content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
difficult antiderivative
August 31st 2007, 04:15 PM #1
Member
Joined
Aug 2007
Posts
148
difficult antiderivative
Hi,
Can someone please explain to me how to find the antiderivative of x^3/3(cosmx)? I'm trying to solve the interval of x^2cosmx dx and I am at the point where I need to find the antider... | 5 | [
-0.01458740234375,
0.01263427734375,
0.00860595703125,
0.006561279296875,
-0.06298828125,
-0.0162353515625,
-0.01300048828125,
0.019287109375,
-0.044921875,
0.019775390625,
0.037109375,
-0.0115966796875,
-0.0140380859375,
-0.01434326171875,
0.033203125,
-0.01068115234375,
0.071289062... | 7,400 | 7400 | |
Greatest Integer Equation
Date: 08/06/2003 at 16:09:10
From: Michael McQuilken
Subject: Greatest Integer
I am trying to correctly interpret [[x]]^2 + [[y]]^2 = 1, where
f(x) = [[x]], is the Greatest Integer function.
I read the answer in the Dr. Math archives:
Greatest Integer Functions
http://mathforum.org/l... | 4 | [
0.04052734375,
0.0166015625,
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0.0322265625,
0.01483154296875,
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0.06494140625,
0.0302734375,
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-0.09130859375,
0.087890625,
0.052978515625,
0.09423828125,
0.031005859375,
0.05615234375,
0.03173828125,
-0.09375,
0... | 7,401 | 7401 | |
Polar Calculus Help Needed
March 20th 2007, 02:06 PM
phack
Polar Calculus Help Needed
I have a graph of a polar function, r=1-2cos(theta). The graph produces a limacon. I had no problem graphing it, but I'm a bit confused as to how to find the area. The area I need to find is the
area within the larger, oute... | 5 | [
0.046875,
-0.053955078125,
-0.076171875,
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0.03759765625,
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0.0859375,
-0.00653076171875,
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0.0576171875,
0.0634765625,
-0.00830078125,
0.0625,
0.029052734375,
0.04541015625,
-0.07763671875,
0.0072021484375,
-0.027587... | 7,402 | 7402 | |
paramatised curve and self-intersection points.
August 21st 2010, 05:36 AM #1
paramatised curve and self-intersection points. Need Extra help!
So i have the curve:
$\gamma(t) =(t^2-t+1, t^2-t)$
And i need to show that it has one self-intersection point.
To me, it is obviously at 0 and 1, as at thes... | 5 | [
-0.035400390625,
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0.0081787109375,
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0.0306396484375,
0.0262451171875,
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0.08544921875,
-0.0556640625,
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0.013427734375,
-0.05419921875,
-0.0228271484375,
-0.022216796875,
... | 7,403 | 7403 | |
Euler's Formula
Date: 11/28/2001 at 13:33:13
From: Amanda Cornett
Subject: Euler's formula
I have to find Euler's formula for two-dimensional figures and
explain it at a university level and at an elementary-school level.
Date: 11/28/2001 at 13:37:31
From: Doctor Tom
Subject: Re: Euler's formula
Hi Amanda,
Here'... | 4 | [
0.0206298828125,
0.08984375,
0.04931640625,
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0.0341796875,
0.01611328125,
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0.05810546875,
-0.020751953125,
0.09912109375,
0.0233154296875,
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0.11328125,
0.0220947265625,
-0.0281982421875,
-0.0164794921875,
0.03491210937... | 7,404 | 7404 | |
Variance and Expected Value
Date: 09/12/2004 at 19:57:58
From: Frank
Subject: Variance is equal to the expected value
How can you prove that the variance is equal to the expected value of
the square of the random variable minus the mean squared?
Date: 09/13/2004 at 09:32:23
From: Doctor Luis
Subject: Re: Variance ... | 4 | [
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-0.043701171875,
0.01391601562... | 7,405 | 7405 | |
Proof of Divisibilty propery of Fibonaccia numbers.
December 2nd 2013, 06:24 AM #1
Member
Joined
May 2009
Posts
109
Proof of Divisibilty propery of Fibonaccia numbers.
I'm struggling with understanding part of this proof.
It makes use of this relationship.
$F_{m + n} = F_{m-1}F_n + F_mF_{n + 1}... | 4 | [
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0.061279296875,
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0.00604248046875,
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0.041259765625,
-0.051513671875,
-0.06787109375,
-0.0230712890625,
0.01... | 7,406 | 7406 | |
Math Help
January 10th 2008, 12:44 AM #1
Newbie
Joined
Dec 2007
Posts
8
couples
How many ways are there to seat n married couples at a round table with 2n chairs in such a way that the couples never sit next to each other?
Edit: You may ignore this incorrect solution, I leave it for people to see w... | 4 | [
-0.02734375,
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0.06396484375,
0.018798828125,
-0.04248046875,
0.0103759765625,
-0.0264892578125,
-0.0598... | 7,407 | 7407 | |
Differential question
October 31st 2009, 04:06 PM #1
Differential question
Solve the following initial value problem:
So I isolated the y and it became
8y=(9-dy/dt)t
how would I finish the rest?
You can also do this as a "homogeneous" equation. Write it as $\frac{dy}{dt}= \frac{9t- 8y}{t}= 9... | 5 | [
-0.05419921875,
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0.062255859375,
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-0.032958984375,
-0.058837890625,
-... | 7,408 | 7408 | |
Equivalence class mod problem
December 8th 2008, 05:43 AM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Equivalence class mod problem
Let $G = \frac { \mathbb {Q} } { \mathbb {Z} }$ under +, so the elements are the equivalence classes $\hat {r} = \{ s \in \mathbb {Q} : s-r \in \mathbb {Z} \}$. W... | 5 | [
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-0.0181884765625,
-0.00109100341796875,
-0.05078125,
0.032958984375,
-0.0351... | 7,409 | 7409 | |
Napier's Logs
Napier’s Logs
(In an earlier post, I referred to a way to understand the invention of logarithms by John Napier. This post fleshes this out.)
Imagine an era long ago where calculators and computers didn’t exist, and the engineers and crafts people spent large amounts of time doing long and tedious and ... | 4 | [
-0.0859375,
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-0.126953125,
0.096679687... | 7,410 | 7410 | |
Number of Ways to Move
Date: 1/30/96 at 21:33:23
From: Anonymous
Subject: Permutations?
I have a group of squares which together form a larger square, i.e. a
square that is 8 squares by 8 squares.
In how many ways can you travel from the upper left corner of the
large square to the lower right corner by only going ... | 4 | [
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0.07568359375,
-0.024658203125,
0.02978515... | 7,411 | 7411 | |
SF&PA: One more example
SF&PA: One more example April 9, 2008
Posted by Noah Snyder in planar algebras, subfactors, Uncategorized.
trackback
Sorry for the delay, Scott’s been in town and so I’ve been too busy doing actual research to get much blogging done. This post was also a little delayed because I didn’t underst... | 4 | [
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0.036376953125,
-0.024658203125,
... | 7,412 | 7412 | |
Error in Rudin Chapter 5 Exercise 25?
June 9th 2010, 10:15 AM #1
Member
Joined
Mar 2010
Posts
98
Error in Rudin Chapter 5 Exercise 25?
This is driving me crazy, because it seems wrong but I haven't found it in any of the errata.
Problem:
Suppose $f$ is twice differentiable on $[a, b], f(a) < 0, ... | 4 | [
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0.08056640625,
-0.01251220703125,
-0.0495605468... | 7,413 | 7413 | |
Probability notations
June 27th 2008, 08:43 PM
peanutbutter
Probability notations
I have a 3 part question and I am fairly confident I have the correct final answer. It goes
A region's population is 7,800 and it's per capita income approximately observes a normal distribution with the mean being $12,100 and... | 4 | [
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-0.0... | 7,414 | 7414 | |
function of area of isosceles triangle
January 1st 2011, 09:49 PM #1
Junior Member
Joined
Nov 2010
From
NY
Posts
64
function of area of isosceles triangle
The equal sides of an isosceles triangle are 2. If x is the base, express the area as a function of x.
The area of a triangle is 1/2 BH and t... | 4 | [
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0.061767578125,
0.045654296875,
0.10693359375,
0.039794921875,
-0.059570... | 7,415 | 7415 | |
Familiar Triangles
Date: 01/19/99 at 21:56:41
From: Noel
Subject: Integrated math 2b
I need help figuring out special right triangles. I've tried to start
with a and b but I get confused. I don't know the next step.
For example one problem is:
Find a and b. Simplify radicals whenever possible.
| .
|60 .... | 4 | [
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Question about second order differential equation
April 30th 2011, 01:55 PM
Ulysses
Question about second order differential equation
I have this problem, which says: If the graph of one solution for the equation $y''+P(x)y'+Q(x)y=0$ is tangent to the x axis in some point of an interval [a,b], then that solution... | 4 | [
-0.09619140625,
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0.052734375,
-0.078125,
-0.05175781... | 7,417 | 7417 | |
Count of numbers between A and B (inclusive) that have sum of digits equal to S
up vote 2 down vote favorite
2
The problems is to find the count of numbers between A and B (inclusive) that have sum of digits equal to S.
Also print the smallest such number between A and B (inclusive).
Input:
Single line consisting o... | 5 | [
-0.0751953125,
0.04931640625,
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-0.1005859375,
-0.03369140625,
0.083984375,
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0.0184326171875,
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0.0198974609375,
-0.022216796875,
0.01202392578125,
0.00311279296875,
0.019653320... | 7,418 | 7418 | |
definite integral
find the indefinite integral of x/(1+x^4)
Let u = x^2; then du = 2x dx, so
∫ x dx /(1+x^4) = (1/2) ∫ 2x dx / (1+x^4) = (1/2) ∫ du / (1 + u^2)......blanked out
ans: arctan (x^2)/2....huh??
| 5 | [
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0.10595703125,
-0.1005859375,
0.009765625,
0.044677734375,
0.022949... | 7,419 | 7419 | |
Prove (1+cos x/1+cot x) = tan x
November 15th 2010, 04:03 PM #1
Junior Member
Joined
May 2010
Posts
26
Prove (1+cos x/1+cot x) = tan x
So when I did this the proof I got was -tanx and i can't really see where i went wrong:
1+tanx/1+cotx =tanx
(1-cotx/1-cotx) (1+tanx/1+cotx)
1+tanx-cotx-cot... | 4 | [
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0.062255859375,
-0.043701171875,
0.007781982421875,
-0.0162353515625,
... | 7,420 | 7420 | |
Bayes Problem
February 4th 2010, 06:21 PM
GoodRobot
Bayes Problem
A diagnostic test is designed to detect whether subjects have a certain disease. A positive test outcome predicts that a subject has the disease. Given that a subject has the disease, the
probability the diagnostic test is positive is called t... | 5 | [
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0.0255126953125,
0.03466796875,
-0.014587... | 7,421 | 7421 | |
First Order Separable Differential equation
February 24th 2009, 09:01 PM #1
Newbie
Joined
Feb 2009
From
Bay Area, CA
Posts
6
Hello,
I'm in Differential Equations and I have my midterm tomorrow... I can do most everything on my review sheet, but I'm a bit confused when it comes to a very simple ini... | 5 | [
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Hyperbinary conjecture seeking proof for a good time, long walks on the beach
Here’s the latest progress on the hyperbinary sequence. We’re trying to figure out the inverse relation of the function $h$: given a particular number $n$, where does it occur in the hyperbinary
sequence? That is, what are the values of $k$ ... | 4 | [
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-0.036865234375,
-0.0220... | 7,423 | 7423 | |
Surpassing "Graham's number"
This posting describes a
64
-state 2-symbol Turing machine (GTM64) that computes a number greater than Graham's number (G), starting with a blank tape.
GTM64 implements the same pair-rewriting algorithm as the machines described in the previous posting, now restricted to ordinals less th... | 4 | [
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-0.00811767578125,
-0.07763671875,
0.003372192382... | 7,424 | 7424 | |
dy
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Akshay_Budhkar Group Title
B... | 4 | [
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0.078125,
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0.01953125,
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-0.01519775390625,
-0.02038574218... | 7,425 | 7425 | |
L'Hopital's Rule and Improper Integrals
March 6th 2009, 06:17 PM #1
Member
Joined
Jan 2009
Posts
100
L'Hopital's Rule and Improper Integrals
$\lim (e^x+x)^\frac{2}{x}$
$x->0^+$
Describe the type of indeterminate form that is obtained by direct substitutions.
Evaluate the integral using L'Hop... | 5 | [
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-0.041748046875,
-0.012451171875... | 7,426 | 7426 | |
this is so confusing...
August 6th 2008, 08:03 PM #1
Newbie
Joined
Jul 2008
Posts
7
this is so confusing...
i have to solve for y for these 3 problems...where do i start?
yx^2 + yz^3 = t
x/r + 2/3(yz) = 4y
y(3^2) + 1 = 2^4 - y(1^3)
i have to solve for y for these 3 problems...where ... | 4 | [
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0.03515625,
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0.0693359375,
0.017822265625,
0.009033203125,
0.018310546875,
-0.020751953125,
-0.0208740234375,
-0.03369140625,
0.0303955078125,
-0.01068115234375,
0.0216064453125,
0.0771484375,
-0.00066375732421875,
0.03173828125,
-0.087890625,
-0.0186... | 7,427 | 7427 | |
[SOLVED] Numerical solutions of ordinary dif eqs
January 8th 2008, 01:22 AM
olionel
[SOLVED] Numerical solutions of ordinary dif eqs
Hello there;
I have a wee question, itd be great if I can get a solution for this. (I am putting it up on behalf of a friend as Im not really sure where to start, hes studying... | 4 | [
-0.05029296875,
-0.01275634765625,
0.03466796875,
-0.046142578125,
-0.003509521484375,
0.0086669921875,
0.0274658203125,
-0.0002574920654296875,
-0.07763671875,
-0.01519775390625,
0.015869140625,
-0.041748046875,
-0.006195068359375,
-0.068359375,
-0.032470703125,
0.007415771484375,
-... | 7,428 | 7428 | |
Apply the generalized product rule.
November 26th 2013, 07:57 PM
sepoto
Apply the generalized product rule.
$x^x$
Online Derivative Calculator ? Shows All Steps!
My derivative calculator says to apply the generalized product rule so that:
$x^x*\frac{d}{dx}(ln(x)*x)$
At first I thought it look... | 5 | [
-0.0003795623779296875,
-0.095703125,
0.056640625,
-0.01104736328125,
0.01519775390625,
-0.060791015625,
0.03857421875,
0.0030059814453125,
0.02685546875,
0.04931640625,
0.0966796875,
0.015625,
0.054931640625,
0.0186767578125,
0.04541015625,
0.061279296875,
-0.1279296875,
0.0216064... | 7,429 | 7429 | |
Cannot find the contradiction
January 14th 2011, 04:56 AM #1
Cannot find the contradiction
Hello all. I have something in which there must be a contradiction but I cannot find it.
So let $\phi$ be the usual Euler phi/totient function, and let $G$ be a finite group. Then we have
(1) $\phi_G(d) = \phi(d) ... | 4 | [
-0.076171875,
0.019287109375,
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0.0252685546875,
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0.06640625,
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-0.0478515625,
-0.0712890625,
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-0.021728515625,
0.018920... | 7,430 | 7430 | |
find vector same direction as .. but has length ..
September 9th 2008, 05:51 PM
Craka
find vector same direction as .. but has length ..
Hi having trouble understanding this. Question asks find the vector that has same direction as -2i+4j+2k but that has length 6.
To get the unit vector is did this.
$<b... | 4 | [
0.052001953125,
0.048095703125,
-0.040771484375,
-0.031494140625,
-0.003021240234375,
0.0048828125,
-0.09716796875,
-0.019775390625,
-0.0255126953125,
0.00421142578125,
0.044677734375,
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-0.053955078125,
-0.054931640625,
-0.08251953125,
-0.0281982421875,
-0.06591796875... | 7,431 | 7431 | |
Rate Problem
September 17th 2009, 08:09 AM #1
Newbie
Joined
Sep 2009
Posts
1
Rate Problem:
"In a bike race, Jake and Kevin started at the same time and rode with constant speeds. Jake rode at 30miles per hour, and Kevin rode at 35miles per hour. If Jake crossed the finish line 10
minutes after Kev... | 4 | [
0.0035247802734375,
0.05419921875,
0.0252685546875,
-0.05419921875,
-0.091796875,
0.034423828125,
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0.0205078125,
0.0159912109375,
0.04150390625,
0.04150390625,
-0.0693359375,
0.041748046875,
0.04833984375,
-0.039306640625,
0.03076171875,
0.03125,
0.01470947265625,
... | 7,432 | 7432 | |
Average temperature vs average irradiance
Vincent Gray and Alan Siddons have been emphasizing an important point that the (arithmetic) average temperature is not the relevant quantity that should be substituted into various calculations of
the heat and energy budget of Earth.
Why? Because what matters for the energy b... | 4 | [
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0.08056640625,
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0.0299072265625,
-0.03369140625,
0.0213623046875,
0.014404296875,... | 7,433 | 7433 | |
Write Expression In Partial Fraction
November 8th 2011, 05:42 PM #1
Junior Member
Joined
Oct 2011
Posts
36
Write Expression In Partial Fraction
x^2/(x-1)(x+1) = x^2/x^2-1 = 1,-1
Therefore,
x^2/(x-1)(x+1) = 1 + -1/(x-1)(x+1)
-1/(x-1)(x+1) = A/(x-1) + B/(x+1)
-1 = Ax + A + Bx - B
-1 =... | 4 | [
-0.08740234375,
0.05029296875,
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0.06640625,
0.050048828125,
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0.05712890625,
0.016357421875,
-0.015... | 7,434 | 7434 | |
Confusing Conditional Probability Question
May 11th 2009, 06:48 PM
jstluise
Confusing Conditional Probability Question
Hello all!
I'm trying to work through a problem involving conditional probability and I am more than confused. I need some guidance. Here is a brief description of the problem statement:
... | 5 | [
0.07568359375,
-0.08642578125,
0.056640625,
-0.01220703125,
0.08154296875,
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0.048583984375,
0.09521484375,
-0.0038299560546875,
-0.061279296875,... | 7,435 | 7435 | |
Partial Derivatives
February 22nd 2009, 05:07 PM #1
Junior Member
Joined
May 2008
Posts
56
Partial Derivatives
f(x,y)=x^2y + xsiny -ln[x-y^2]
Find fy and fxy
I found fy but to get xy you take the x derivative, which I found to be 2xy+siny-1/(x-y^2) and then take the y. The answer is 2x-xsiny-2y... | 5 | [
0.0255126953125,
-0.032958984375,
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0.0172119140625,
-0.035888671875,
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0.0869140625,
0.0205078125,
0.01397705078125,
0.048095703125,
0.06494140625,
0.055908203125,
-0.11474609375,
-0.... | 7,436 | 7436 | |
Domain and Range of a Function
Date: 03/05/2004 at 08:00:58
From: Veronica
Subject: how do you do domain and range in algebra
Given f(x) = 2x, find the domain and range of the function.
Date: 03/06/2004 at 00:25:39
From: Doctor Achilles
Subject: Re: how do you do domain and range in algebra
Hi Veronica,
Thanks f... | 4 | [
-0.005889892578125,
-0.020263671875,
-0.0003452301025390625,
-0.038818359375,
-0.06884765625,
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0.040771484375,
-0.0206298828125,
0.0673828125,
0.0162353515625,
-0.03955078... | 7,437 | 7437 | |
Indefinite integral , how to start
$\mbox{If someone tell me how to start in evaluating the indefinite integral}\\ \\ \phantom{xxxxxxx} \int{tan^{-1}\sqrt{\frac{1-x}{1+x}}$
Last edited by CaptainBlack; July 24th 2011 at 05:21 AM. Reason: sort out LaTeX post
Maybe with integration by parts: $\int \arctan\left(\sqrt{\f... | 5 | [
0.033203125,
-0.0888671875,
0.0732421875,
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-0.02294921875,
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0.0859375,
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0.076171875,
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0.029052734375,
0.057861328125,
-0.051513671875,
... | 7,438 | 7438 | |
I do not understand problmes 9 to 15 how do you determine domains and ranges again?
Let's look at 9 first: $y=(x+1)^2-3$ A function's domain is all the possible x values that work within a function. A domain is often restricted by functions like $\frac{x}{x-1}\$where $x eq 1$
because that would result in dividing by 0... | 4 | [
-0.03515625,
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0.020751953125,
0.052001953125,
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0.0361328125,
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0.04443359375,
0.11083984375,
0.0703125,
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-0.005889892578125,
-0.060791015... | 7,439 | 7439 | |
an algebra question
September 25th 2005, 10:57 AM
rpatel
an algebra question
hello.
i have got this one algebra question for homework.
however i had no idea on how to do this attached one.
i need to find answers for both a= and b=.
September 25th 2005, 11:40 AM
ticbol
One way is to expand t... | 4 | [
-0.0791015625,
0.007476806640625,
-0.037353515625,
0.0419921875,
-0.031982421875,
0.0634765625,
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-0.049072265625,
0.033203125,
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0.06396484375,
-0.05419921875,
0.039306640625,
-0.06689453125,
0.0223388671875,
0.068359375,
-0.0673828125,
-0.0133666992... | 7,440 | 7440 | |
Verification of tensor product
December 3rd 2009, 03:02 AM #1
Newbie
Joined
Nov 2009
Posts
12
Verification of tensor product
Hi,
I just wondered if someone could verify my calculation that the tensor product of Z + Z/3 and Z/6 is isomorphic to Z/6 + Z/3.
The calculation is as follows:
(Z + ... | 5 | [
-0.134765625,
-0.00115966796875,
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0.0311279296875,
0.022216796875,
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0.03466796875,
-0.0032501220703125,
-0.05224609375,
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0.025634765625,
-0.0478515625,
-0.029052734375,
-0.00421142578125,
0.0150146484375,
0.0111083984375,
-0.0732421875,... | 7,441 | 7441 | |
possible value
October 21st 2009, 07:40 AM #1
Member
Joined
Aug 2009
Posts
211
possible value
hi, my question is:
find the possible value of the constant c so that the line $y = 2x + c$ is a tangent to the circle $x^2 + y^2 = 4$
i treated it as a simultaneous equation (if thats the right thing ... | 4 | [
0.00323486328125,
-0.0037689208984375,
-0.033935546875,
0.103515625,
0.003387451171875,
0.0712890625,
-0.032470703125,
0.10693359375,
0.0181884765625,
-0.09033203125,
0.04443359375,
-0.07568359375,
-0.058349609375,
0.031005859375,
-0.028076171875,
0.052001953125,
-0.01544189453125,
... | 7,442 | 7442 | |
Amortization - LOGS!! Help
September 12th 2008, 01:02 AM
FANBLADE
Amortization - LOGS!! Help
I'm actually working on an amortization problem.
I am trying to solve for n. I have all of the other values.
In order to do this I end up using logs (i think...)
A/P/r = (1+r) ^n /((1+r)^n - 1)
Does ... | 5 | [
-0.042724609375,
0.043701171875,
-0.0277099609375,
0.043212890625,
0.04248046875,
-0.08203125,
0.053466796875,
-0.0252685546875,
0.06591796875,
0.05859375,
-0.03369140625,
0.0281982421875,
-0.036865234375,
0.130859375,
0.0234375,
0.01361083984375,
-0.07373046875,
0.0020294189453125... | 7,443 | 7443 | |
challenging ratio question
June 29th 2011, 06:41 AM
kingman
challenging ratio question
Dear sir,
I would be most grateful if someone can help me to solve the below question.
Thanks
There are 42 fruits in each of the 2 boxes, box A and box B. The ratio of the number of apples in box A to the number o... | 4 | [
0.0703125,
0.01373291015625,
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0.03369140625,
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0.0419921875,
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0.01611328125,
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0.0035247802734375,
0.06689453125,
0.0751953125,
-0.014892578125,
0.0191650390625,
-0... | 7,444 | 7444 | |
Complex Numbers
June 7th 2011, 04:57 AM #1
Junior Member
Joined
May 2011
Posts
30
Complex Numbers
Hi guys, need help with this question:
Find the 2 complex numbers z1 and z2 each of which satisfies the following EQN:
3zz* + 2(z-z*) = 39 + 12i
To solve this, I let z = x + yi
3zz* + 2(z-... | 4 | [
-0.0908203125,
0.046142578125,
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0.042724609375,
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0.0234375,
0.019287109375,
-0.01422119140625,
-0.09033203125,
-0.04565... | 7,445 | 7445 | |
existence of linearly independent subsets of finite vector spaces
December 11th 2009, 11:00 AM #1
Newbie
Joined
Dec 2009
Posts
11
existence of linearly independent subsets of finite vector spaces
Let F_2 be the field with two elements and F_256 the field with 256 elements.
1) Proof that there is no s... | 5 | [
-0.02587890625,
0.03759765625,
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0.08251953125,
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0.0810546875,
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0.0245361328125,
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-0.022216796875,
-0.0576171875,
0.054443359375,
-0.061279296875,
... | 7,446 | 7446 | |
Sphere volume derivation with the correct variable of integration
December 22nd 2010, 08:24 PM #1
Newbie
Joined
Sep 2010
Posts
20
Sphere volume derivation with the correct variable of integration
Hello all,
So I'm trying to figure out why setting up integrals to find volume of a sphere with the corr... | 5 | [
0.007537841796875,
0.0142822265625,
0.044189453125,
-0.0252685546875,
0.0277099609375,
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0.03271484375,
0.0625,
0.08251953125,
-0.0301513671875,
0.07080078125,
0.01007080078125,
0.05908203125,
0.0224609375,
-0.03515625,
0.025390625,
0.08203125,
-0.0... | 7,447 | 7447 | |
Probability
May 19th 2013, 07:06 AM
Tutu
Probability
Two students, Karl and Hanna, play a game in which they take it in turns to select a card, with replacement from a well-shuffled pack of 52 playing cards. The first person to select an ace wins
the game. Karl has the first turn.
ai.) Find the probabil... | 4 | [
-0.01556396484375,
-0.00640869140625,
-0.05419921875,
-0.11669921875,
-0.08056640625,
0.020751953125,
0.054931640625,
0.05224609375,
0.0654296875,
0.0225830078125,
-0.004638671875,
-0.0135498046875,
-0.072265625,
-0.05224609375,
-0.00439453125,
0.049072265625,
0.021728515625,
-0.04... | 7,448 | 7448 | |
Circular Motion
February 22nd 2008, 02:06 PM #1
Member
Joined
Mar 2007
From
England
Posts
104
Circular Motion
I would like some help on this question please, just spent the last hour trying to figure it out.
A smooth hemispherical bowl of radius a has its rim horizontal. A particle P os projecte... | 4 | [
0.01904296875,
0.05419921875,
0.05224609375,
-0.022705078125,
0.04296875,
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0.05712890625,
0.060546875,
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-0.03759765625,
-0.0556640625,
0.01080322265625,
0.015380859375,
-0.0107421875,
0.010009765625,
-0.000652313232421875,
0.022216796... | 7,449 | 7449 | |
Proof by Induction ?
May 27th 2007, 03:58 AM #1
Newbie
Joined
May 2007
Posts
2
Hi,
I cannot believe I am having to ask for help, but I have left this far too late and have a ton of work to do. Can someone solve the following problem for me ? Your assistance will be greatly
appreciated. Perhaps so... | 5 | [
-0.103515625,
0.10205078125,
0.1083984375,
0.01416015625,
-0.043701171875,
-0.0537109375,
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-0.006866455078125,
0.002532958984375,
0.011962890625,
-0.09423828125,
-0.07568359375,
0.036376953125,
0.08349609375,
-0.032958984375,
0.0137939453125,
0.04296875,
0.042968... | 7,450 | 7450 | |
General and Particular Solutions
Date: 01/08/99 at 05:57:52
From: Abbas
Subject: Differential Equations
Can you please explain me in simple terms the difference between a
general solution and a particular solution of a differential
equation? When does this occur, and what is its physical significance?
Date: 01/08/... | 5 | [
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-0.0023193359375,
0.1103515625,
0.042236328125,
0.048095703125,
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0.09619140625,
0.0135498046875,
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0.044677734375,
-0.026123046875,
-0.08837890625,
-0.0498046875,
-0.085... | 7,451 | 7451 | |
Functional equation
May 20th 2007, 03:55 PM #1
Newbie
Joined
May 2007
Posts
4
Functional equation
Hi, I need help on these two problems dealing with functional equation
Let f be a function defined everywhere on the real axis. Suppose also that f satisfies the functional equation
f(x+y) = f(x)f(... | 4 | [
0.031494140625,
-0.0089111328125,
0.005218505859375,
0.09619140625,
-0.0255126953125,
0.099609375,
0.0267333984375,
-0.0054931640625,
0.029052734375,
-0.0279541015625,
0.040771484375,
-0.0194091796875,
-0.056640625,
0.1259765625,
0.03662109375,
0.037109375,
-0.09130859375,
-0.02490... | 7,452 | 7452 | |
Falling Football
Date: 11 Jan 1995 10:36:57 -0500
From: Merr
Subject: (none)
Would you answer the following question?
If I were to drop a football off the top of Mile High Stadium, how long
would it take for the football to hit the ground? The height of
the stadium is 305 ft.
Date: 13 Jan 1995 02:18:13 -0500
Fro... | 4 | [
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0.055908203125,
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0.15234375,
-0.00396728515625,
0.052490234375,
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0.064453125,
-0.00191497802734375,
0.08642578125,
-0.0257568359375,
-0.... | 7,453 | 7453 | |
Help solving Trig integral
September 29th 2009, 05:43 PM #1
Member
Joined
Apr 2009
Posts
85
Help solving Trig integral
Hey all, I need help finishing this integration problem
$\int_0^\frac{\pi}{2} \!16sec^4(\frac{t}{2}) \, dt$
$16\int_0^\frac{\pi}{2} \!sec^4(\frac{t}{2}) \, dt$
$x=\frac{t}{2... | 4 | [
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0.052490234375,
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0.042724609375,
0.0033416748046875,
0.0498046875,
0.07861328125,
... | 7,454 | 7454 | |
gauss jordan help
March 30th 2009, 11:22 AM
wonderstrike
gauss jordan help
Ok here I am working on this problem for like 3 hours to no avail.
x1 + x2 = 1
-x1 + x2 + x3 = -1
-1x2 + x3 = 3
I am trying to solve this in matrix form and get the point of multiplaying a cooefficiant but applying it t... | 5 | [
-0.0400390625,
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0.013671875,
-0.0849609375,
0.0366... | 7,455 | 7455 | |
Inverted Cone
August 13th 2010, 08:48 PM #1
Newbie
Joined
Aug 2010
Posts
2
Inverted Cone
We want to use an inverted cone with a radius of 9cm to dispense 100mL of a chemical. To be certain that we dispense the correct quantity we want markings in 100mL increments on the outside of
the cone. Where sho... | 5 | [
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0.05078125,... | 7,456 | 7456 | |
Area bounded by parametric equations
August 22nd 2011, 06:03 AM
Punch
Area bounded by parametric equations
The curve $L$ is defined by the parametric equations
$x=e^t$ , $y=t-2$
Find the area of the region enclosed by the curve $L$, the x-axis and the lines $x=e$ and $x=e^3$
$Area=\int^{e^3}_et-2d... | 5 | [
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0.0390625,
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Three Dimensional Pythagorean Tree
From Math Images
3-D Pythagorean Tree
Fields: Geometry and Algebra
... | 5 | [
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Probability-coin tossing
April 28th 2010, 02:33 AM #1
Newbie
Joined
Apr 2010
Posts
2
Probability-coin tossing
3 persons play a game by tossing a fair coin each independently. The game ends in a trial if all of them get the same outcome in that trial,otherwise they continue to the next trial. what is the
... | 4 | [
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Finding for interval of m in quadratic equation.
August 23rd 2011, 10:44 PM
sumedh
Finding for interval of m in quadratic equation.
Find the interval in which 'm' lies so that the expression
$\frac{mx^2+3x-4}{-4x^2+3x+m}$
can take all real values ,where x is real.
i have equated this equation to y
... | 4 | [
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0.08447265625,
-0.05078125... | 7,460 | 7460 | |
find t when vectors are parallel
January 10th 2011, 02:37 PM #1
Member
Joined
Jan 2011
Posts
75
find t when vectors are parallel
I have this question vector a = (2,5) vector b = (-1,t)
find t when a and b are parallel.
I can't seem to figure this one out. Theres nothing in my text about how to s... | 4 | [
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... | 7,461 | 7461 | |
Find value of n
Divide both sides by 3 to obtain: $\sqrt{27} = 3^{n-1}$ Now take the square of both sides to get: $27 = 3^{2(n-1)}$ We know that $27 = 3^3 = 3^{2(n-1)}$ so $3 = 2(n-1)$. This gives: $5 = 2n$ so $\
frac{5}{2} = n$ (you can ofcourse save some steps: $3\cdot \sqrt{27} = 3\cdot \sqrt{3^3} = 3^{\frac{3}{2}+1... | 4 | [
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0... | 7,462 | 7462 | |
A 'trivial' question...
August 21st 2009, 11:41 AM #1
A 'trivial' question...
It is well known that the derivative of a 'function of function' $y\{u(x)\}$ is...
$\frac {dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$
A question for you: does it exist a similar expression for the second derivative $\frac {d... | 5 | [
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Complex Fraction Help
Can someone help me in detail showing their steps to get the answer to this problem:
Here's a Hint: $\frac{{y - \dfrac{{5y - 7}}<br /> {7}}}<br /> {{\dfrac{6}<br /> {{14}} + \dfrac{3}<br /> {{2y}}}} = \frac{{14\left( {y - \dfrac{{5y - 7}}<br /> {7}} \right)}}<br /> {{14\left( {\dfrac
{6}<br /> {{... | 4 | [
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Napoleon's Theorem & Vectors
February 19th 2008, 05:48 PM #1
Newbie
Joined
Jan 2008
From
Boise
Posts
16
Napoleon's Theorem & Vectors
Napoleon's theorem is easy enough to prove using a geometric approach. What I am unable to do is complete a proof using vector methods. For the purposes of discussion, ... | 4 | [
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... | 7,465 | 7465 | |
Epsilon-Delta Proof for Discontinuous Functions
November 14th 2013, 12:18 AM
twilightmage13
Epsilon-Delta Proof for Discontinuous Functions
THE QUESTION:
Suppose we have f:R --> R defined by the piecewise function:
f(x) = 1/(x^2), when x ≠ 0
f(x) = 7, when x = 0.
Prove that f is not continuous at... | 4 | [
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Distance Calculations
Star Cluster Distances
Hyades
The Hyades cluster is also an open star cluster of around 200 stars in the constellation Taurus (White, J., p. 7). Located in the "nose" of the bull by the bright star Al... | 4 | [
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-0.09... | 7,467 | 7467 | |
Exponential equations
October 27th 2007, 04:56 PM #1
Junior Member
Joined
Oct 2007
Posts
44
Exponential equations
Sorry for the repost, but I missed up when I typed the problem in.
Solve the exponential equation. Express the solution set in terms of natural logarithms.
4^(x + 4) = 52^(x + 5 )
... | 5 | [
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fourier series representation
May 11th 2010, 05:18 PM #1
Newbie
Joined
Apr 2010
Posts
4
fourier series representation
f(x) = cosax between pi and -pi and a is a constant
can find the an coefficent to be (sin(n+a)x)/(n+a) + (sin(n-a)x)/(n-a) but cant get any further.
This makes no sense. The co... | 5 | [
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Constructing a Conditional Table
Date: 04/14/98 at 12:15:00
From: Dave Brown
Subject: Magic Squares (sort of)
Are you aware of any method to solve the following problem?
I have a table that is, for example, 5 columns wide and 7 rows high
and contains either a 0 or a 1 in each cell. If I told you that the
total numb... | 4 | [
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Finding the Domain Problems:
January 9th 2007, 12:57 PM
qbkr21
Finding the Domain Problems:
Please help me find the domain of the following problems:
1. 5throot(-4+3x)
The function is defined on the interval from _________ to __________
2. 6throot(-4+3x)
The function is defined on the interva... | 4 | [
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-0.07714... | 7,471 | 7471 | |
Trouble finding limits
April 6th 2008, 01:26 PM #1
Junior Member
Joined
Nov 2007
From
california
Posts
74
Trouble finding limits
Hi, Im having trouble finding the limit as n goes to infiniti of ((n+1)(n+2))/(2n^2). Can someone please help me start this problem?
Thank you
Sure
$\lim_{n \to {... | 5 | [
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0.0186767578125,
-0.008483... | 7,472 | 7472 | |
Dividing a plane
Let's say we have a plane. Draw N straight lines on the plane, any way you wish. Try to divide the plane into as many different regions as possible. How many regions is that? For example, if we draw
1 line on the plane, we can divide it into two regions. If we draw 2 lines, we can divide it into four r... | 5 | [
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-0.... | 7,473 | 7473 | |
Center of mass
Let us now look at a baseball bat closely. It has a peculiar shape. Where should the COM lie? By experience, we can say that it should lie on the heavier side. This perception comes from the
realization that heavier part has most of the mass. It gives us the clue about COM that it lies on the heavier sid... | 4 | [
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-0.03... | 7,474 | 7474 | |
Regression Avoids Depression: Part Four
Reconciling Win-Rate With Roll-Survival Rate
If we look at strictly flat-betting a wager like $22-Inside, we know that it takes several hits to pay for itself before finally emerging with a profit:
$22-Inside Payout Rate
┌──────────────────┬────────────... | 4 | [
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Scientific Papers - Vi
1913] - FINE SLITS IN THIN OPAQUE SCREENS 163
This %-solution makes d%m/dn — 0, d^p/dn — 0 over the whole plane x — 0, and over the same plane %m = 2, %p = 0.
For the supplementary solution, distinguished in like manner upon the two sides, we have
... | 4 | [
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Differentiation question
October 15th 2008, 07:25 PM
alberty02
Differentiation question
The equation of a curve is xy(x+y)=2(a)^3 where a is a non-zero constant. show that there is only one point on the curve at which the tangent is parallel to the x-axis, and find the coordinates
of this point.
can so... | 4 | [
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-0... | 7,477 | 7477 | |
Super Simple Algebra...
March 5th 2009, 12:57 PM #1
Newbie
Joined
Mar 2009
Posts
1
Super Simple Algebra...
...yet I'm unable to figure it out.
Simplify:
(15x^2-8x-8)/(3x+2)
(Edit)
Seem to have broken forum rules! I've tried to divide it out as so:
15x^2/3-8x/x-8/2
which gets me
... | 4 | [
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0.02099609375,
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Statistics proof
September 29th 2009, 06:07 PM #1
Senior Member
Joined
Jan 2009
Posts
290
Statistics proof
Given that random variable $X$, its mean value $\mu$, its variance $\sigma ^2$, and the mean value $X^2$, which is $\mu _{X^2}$, prove that $\sigma ^2=\mu _{X^2} - \mu _X^2$.
Letting X be the v... | 4 | [
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More Triangles
April 30th 2007, 05:58 PM
whytechocolate01
More Triangles
Please help me solve this!
Prove: If an isoceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
Given: Triangle ABC is isosceles; Line CD is the altitude to base Line AB
To P... | 4 | [
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0.0093... | 7,480 | 7480 | |
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Topic: 6 QUANTIFIER ELIMINATION METHODS!
Replies: 1 Last ... | 4 | [
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Archimedes Principle
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Archimedes Principle 11,640 views
Archimedes' principle states that the buoyant force on a fluid is equal to the weight of the displaced fluid. To calculate the buoyant force, we use the eq... | 4 | [
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... | 7,482 | 7482 | |
The number of homomorphisms
August 16th 2008, 05:11 AM
Aedolon
The number of homomorphisms
Find the number of homomorphisms between:
#Hom(S_4, C_4) (intuitively something tells me this is two)
#Hom(C_4, S_4)
#Hom(C_6, S_3)
#Hom(D_3, A_4) (D_3 has order 6)
Any help would be appreciated!
Augu... | 5 | [
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2011 MIT Integration Bee Qualifying Test
January 27th 2011, 12:31 AM
Prove It
7. $\displaystyle \int{\sec^4{x}\tan^2{x}\,dx} = \int{\sec^2{x}\sec^2{x}\tan^2{x}\,dx}$.
Now using Integration by Parts with $\displaystyle u = \sec^2{x} \implies du = 2\tan{x}\sec^2{x}\,dx$ and $\displaystyle dv = \sec^2{x}\tan^2... | 5 | [
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0.0571289... | 7,484 | 7484 | |
Finite sums to approximate integrals
October 11th 2011, 02:52 PM
insanic1
Finite sums to approximate integrals
Attachment 22546
Hmm not sure if I copied that image properly. Anyways I'm really confused on what exactly I need to do. The question is related to an introduction to calculus course. Where you take... | 5 | [
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-0.015747070... | 7,485 | 7485 | |
In how many ways can an iterated tangent bundle (T^k)M be viewed as a fibre bundle over (T^(k-1))M?
up vote 11 down vote favorite
5
Let M be a smooth manifold. The double tangent bundle, TTM,can be viewed as a fibre bundle over TM in two ways, with the projection maps given by T_πM (i.e. the derivative of the projecti... | 4 | [
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0.049... | 7,486 | 7486 | |
Solve e^z - 2 = 2i.
Hi, could someone help me with this one? Find all solutions of $e^{z}-2 = 2i$ Thanks.
Last edited by mr fantastic; March 23rd 2011 at 03:40 AM. Reason: Re-titled.
Define $\displaystyle z = x + iy$. $\displaystyle e^z - 2 = 2i$ $\displaystyle e^z = 2 + 2i$. Working on the RHS: $\displaystyle 2 + 2i... | 5 | [
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-0.015869140625... | 7,487 | 7487 | |
picard's method of iteration
February 14th 2010, 07:07 AM
collegestudent321
picard's method of iteration
Hey guys, I'm having some trouble with this problem using picard's successive approximations:
y' = 2e^x - y, y(0) = 1
I thought the equation to begin the approximations would be:
y = 1 + integr... | 5 | [
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... | 7,488 | 7488 | |
Basic domain.
October 21st 2011, 12:33 PM #1
Junior Member
Joined
Oct 2011
Posts
58
[SOLVED]Basic domain.
$y=$$\sqrt{-x^3+x}$
$(-x^3+x)\geq0$
$\equiv$$x(-x^2+1)\geq0$
$\equiv$$x\geq0\cap(x\geq-1\cap~x\leq1)$
Domain = $0\leq~x\leq1$
Is that correct??
because in my calculator i... | 4 | [
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Tension in Spider-Man's Webs
The Physics Factbook
Edited by Glenn Elert -- Written by his students
An educational, Fair Use website
topic index | author index | special index
Spider-Man (2002)
The feature film Spider-Man is about a young man who obtains extraordinary powers by being bitten by a genetically altered ... | 4 | [
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0.052001... | 7,490 | 7490 | |
Linear Inequalities in Two Variables
Graphing Linear Inequalities in Two Variables
A linear inequality in the two variables x and y looks like
ax + by < c ax + by < c ax + by > c ax + by > c
where a, b, and c are constants.
A solution to an inequality is any pair of numbers x and y that satisfy the inequality.
... | 4 | [
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-0.0284423828... | 7,491 | 7491 | |
solving equations
April 18th 2013, 06:38 AM #1
Junior Member
Joined
Jul 2012
From
Bangladesh
Posts
55
solving equations
I was looking for critical points and found my f'(x)=-12/(4x^2+1)(\sqrt{4x^2+1})
Now I want to solve that equation , by setting
-12/(4x^2+1)(\sqrt{4x^2+1}=0
will there... | 4 | [
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0.039794921875,
0.0008239746093... | 7,492 | 7492 | |
Triple integral
August 8th 2011, 01:19 PM #1
Member
Joined
May 2010
Posts
241
Triple integral
Hi, I have to compute de volume for the region:
$\{(x,y,z):x^2+y^2+z^2\leq{16};z\geq{1} \}$
I've tried to do by two different parametrizations, in spherics and cylindrical coordinates
For cylindri... | 5 | [
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... | 7,493 | 7493 | |
Math Images
Matrix
From Math Images
(Difference between revisions)
Lpeng1
(
... | 4 | [
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... | 7,494 | 7494 | |
Axiom of Replacement in Category Theory
up vote 9 down vote favorite
1
Does the usual development of category theory (within Goedel-Bernays set theory, for example) require the axiom of replacement? I would have asserted that this was obviously true, but it seems to be
common wisdom that the axiom of replacement is an... | 4 | [
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0.005004882812... | 7,495 | 7495 | |
ic
Comparing a within subjects group difference to that of a single case
Pairwise case
Suppose a group of controls and a single case do a pair of conditions (c1, c2, say) and we are interested in seeing if the relationship between the conditions in the controls is the same as that in
the single case.
Since we have a... | 5 | [
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0.06640625,
... | 7,496 | 7496 | |
Is an algebraic space group always a scheme?
up vote 25 down vote favorite
8
Suppose G is a group object in the category of algebraic spaces (over a field, if you like, or even over ℂ if you really want). Is G necessarily a scheme?
My feeling is that the answer is "yes" because an algebraic space group which is not a... | 4 | [
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-0.0053710937... | 7,497 | 7497 | |
Power Series Solution
November 30th 2010, 06:47 PM #1
Member
Joined
Nov 2009
Posts
92
Power Series Solution
Question: The differential equation $y'' + ty' + (t^2-2)y = 0, y(0) = -2, y'(0) = -2$ has a power series solution about t = 0 of the form $\displaystyle\sum\limits_{n=0}^\infty c_{n}t^{n}$. The
... | 5 | [
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0... | 7,498 | 7498 | |
Isomorphic
October 23rd 2009, 11:24 AM
ux0
Isomorphic
Let G be the additive group if all polynomials in x with coefficients in $\mathbb{Z}$, and let H be the multiplicative group of all positive rationals. Prove that G $\cong$ H
I'm think if I list the prime numbers $p_0=2$, $p_1=3$, $p_2=5$,..., and defin... | 4 | [
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0.... | 7,499 | 7499 |