June 22nd 2011, 01:33 PM #1
MHF Contributor
Joined
Nov 2008
Posts
1,401
block matrix question
there is a space V of dimention n
T:V->V
i am givem also the thing in the photo
prove that there is a basis B for such [T]_B on in the photo.
where A C D are mxm matrices.
... | 4 | [
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-0.01141... | 40,782 | 40782 | |
Partitions
Joe is a database consultant and contributing editor to DBMS magazine. He can be contacted on CompuServe at 71062,1056.
Formally, a partition of a set of objects is a collection of subsets such that: 1. The union of all the subsets in the collection is equal to the original set; 2. the intersection of all t... | 4 | [
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Limits of e functions
September 29th 2008, 08:32 AM
jbecker007
Limits of e functions
Help! (Speechless)
How do I find the limits for the following:
lim x-> 0+ of e^(1/x)
Lim x->-inf of (1-e^x)/(1+e^x).
I can't figure these out...please help!
Jeannine
September 29th 2008, 08:50 AM
Sorob... | 5 | [
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0... | 40,784 | 40784 | |
Need step by step instruction for this factoring
June 5th 2008, 05:57 AM
mathdonkey
Need step by step instruction for this factoring
I know y = (x^2 - 12x + 36) - 36 +7 factored becomes y = ( (x - 6)(x - 6) ) - 36 + 7, but what is the step by step method for doing this? Please be clear and concise (no short cuts... | 4 | [
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0.090820... | 40,785 | 40785 | |
Non-vanishing of p-adic L-functions
up vote 15 down vote favorite
6
In Non-vanishing of L-series of modular forms (easy case?) it was answered that for a cuspidal newform $f$ of weight strictly greater than 2, then $L(f,1)$ is non-zero. (Here the $L$-series is
normalized so that the center of the critical strip is giv... | 4 | [
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Episode 1 of Q.E.D.: Math, Proofs, and Awesomeness
I’ve been anticipating the new detective drama Q.E.D. starring Takahashi Ai and Nakamura Aoi since it looked like it would involve a lot of awesome math, and now that the first episode is out, we can
see that there is indeed a lot of awesome math! And correct, non-triv... | 5 | [
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Integrating Monotonically Increasing Functions
February 12th 2009, 07:08 PM #1
Member
Joined
Oct 2008
Posts
135
Integrating Monotonically Increasing Functions
Hey, I tried reading over this in one of my classes today since I fell way behind in all my work. Any ideas?
Let f: [a,b] --> R be increasing... | 5 | [
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0.... | 40,788 | 40788 | |
Did I do this problem correctly?
March 27th 2007, 10:42 PM #1
Newbie
Joined
Mar 2007
Posts
10
Did I do this problem correctly?
Annual sales of fountain pens in Littleville are presently 4000 per year and are increasing 10% by year. How many fountain pens will be sold over the next 5 years.
I evulate... | 5 | [
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Economics 322 > Dellia > Notes > LECTURE - applying mult reg.doc | StudyBlue
Department of Economics Prof. Derek DeLia Econometrics 220:322:B6 Summer 2009 APPLICATIONS OF THE MULTIPLE REGRESSION MODEL The model: EMBED Equation.3 ( EMBED Equation.3 ). Isolate the impact of one
independent variable while holding others f... | 5 | [
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Decompose a Vector
August 23rd 2009, 07:01 AM #1
Junior Member
Joined
Aug 2009
Posts
37
Decompose a Vector
Let n = (-2, 1). Decompose the vector g = (0, -9.8) into the sum of two orthogonal vectors, one parallel to n and the other orthogonal to n.
I'm not sure how to go about doing this.
From $... | 5 | [
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CRpuzzles Logic Problem Solution - The Krispy Kreme Prom
Logic Puzzle # 98 Logic Problems Help
Logic Problem Solution:
The Krispy Kreme Prom
... | 4 | [
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Completing the square.
April 14th 2008, 09:59 AM
Mymble
Completing the square.
I need to solve this equation by completing the square:
2x^2 + x - 8 = 0
In my textbook the answer is x = 1.77 or x = -2.27
I've tried to do it but can't get the right answer...
2x^2 + x - 8 = 0
x^2 + 0.5x - 4 =... | 4 | [
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Vector field
April 27th 2009, 06:59 AM #1
Super Member
Joined
Jun 2008
Posts
829
Vector field
$F(x,y) = - \frac{y}{x^2+y^2}i + \frac{x}{x^2+y^2}j$
1) What domain of the field?
2) Prove that:
$\oint_{\alpha} - \frac{y}{x^2+y^2}dx + \frac{x}{x^2+y^2}dy = 2 \pi$
$\alpha$ is a circumferenc... | 5 | [
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Proving a generalization of Fermat's Little Theorem, involving the Euler phi function
March 14th 2012, 12:21 PM
DoctorProfessorMath
Proving a generalization of Fermat's Little Theorem, involving the Euler phi function
Here is a simplified idea of what I am working to solve. I am unsure where to start (besides wh... | 5 | [
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brain teaser
October 1st 2005, 03:08 AM #1
Junior Member
Joined
Oct 2005
Posts
29
brain teaser
given that 2^x = 1/square root of 2 and 2^y = 4(square of 2), find exact values of x and y.
calculate the exact value of 2^y-x
thanks..
Ok... because sqrt(n) = n^(1/2) and 1/(n^p) = n^(-p)
2^x... | 4 | [
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home-made devices and soft
MPPT Theory
In general, the maximum power from the source to the load is transferred when impedances of source and load is equal. This means that we have only one maximum point in the function of power of the
source. Because we can use a simple algorithm for finding the maximum of the functi... | 4 | [
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How large (small) can be the measure of a set where a polynomial takes small values ?
up vote 6 down vote favorite
4
A $n$-th degree polynomial has precisely $n$ roots. So it is natural to ask the question how large ( and small) can be the measure of a set where a polynomial takes small values ?
This, and other inter... | 4 | [
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.
5. STRUCTURE FORMATION IN THE UNIVERSE
The conventional paradigm for the formation of structures in the universe is based on the growth of small perturbations due to gravitational instabilities. In this picture, some mechanism is invoked
to generate small perturbations in the energy density in the very early phase ... | 4 | [
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