content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
transformation function of random variables
September 29th 2009, 06:14 AM #1
Newbie
Joined
Sep 2009
Posts
12
transformation function of random variables
If X and Y are exponentially distributed with the same parameter and they are also independent:
To compute the density function of :
Case 1) Z... | 4 | [
-0.06787109375,
0.00738525390625,
-0.03564453125,
-0.055419921875,
0.0439453125,
-0.06298828125,
0.054931640625,
-0.01953125,
-0.0751953125,
-0.00341796875,
0.010009765625,
0.020751953125,
0.11279296875,
0.03662109375,
0.040283203125,
-0.042724609375,
-0.00799560546875,
-0.08789062... | 16,100 | 16100 | |
EM field integral
September 30th 2013, 10:46 PM #1
Junior Member
Joined
Dec 2012
From
ny
Posts
63
Thanks
6
EM field integral
this is the E field above a square loop with side=a at distance z on the z axis. by symmetry the Ex, Ey field cancel out. it really kind of bothers me that I can't see this... | 5 | [
0.008056640625,
0.11572265625,
0.01458740234375,
-0.039306640625,
0.0458984375,
-0.052734375,
-0.006591796875,
-0.0146484375,
0.031494140625,
0.02197265625,
0.09423828125,
0.024169921875,
-0.035888671875,
0.031494140625,
-0.03125,
0.01275634765625,
-0.0174560546875,
-0.052001953125... | 16,101 | 16101 | |
square circle
October 25th 2007, 09:11 AM #1
Newbie
Joined
Oct 2007
Posts
9
square circle
The perimeter of a semi-circle is same as the perimeter of a square . Than whether the area of the semi-circle is greater than area of square or vice versa????
Hello, saroja!
The perimeter of a semicircle ... | 4 | [
0.047607421875,
0.08056640625,
-0.0034332275390625,
0.04638671875,
0.0179443359375,
0.034423828125,
-0.0166015625,
0.08642578125,
0.022216796875,
-0.042724609375,
-0.06396484375,
0.005889892578125,
0.0634765625,
0.07177734375,
0.050048828125,
-0.05810546875,
0.057373046875,
0.01599... | 16,102 | 16102 | |
equations system
February 29th 2008, 12:55 AM #1
Newbie
Joined
Feb 2008
Posts
3
ive been trying to answer these questions all night, 19 of them for homework and ive got 8 done. only 8 to go...
10. Solve the following systems of equations by substitution. Show your work.
a) y= 2x+10
y = 130
... | 4 | [
-0.10498046875,
0.03173828125,
-0.05224609375,
-0.0625,
0.0162353515625,
0.09375,
0.04736328125,
-0.005523681640625,
-0.11865234375,
0.032470703125,
0.08349609375,
-0.033203125,
0.060791015625,
0.017822265625,
0.0224609375,
0.0673828125,
-0.10986328125,
0.0225830078125,
-0.069335... | 16,103 | 16103 | |
Derivatives of Inverse Functions
November 12th 2009, 01:37 AM #1
Newbie
Joined
Nov 2009
Posts
5
Derivatives of Inverse Functions
Let f(v) be the gas consumption (L/km) of a car going at velocity v (km/h). In other words, f(v) tells you how many liters of gas the car uses to go one kilometer, if it is goi... | 5 | [
-0.00025177001953125,
0.06396484375,
0.06689453125,
0.03173828125,
0.001617431640625,
-0.0498046875,
0.01239013671875,
0.045166015625,
-0.003692626953125,
0.04248046875,
0.041259765625,
0.0252685546875,
0.0029296875,
0.035400390625,
-0.033203125,
0.01171875,
0.0024261474609375,
0.0... | 16,104 | 16104 | |
Surface Area (Calculus)
May 28th 2007, 09:27 PM
turtle
Surface Area (Calculus)
I'm getting confused on this problem, such as when to use dy and dx. If someone can please help me solve these problems and explain them, I would greatly appreciate it. Thank you.
Find the surface area generated by revolving the ... | 5 | [
-0.049072265625,
-0.0137939453125,
0.0791015625,
-0.12890625,
-0.002899169921875,
-0.05859375,
-0.0478515625,
0.10986328125,
-0.0228271484375,
0.0279541015625,
0.04541015625,
0.039306640625,
0.029296875,
0.027099609375,
-0.002105712890625,
0.08544921875,
-0.041259765625,
-0.0654296... | 16,105 | 16105 | |
Integral Question using Fundamental Theorem of Calculus
November 29th 2010, 11:45 AM #1
Newbie
Joined
Nov 2010
Posts
11
Integral Question using Fundamental Theorem of Calculus
Hi everyone,
I am working on this question for calculus, but I am a bit confused by the y's in the range of the integral.
... | 5 | [
0.00555419921875,
-0.059326171875,
-0.0029754638671875,
-0.07958984375,
0.0458984375,
0.006683349609375,
-0.01373291015625,
0.0849609375,
-0.057861328125,
-0.0185546875,
0.026611328125,
0.08984375,
0.0185546875,
0.0289306640625,
0.078125,
0.048095703125,
-0.036376953125,
-0.0149536... | 16,106 | 16106 | |
Infinite-D problem
January 26th 2008, 02:34 PM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Infinite-D problem
Let V be the set of real numbers regarded as a vector space over the field of rational numbers. Prove that V is infinite-dimensional.
I'm trying to prove by contradiction. I selec... | 5 | [
0.005645751953125,
0.021484375,
0.005218505859375,
0.037353515625,
0.02099609375,
0.0849609375,
-0.00250244140625,
-0.006103515625,
0.0098876953125,
-0.1279296875,
-0.06298828125,
-0.009033203125,
-0.03955078125,
0.00799560546875,
-0.1103515625,
0.00897216796875,
0.005035400390625,
... | 16,107 | 16107 | |
Intermediate/Advanced Factoring
I know I've done things like this before, but I don't have my book on hand and I've forgotten quite a bit over summer. I've been looking online and can't find any problems similar to this. :/ Help
please?
1. Factor
2. Factor
For number two I got an answer of (x+7)^1/4[1+(x+7)^1/2]... ... | 4 | [
0.07373046875,
-0.045654296875,
0.043701171875,
0.11181640625,
0.0279541015625,
-0.01092529296875,
-0.03466796875,
-0.01226806640625,
-0.052734375,
0.01092529296875,
0.002532958984375,
-0.055908203125,
0.030029296875,
0.10400390625,
-0.062255859375,
0.0277099609375,
-0.006591796875,
... | 16,108 | 16108 | |
Finding an expression for charge (Q) given an I-V equation
P: 492
An ideal semiconductor diode is a nonlinear element that obeys the following I-V equation:
[tex]I\,=\,I_s\,\left(\,e^{\frac{V}{V_{th}}}\,-\,1\right)[/tex]
where [itex]I_s[/itex] is a constant (saturation current) and [itex]V_{th}[/itex] is a constant ... | 5 | [
-0.07861328125,
0.16796875,
0.04248046875,
0.048583984375,
0.0191650390625,
0.046875,
0.10595703125,
-0.03125,
-0.0118408203125,
0.06982421875,
-0.020751953125,
-0.11767578125,
0.08154296875,
0.0966796875,
0.01177978515625,
0.03564453125,
-0.022216796875,
0.00811767578125,
0.0344... | 16,109 | 16109 | |
Trying to determine the height of a weather balloon. I think i have it right
December 10th 2011, 10:11 AM #1
Newbie
Joined
Nov 2011
Posts
22
Trying to determine the height of a weather balloon. I think i have it right
Two observers 5000m apart, standing at A and B measure the angle of elevation to a weat... | 4 | [
0.00958251953125,
0.109375,
-0.005218505859375,
0.02978515625,
-0.033203125,
0.0264892578125,
-0.0252685546875,
0.0751953125,
-0.0625,
-0.0081787109375,
-0.00823974609375,
-0.053466796875,
0.0003681182861328125,
0.042724609375,
0.0030517578125,
0.025390625,
-0.06982421875,
-0.00427... | 16,110 | 16110 | |
logarithmic word problem
April 30th 2012, 09:26 PM #1
Newbie
Joined
Apr 2012
From
Canada
Posts
5
logarithmic word problem
Hello, here is my problem:
Alex invests $50,000 at an interest rate of 0.7% compounded monthly. Laura invests $40,000 at 9.5% compounded annually. After how many years will t... | 4 | [
0.0888671875,
0.033203125,
-0.00604248046875,
-0.004119873046875,
-0.09423828125,
-0.08544921875,
0.048095703125,
0.0380859375,
-0.020263671875,
0.09814453125,
0.02783203125,
-0.0205078125,
0.041748046875,
0.08203125,
0.024169921875,
0.09423828125,
-0.11865234375,
-0.00650024414062... | 16,111 | 16111 | |
Momentum/impulse check & help needed
Register to reply
by JWDavid
Tags: check, momentum or impulse
P: 23 1. The problem statement, all variables and given/known data
A 52.4 g ball is thrown from the g... | 5 | [
0.037353515625,
0.10546875,
0.0286865234375,
-0.05078125,
0.007415771484375,
-0.02734375,
0.0279541015625,
0.076171875,
-0.034423828125,
0.0634765625,
0.09130859375,
-0.037353515625,
-0.0673828125,
0.00286865234375,
0.005157470703125,
0.031494140625,
-0.00823974609375,
0.0072326660... | 16,112 | 16112 | |
Writing an algebraic equation
February 28th 2007, 09:36 PM #1
Writing an algebraic equation
Subtract 5 from the sum of
x and 7 times 3 and the result is 20.
My answer is
x-5 + 7 x 3 = 20
x = 4 is that right?
Is that exactly how the question was phrased? if so, i'd interpret it like this:
... | 4 | [
-0.1083984375,
0.04345703125,
0.0311279296875,
0.033447265625,
-0.058349609375,
0.0311279296875,
0.07177734375,
-0.0306396484375,
-0.0260009765625,
0.0223388671875,
0.04150390625,
-0.07763671875,
0.076171875,
0.03662109375,
-0.006378173828125,
0.0439453125,
-0.08056640625,
0.102539... | 16,113 | 16113 | |
Power series - Differential equation
March 26th 2011, 01:08 AM #1
Member
Joined
Nov 2009
Posts
177
Power series - Differential equation
Seek the solutions that are power series to the differential equation:
$(1-z)f'(z)=2f(z),\ f(0)=1$
I assume we first need to assume that $|z|<R$ so that $f(z)=\... | 5 | [
-0.06787109375,
0.0186767578125,
-0.0098876953125,
0.10205078125,
0.004241943359375,
0.0084228515625,
-0.08251953125,
0.041259765625,
-0.0272216796875,
0.0634765625,
-0.060791015625,
-0.06787109375,
-0.002410888671875,
0.016845703125,
-0.01458740234375,
-0.0439453125,
-0.040771484375... | 16,114 | 16114 | |
Evaluate this integral
February 22nd 2013, 12:34 PM #1
Member
Joined
Dec 2012
From
NY
Posts
105
Thanks
1
Evaluate this integral
Evaluate the integral. (Give your answer as an improper fraction.)
Ok my work:
b/c of abs value law x { x when x>/= to 0
{ -x when x<0
Intergral from... | 4 | [
-0.031005859375,
-0.00823974609375,
0.0272216796875,
-0.058837890625,
0.028564453125,
-0.044189453125,
-0.031982421875,
0.050537109375,
-0.0238037109375,
0.00982666015625,
0.05029296875,
-0.11279296875,
0.01531982421875,
-0.002349853515625,
0.00445556640625,
0.0213623046875,
0.048828... | 16,115 | 16115 | |
finding x when it appears in the equation more than once
August 22nd 2011, 11:15 PM #1
Junior Member
Joined
Aug 2008
Posts
26
finding x when it appears in the equation more than once
Hi, this is the first time I have come across a question where x has appeared in an equation more than once so I am a bit ... | 4 | [
0.036376953125,
0.0157470703125,
0.06640625,
0.053955078125,
0.046142578125,
-0.09912109375,
-0.0194091796875,
-0.07080078125,
0.05078125,
0.02734375,
-0.01055908203125,
-0.043701171875,
0.0299072265625,
0.03125,
0.07373046875,
0.06982421875,
-0.02294921875,
-0.0037078857421875,
... | 16,116 | 16116 | |
Semientwining Structures and Their Applications
ISRN Algebra
Volume 2013 (2013), Article ID 817919, 9 pages
http://dx.doi.org/10.1155/2013/817919
Research Article
Semientwining Structures and Their Applications
^1Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Rom... | 4 | [
-0.0380859375,
0.0218505859375,
0.0072021484375,
-0.03759765625,
-0.041748046875,
-0.01806640625,
-0.080078125,
0.08203125,
0.031494140625,
0.019775390625,
-0.03466796875,
-0.0166015625,
0.0167236328125,
0.05859375,
-0.024169921875,
0.037109375,
-0.07568359375,
0.037109375,
-0.08... | 16,117 | 16117 | |
integration of an absolute value function??
November 27th 2008, 05:06 PM #1
Newbie
Joined
Nov 2008
Posts
21
integration of an absolute value function??
I'm very stuck on this problem because when I did it the way I thought it was supposed to be done I ended up with an answer of zero which definitely isn'... | 5 | [
0.003631591796875,
0.0054931640625,
-0.005462646484375,
-0.07568359375,
0.0177001953125,
-0.050048828125,
-0.021728515625,
0.048095703125,
-0.05859375,
-0.041259765625,
0.0272216796875,
-0.06494140625,
0.07568359375,
0.028076171875,
-0.056640625,
0.00384521484375,
0.07373046875,
-0... | 16,118 | 16118 | |
Physics problem on mechanics
November 4th 2007, 09:21 AM #1
Member
Joined
Jul 2007
Posts
147
Physics problem on mechanics
I have a following problem
A rock is dropped from a sea cliff. After 3.4 s a splash of the rock hitting the ocean is heard. The speed of sound is 340 m/s. How tall is the cliff?
... | 4 | [
0.051025390625,
0.0174560546875,
0.03466796875,
-0.0634765625,
-0.05126953125,
0.07666015625,
-0.045654296875,
0.06689453125,
0.02783203125,
-0.00830078125,
0.033935546875,
-0.05322265625,
0.0234375,
0.0269775390625,
0.0157470703125,
0.06201171875,
0.050048828125,
0.046875,
-0.02... | 16,119 | 16119 | |
Examples of Rewrite Rules - GNU Emacs Calc Manual
11.11.13 Examples of Rewrite Rules
Returning to the example of substituting the pattern ‘sin(x)^2 + cos(x)^2’ with 1, we saw that the rule ‘opt(a) sin(x)^2 + opt(a) cos(x)^2 := a’ does a good job of finding suitable cases. Another
solution would be to use the rule ‘cos... | 4 | [
-0.05029296875,
0.06201171875,
-0.0036468505859375,
0.06640625,
-0.056396484375,
-0.01287841796875,
-0.015869140625,
-0.03369140625,
0.0196533203125,
0.053466796875,
0.08837890625,
-0.0018463134765625,
-0.022216796875,
0.09130859375,
0.1357421875,
-0.01190185546875,
-0.04345703125,
... | 16,120 | 16120 | |
Summation formula
February 25th 2011, 02:23 PM #1
Member
Joined
Nov 2010
Posts
86
Summation formula
Some help with the following would be appreciated!
Find (and prove) a formula for Σ from j=1 to k of j^3
Known propositions:
Σ from j=1 to k of j = k(k+1) / 2
Σ from j=1 to k of j^2 = k... | 5 | [
-0.01373291015625,
0.017333984375,
0.052490234375,
0.015869140625,
-0.0654296875,
0.043701171875,
-0.0028228759765625,
0.018310546875,
0.03759765625,
-0.0186767578125,
-0.0693359375,
-0.039306640625,
-0.009521484375,
0.00433349609375,
-0.08642578125,
0.0177001953125,
-0.0013351440429... | 16,121 | 16121 | |
What am I doing wrong?
December 6th 2012, 03:09 PM
Nervous
What am I doing wrong?
Integrate f(x)=2x. Lower limit is 1 and upper limit is 2.
Using the shortcuts, it's easy for me to find F(2) - F(1) = 3.
However, I was asked to use the limit of Reinmann sums in order to solve the problem...
$\int f... | 4 | [
-0.004974365234375,
-0.032470703125,
0.06640625,
-0.0284423828125,
-0.0115966796875,
-0.034912109375,
0.0211181640625,
-0.00860595703125,
-0.0306396484375,
0.06787109375,
-0.0172119140625,
-0.07861328125,
-0.057373046875,
-0.042236328125,
-0.0179443359375,
-0.038330078125,
0.01953125... | 16,122 | 16122 | |
The potential ability of TC
back
see;
A*(2)=A x A
examples; 2*(2)=4, 4*(1/2)=2, (4/9)*(1/2)=2/3, 3(4/9)*(1/2)=2, k4*(1/2)=2k
//About the correlativity of energy multiplying phenominon of Tesla Coil and Hutchison effect
//Generally, we make the tank circuit to oscillate cosine-curved electric vibration. In use of Tes... | 4 | [
-0.11328125,
0.07958984375,
-0.039794921875,
0.01953125,
-0.03076171875,
0.01031494140625,
-0.0162353515625,
0.08154296875,
-0.00113677978515625,
-0.05126953125,
-0.0267333984375,
-0.0546875,
0.154296875,
0.044921875,
-0.0021514892578125,
-0.07666015625,
0.007720947265625,
0.026367... | 16,123 | 16123 | |
Method of Undetermined Coefficients
May 4th 2010, 06:30 PM
ur5pointos2slo
Method of Undetermined Coefficients
Find yc(complimentary solution) and set up yp(particular solution) by the method of undetermined coefficients.
y''+y'+(1/2)y = x*e^(-x/2)+x*cos(x/2)
ok so
yc = c1 e^(-x/2) cos(x/2) + c2 e^(... | 5 | [
-0.1611328125,
0.0091552734375,
0.06396484375,
0.05859375,
0.08154296875,
0.06298828125,
-0.061767578125,
0.0201416015625,
-0.022705078125,
0.04931640625,
0.12060546875,
-0.08349609375,
-0.03369140625,
-0.038818359375,
0.005279541015625,
0.015869140625,
-0.01544189453125,
-0.051513... | 16,124 | 16124 | |
system of linear equations
May 19th 2008, 06:16 PM #1
Newbie
Joined
May 2008
Posts
4
Solve the following systems of equations
4x + y -2z = 0
2x - 3y + 3z = 9
-6x - 2y + z = 0
Simplify the following expressions
(6x^2 - 3x + 2) - (4x^2 + 2x - 5)
Simplify the following to th... | 5 | [
-0.0361328125,
-0.00836181640625,
-0.01116943359375,
-0.022216796875,
0.033447265625,
0.01312255859375,
-0.04931640625,
0.028076171875,
-0.0458984375,
-0.004608154296875,
-0.0400390625,
0.01287841796875,
0.08349609375,
-0.0174560546875,
-0.0849609375,
0.0301513671875,
-0.01611328125,... | 16,125 | 16125 | |
Energy in elliptic orbits
Päällikkö
How does one derive the total energy in an elliptic orbit:
[tex]E= - \frac{GMm}{2a}[/tex]
where a is the semi-major axis?
I did manage to get the result for the special case of circular orbit, as
[tex]v = \sqrt{\frac{GM}{R}}[/tex]
But the problem is that I can't figure out a way to... | 4 | [
0.06396484375,
0.068359375,
-0.0262451171875,
0.01025390625,
0.00830078125,
-0.023193359375,
-0.012451171875,
0.06103515625,
0.025146484375,
0.008544921875,
0.00640869140625,
-0.02392578125,
-0.1005859375,
-0.039306640625,
0.044921875,
-0.007049560546875,
0.0267333984375,
0.1040039... | 16,126 | 16126 | |
Simple eqN of a line question
July 30th 2006, 03:35 PM #1
Junior Member
Joined
Jul 2006
From
New York, NY
Posts
33
Simple eqN of a line question
Hey,
I have this question thats been bugging me for a few days now.
$3y-15=2x-8$
Whats the answer if we put it in the eqN of a line?
$2x... | 4 | [
-0.1357421875,
0.0308837890625,
0.006256103515625,
0.059814453125,
0.04443359375,
0.03662109375,
0.0216064453125,
0.0014495849609375,
-0.046875,
0.08203125,
0.06689453125,
-0.0830078125,
0.048828125,
0.06884765625,
0.0186767578125,
0.06689453125,
-0.1357421875,
-0.1005859375,
-0.... | 16,127 | 16127 | |
Need a function
Hi, I need a function f(x) such that: f(1)=10 f(2)=8 f(3)=6 f(4)=4 f(5)=2
I think what you want is a continuous function: But the function $f(x) = 12-2x$ works
If we assume that f is of the form $f(x)=ax+b$ then $a=\frac{f(x_1)-f(x_2)}{x_1-x_2} \equiv -2 ~ \forall x_1,x_2 \in \{1,2,3,4,5\} \implies a ... | 4 | [
-0.042236328125,
0.002227783203125,
-0.042724609375,
-0.0810546875,
-0.052978515625,
0.0791015625,
0.046630859375,
0.038330078125,
-0.0179443359375,
0.00701904296875,
0.0712890625,
-0.056640625,
-0.000024318695068359375,
-0.0001926422119140625,
0.033447265625,
0.07470703125,
-0.07910... | 16,128 | 16128 | |
continuety of a complex function question..
What do you mean by complex function? I assme you mean that a difficult function...I assume this because the sign function is only defined on the reals. 1. $f(g(x))=1+\text{sign}(x)^2$ Note that $\
text{sign}(x)=\left\{\begin{array}{rcl} -1 & \mbox{if} & x<0 \\ 0 & \mbox{if} ... | 5 | [
0.020263671875,
0.0040283203125,
0.05810546875,
0.091796875,
-0.051025390625,
0.01129150390625,
0.01434326171875,
-0.02978515625,
0.024169921875,
-0.00445556640625,
0.09765625,
-0.01226806640625,
0.002716064453125,
0.08349609375,
-0.021240234375,
-0.03759765625,
0.00128936767578125,
... | 16,129 | 16129 | |
Symmetric convex curve
up vote 3 down vote favorite
a) Assume that $\gamma$ is a symmetric convex curve w.r.t. two orthogonal lines (such a curve is the ellipse). Is the following statement true. There exists a $(l,L)$-bi-Lipschitz mapping of the unit
circle onto $\gamma$ such that $L=\mathbf{diam}(\gamma)/2$ and $l=\... | 5 | [
0.0157470703125,
-0.060791015625,
-0.013916015625,
-0.080078125,
-0.0291748046875,
-0.0166015625,
0.0615234375,
0.083984375,
-0.00921630859375,
-0.04345703125,
0.0216064453125,
0.0537109375,
-0.044189453125,
-0.0291748046875,
0.0164794921875,
0.00189971923828125,
0.01312255859375,
... | 16,130 | 16130 | |
the encyclopedic entry of change magnitude
The centripetal force is the external force required to make a body follow a curved path. Hence centripetal force is a kinematic force requirement, not a particular kind of force, like gravity or
electromagnetic force. Isaac Newton's description is found in the Principia. Many... | 5 | [
-0.0208740234375,
-0.0252685546875,
-0.091796875,
-0.0458984375,
-0.01373291015625,
0.005523681640625,
-0.1142578125,
0.052490234375,
0.0498046875,
0.1142578125,
0.0255126953125,
-0.046875,
0.0201416015625,
0.00653076171875,
0.0311279296875,
-0.0272216796875,
0.02197265625,
0.01483... | 16,131 | 16131 | |
Pascal's Rule
July 6th 2010, 10:03 AM #1
Junior Member
Joined
Jun 2010
Posts
36
Pascal's Rule
Hi this question was in Advanced Higher Maths in the UK
Show that (n+1 , 3) - (n ,3 )=(n ,2)
They are written in column vector form ie n+1 at top and 3 at the bottom for example for the first. I think yo... | 4 | [
-0.031494140625,
0.00022983551025390625,
-0.10009765625,
-0.10107421875,
0.0245361328125,
0.007568359375,
-0.01251220703125,
-0.038818359375,
-0.0086669921875,
0.053466796875,
-0.1279296875,
0.0028228759765625,
0.00823974609375,
0.01300048828125,
0.039306640625,
-0.0267333984375,
-0.... | 16,132 | 16132 | |
derivative
So it is: $f(x)=\left( x^5 - \frac{4}{x} \right) ^{-4}$ It looks like your derivative of $x^5 - \frac{4}{x}$ was wrong. $\frac{d}{dx} \left( x^5 - \frac{4}{x}\right) = 5x^4 + \frac{4}{x^2}$
aww so i needed to use quotient rule on the 4/x
That does work, but you can also do it by rewriting it first as $4x^{... | 5 | [
0.045654296875,
0.020751953125,
0.087890625,
0.08984375,
-0.0196533203125,
-0.1064453125,
-0.040283203125,
0.000759124755859375,
0.0322265625,
0.043701171875,
0.0595703125,
-0.03662109375,
0.00101470947265625,
0.052490234375,
-0.052490234375,
0.080078125,
0.037109375,
0.00509643554... | 16,133 | 16133 | |
Pseudoprimes #2
Let p be prime, prove that if (2^p)-1 is a composite number, then m=(2^p)-1 is a pseudoprime.
n = 2^p -1 == (denotes congruent) 2^(p-1) == 1modp by fermats little theorem since p is an odd prime. p|(2^(p-1)-1) so p|n-1 n = 2^p -1|2^(n-1) -1 2^(n-1) == 1mod n and 2^n == 2 mod n, so n is a
pseudoprime
| 4 | [
0.0255126953125,
-0.002288818359375,
0.039306640625,
0.04833984375,
0.11474609375,
-0.045654296875,
0.02978515625,
0.11572265625,
-0.08447265625,
0.0005035400390625,
-0.0654296875,
-0.035888671875,
0.06005859375,
0.00909423828125,
-0.0556640625,
0.010009765625,
-0.02978515625,
-0.0... | 16,134 | 16134 | |
What's inside the event horizon
ClamShell
I guess then that root(x^2 + y^2 + z^2) might be a metric?
Almost. Metrics are differential, so that you can calculate distances over curves of any shape, not just straight lines. The metric for Euclidean space, then, is:
[tex]ds = \sqrt{dx^2 + dy^2 + dz^2}[/tex]
You calc... | 4 | [
0.02734375,
-0.003936767578125,
0.032958984375,
-0.00750732421875,
0.01348876953125,
-0.04443359375,
-0.07373046875,
0.1162109375,
0.05322265625,
-0.0654296875,
-0.0194091796875,
-0.00787353515625,
-0.058349609375,
-0.00836181640625,
-0.142578125,
0.0238037109375,
-0.037109375,
-0.... | 16,135 | 16135 | |
New Page 1
Chapter 27:
Wave Optics:
In this chapter wavelike behavior of light will be studied. There is a simple experiment that verifies light is a wave. The experiment is called the "Young's Double-slit experiment." Before this
experiment is explained, we need to understand what constructive and destructive interf... | 5 | [
-0.068359375,
-0.01708984375,
0.06689453125,
0.0269775390625,
-0.052490234375,
-0.0264892578125,
0.005279541015625,
-0.042724609375,
-0.0126953125,
0.0272216796875,
0.053955078125,
0.0260009765625,
-0.01513671875,
-0.048095703125,
0.01287841796875,
0.07763671875,
-0.032958984375,
-... | 16,136 | 16136 | |
Patente US5590044 - Method and apparatus for finding aircraft position by integrating accelerations less time averages
The invention relates to a method for determining the position of an aircraft from acceleration data of an inertial system as well as from the output data of a navigation system, and to a device for
ex... | 4 | [
-0.031494140625,
0.02001953125,
-0.058837890625,
-0.09765625,
0.018798828125,
-0.008544921875,
0.030517578125,
0.0634765625,
-0.0244140625,
0.062255859375,
0.0087890625,
0.048583984375,
0.05419921875,
-0.041259765625,
-0.09228515625,
-0.05224609375,
-0.07763671875,
0.00084686279296... | 16,137 | 16137 | |
Chemistry: Activation Energy (Arrhenius equation)
i just did this problem on my homework
we have ln( k2/k1 ) = (Ea/R) * (1/T1 - 1/T2)
where k is the reaction constant, Ea is activation energy, R is gas constant, T is temperature
what are we solving for? well we want to see how k changes. we rearrange the equation:
... | 4 | [
-0.0281982421875,
0.03271484375,
-0.0208740234375,
0.056396484375,
0.059326171875,
-0.08984375,
0.1240234375,
-0.033203125,
0.0732421875,
0.06787109375,
0.0537109375,
-0.0869140625,
0.01361083984375,
0.01214599609375,
0.01458740234375,
0.0206298828125,
-0.08154296875,
0.01684570312... | 16,138 | 16138 | |
Simplify: Write Answer Only Using Positive Exponents
(2x^-2 y^3/6xz^5)^-4 Answer is 81x^12 z^20/y^12 how is this so?
Hello SSKFirst, invert the fraction to get rid of the negative power outside the bracket: $\left(\frac{2x^{-2} y^3}{6xz^5}\right)^{-4}=\left(\frac{6xz^5}{2x^{-2} y^3}\right)^{4}$ Then move the $x^
{-2}$... | 4 | [
0.0322265625,
0.10400390625,
-0.0223388671875,
0.08251953125,
-0.00567626953125,
-0.0634765625,
-0.0150146484375,
-0.048095703125,
0.02783203125,
0.022705078125,
0.00836181640625,
0.08251953125,
0.0272216796875,
0.061767578125,
-0.00185394287109375,
0.1591796875,
-0.03564453125,
0.... | 16,139 | 16139 | |
Circumference of an ellipse
I have two integrals to give the circumference of an ellipse. I can't solve either.
First, using rectangular coordinates,
1/2s=S{[1+(f'(x))^2]^(1/2)}dx taken from x=-a to x=a
Since, y^2=b/a(a^2-x^2)
2y*y'=-2bx/a
y'=-bx/(ay)
[f'(x)]^2=(x^2)/(a^2-x^2)
At this point, I'm already uncomfortable b... | 4 | [
0.029296875,
-0.040771484375,
-0.0294189453125,
-0.01226806640625,
-0.024658203125,
0.01507568359375,
-0.0263671875,
0.08447265625,
0.05322265625,
-0.025146484375,
0.07958984375,
-0.01226806640625,
0.07421875,
0.0169677734375,
-0.01409912109375,
0.0693359375,
0.0272216796875,
-0.00... | 16,140 | 16140 | |
factorsing this expression
March 5th 2010, 06:01 PM #1
Member
Joined
Jun 2009
Posts
108
factorsing this expression
the expression is $6a^2-a-2$
now this is what ive done.......
taken out the common factor of -ve.
1. $-(6a^2+a+2)$
2. $-[(6a^2+a+12)]$
3. $-[(6a^2+4a-3a+12)]$
4.... | 4 | [
-0.02197265625,
0.04833984375,
0.011962890625,
-0.0303955078125,
-0.0296630859375,
0.07666015625,
0.01409912109375,
0.0220947265625,
-0.0024566650390625,
0.015869140625,
0.051025390625,
0.05712890625,
0.0869140625,
0.00482177734375,
-0.0174560546875,
-0.01129150390625,
-0.04467773437... | 16,141 | 16141 | |
Inequality
February 20th 2008, 08:21 AM #1
Senior Member
Joined
Nov 2007
Posts
329
Inequality
Prove that if $ab + ac + bc = 3$:
$8(a + b + c)^2\geq9(a + b)(a + c)(b + c)$
( $a,b,c\ge 0$)
The question says $a,b,c\ge 0$..
Suppose one of $a,b,c$ is 0. Then the other two can’t be 0 if the... | 5 | [
-0.06591796875,
0.041259765625,
-0.0064697265625,
0.0262451171875,
-0.10205078125,
0.1298828125,
-0.0189208984375,
0.03515625,
0.02001953125,
0.0247802734375,
-0.044189453125,
-0.09521484375,
0.044189453125,
0.0177001953125,
0.00101470947265625,
-0.006195068359375,
-0.0306396484375,
... | 16,142 | 16142 | |
GMAT Algebra (Data Sufficiency)
• GMAT Prep (USA)
•
• GMAT Prep (International)
•
• Favorite GMAT Articles
□ 800score GMAT Course Reviews
□ GMAT Course Comparision
□ GMAT Essay Tips & Grading from 800score
•
• Free GMAT Prep
□ Free GMAT ... | 4 | [
0.0208740234375,
-0.03271484375,
0.055419921875,
0.0107421875,
-0.0211181640625,
0.040283203125,
0.027587890625,
0.0203857421875,
-0.09814453125,
-0.007415771484375,
0.07177734375,
-0.03271484375,
0.0296630859375,
-0.0830078125,
0.0228271484375,
0.051025390625,
0.0277099609375,
-0.... | 16,143 | 16143 | |
Factorising
August 14th 2008, 09:13 AM #1
Member
Joined
Aug 2008
Posts
179
Hi! I am having trouble factorising these:
6xsquared - 11x - 35
6xsquared - 37x + 45
Can someone please show me worked examples to these. And sorry, I don't know how to use latex but I will learn it soon to make math... | 4 | [
-0.007354736328125,
-0.04150390625,
0.045654296875,
-0.00396728515625,
0.04150390625,
0.080078125,
0.01904296875,
-0.0179443359375,
-0.12255859375,
0.0211181640625,
0.050537109375,
0.032470703125,
0.0966796875,
0.02001953125,
-0.0234375,
0.050048828125,
0.00970458984375,
0.05102539... | 16,144 | 16144 | |
More rational numbers! Yay!
April 8th 2007, 05:35 PM #1
alrighty. so here we got...
This..
and me and my dad cant figure out how they get the middle number at all!~
Hello, Cait and Dad!
. . . . . . . . . . . . . x + 8 . . . . . x + 1 . . . . . . . . x + 8 . . . . . . . .x + 1
We are gi... | 4 | [
-0.029296875,
0.04931640625,
0.0576171875,
-0.049072265625,
0.0269775390625,
0.053466796875,
0.057373046875,
0.01092529296875,
0.0072021484375,
-0.0010223388671875,
0.0003604888916015625,
-0.016845703125,
0.07470703125,
0.00421142578125,
-0.0703125,
-0.00019073486328125,
-0.074707031... | 16,145 | 16145 | |
Exponential problem
June 21st 2010, 03:36 AM #1
Newbie
Joined
Jun 2010
Posts
6
Exponential problem
A exponential curve relating two quantities 'q' and 't' has the form q=ae^kt where a and k are constants.
The curve passes through two points (0.09036,2) and (3.307,-4)
Determine the values of 'a' a... | 4 | [
-0.0233154296875,
0.0986328125,
-0.01220703125,
-0.0208740234375,
-0.07958984375,
0.0123291015625,
0.0361328125,
0.005889892578125,
0.109375,
0.07958984375,
0.1240234375,
-0.1298828125,
0.0419921875,
0.0849609375,
0.06396484375,
0.01214599609375,
-0.126953125,
-0.021240234375,
-0... | 16,146 | 16146 | |
Decay rates
June 3rd 2008, 09:33 AM
Prod!gy
Decay rates
I'm having second thoughts on the answers I came up with...
Einsteinium-235 decays at a rate of 3.406% per day.
a. find the annual decay rate in exact form:
100(.96594)^365
b. Compute an approximation of your solution in part a accurate t... | 4 | [
0.00058746337890625,
0.032470703125,
0.0120849609375,
0.0115966796875,
0.0228271484375,
-0.1494140625,
-0.03515625,
0.08740234375,
-0.014404296875,
0.05810546875,
0.0257568359375,
-0.06689453125,
-0.001617431640625,
0.07080078125,
0.05419921875,
0.0234375,
-0.09326171875,
-0.002868... | 16,147 | 16147 | |
Characteristic Function on A
November 15th 2011, 06:26 PM #1
Member
Joined
Sep 2010
Posts
151
Thanks
1
Characteristic Function on A
Consider the function f(x)=2-3x with domain R ( real numbers). Let A = [-1,3), B=(2,5].
a.)Sketch the graph of XA•XB
(which has X with an A subscript and X wit... | 5 | [
-0.064453125,
-0.0279541015625,
-0.0322265625,
-0.11962890625,
-0.0213623046875,
0.006591796875,
0.0419921875,
-0.002716064453125,
-0.0673828125,
0.04931640625,
0.0517578125,
-0.0693359375,
0.0654296875,
0.0693359375,
0.138671875,
0.08984375,
-0.037841796875,
-0.095703125,
-0.048... | 16,148 | 16148 | |
Related rates and implicit
April 11th 2009, 07:43 AM #1
Newbie
Joined
Apr 2009
Posts
1
Related rates and implicit
hi i had two questions first one
A spherical balloon is being filled with helium at a rate of 8cm^3/s at what rate is the radius increasing when the radius is 12cm, when the volume is 14... | 5 | [
0.004913330078125,
0.0029296875,
-0.003997802734375,
-0.0031280517578125,
-0.0023193359375,
0.01275634765625,
0.0142822265625,
0.017578125,
-0.001251220703125,
0.0120849609375,
0.05712890625,
0.042724609375,
-0.024169921875,
0.0830078125,
0.0255126953125,
0.0169677734375,
-0.01757812... | 16,149 | 16149 | |
Series error approximation calc 2 - few questions
November 8th 2009, 10:29 AM #1
Newbie
Joined
Nov 2009
Posts
4
Series error approximation calc 2 - few questions
Intergal (arctan(x^2),x,0,3/4) aproximate the value using Rn <= 0.001
I totally can do this.. if it didn't have an intergal... I know arct... | 4 | [
-0.030517578125,
-0.07958984375,
0.08544921875,
0.039794921875,
0.0478515625,
-0.07421875,
-0.035400390625,
0.1171875,
-0.024169921875,
-0.03173828125,
0.0194091796875,
-0.031982421875,
0.0152587890625,
-0.00823974609375,
-0.103515625,
-0.00531005859375,
0.0147705078125,
-0.0361328... | 16,150 | 16150 | |
Help me understand and remember this Theorem
January 8th 2011, 07:59 AM #1
Junior Member
Joined
Oct 2010
Posts
56
I am really struggling with a theorem in my book (Tao; Analysis II).
I don't think I can properly remember this theorem because it contains so much, plus I dont think I really get the Theo... | 4 | [
-0.051513671875,
0.046142578125,
0.038818359375,
-0.023193359375,
0.10693359375,
0.08935546875,
0.0791015625,
0.015869140625,
-0.0001239776611328125,
-0.0177001953125,
0.06103515625,
0.02392578125,
-0.01708984375,
-0.037109375,
0.042724609375,
-0.0081787109375,
-0.053955078125,
-0.... | 16,151 | 16151 | |
Optimization
November 11th 2007, 08:31 AM #1
Junior Member
Joined
Sep 2007
Posts
48
Optimization
One hallway which is 4 feet wide meets another hallway which is 8 feet wide in a right angle (see picture). What is the length of the longest ladder which can be carried horizontally around the
corner? (H... | 5 | [
-0.0103759765625,
0.078125,
-0.05078125,
-0.038330078125,
-0.07177734375,
-0.005645751953125,
-0.07666015625,
0.0272216796875,
-0.03369140625,
0.068359375,
-0.0208740234375,
-0.0218505859375,
0.046630859375,
0.0751953125,
0.0615234375,
0.1318359375,
-0.0198974609375,
0.027465820312... | 16,152 | 16152 | |
Trig Problem
November 24th 2009, 04:17 PM #1
Newbie
Joined
Oct 2009
Posts
5
Trig Problem
Looking for someone to verify my work ....
If $\sin\theta=\frac{1}{3}$ and $\frac{\pi}{2}<\theta<\pi$ then what is $\cos\theta?$
Solution
$\sin^2\theta+\cos^2\theta=1$
$\frac{1}{3}^2+\cos^2\theta=... | 4 | [
-0.055908203125,
-0.053955078125,
0.0240478515625,
0.01171875,
-0.068359375,
-0.00457763671875,
-0.08837890625,
0.04248046875,
0.04296875,
-0.0150146484375,
-0.000949859619140625,
0.0301513671875,
0.0277099609375,
0.01123046875,
-0.0152587890625,
-0.0289306640625,
0.03515625,
-0.03... | 16,153 | 16153 | |
Math Help
March 26th 2008, 11:16 AM #1
Super Member
Joined
Mar 2006
Posts
705
Thanks
2
Module 77
Evalute $2^{100000}$ in mod 77.
I know that $2^{76} \equiv 1 \ (mod \ 77)$, but how should I continue? Thanks.
Sorry, but I'm getting $2^{76} \equiv 9 \text{ (mod 77)}$.
There may be a mor... | 5 | [
0.0179443359375,
0.06201171875,
-0.0625,
0.035888671875,
0.10302734375,
-0.0400390625,
0.0576171875,
0.08984375,
-0.1337890625,
0.0179443359375,
-0.045166015625,
-0.0771484375,
0.05126953125,
0.060791015625,
0.010498046875,
0.03271484375,
-0.050048828125,
0.0751953125,
-0.0654296... | 16,154 | 16154 | |
Patent US5960375 - Transmitter with improved compensation
This application is a Divisional of prior application Ser. No. 08/186,288, filed Jan. 25, 1994, entitled "TRANSMITTER WITH IMPROVED COMPENSATION," now U.S. Pat. No. 5,642,301 issued Jun. 24, 1997 to
Warrior et al. Reference is hereby made to co-pending patent ap... | 4 | [
-0.10009765625,
-0.0078125,
-0.036376953125,
-0.01519775390625,
-0.044677734375,
0.06396484375,
0.099609375,
0.06396484375,
0.032958984375,
0.06689453125,
-0.000156402587890625,
0.042236328125,
0.091796875,
-0.040771484375,
-0.02685546875,
0.0458984375,
0.078125,
0.045166015625,
... | 16,155 | 16155 | |
Derivatives of natual logs
$\frac{d}{dx} \ln(f(x)) = \frac{1}{f(x)} \times \frac{d}{dx} (f(x))$ Hence: $\frac{d}{dx} \ln(x\sqrt{x^2-1}) = \frac{1}{x\sqrt{x^2-1}} \times \frac{d}{dx} (x\sqrt{x^2-1})$ $= \frac{1}{x\sqrt{x^2-1}}
\times \frac{d}{dx} (\sqrt{x^4-x^2})$ $= \frac{1}{x\sqrt{x^2-1}} \times \frac{d}{dx} ({x^4-x^2... | 5 | [
0.06494140625,
-0.01507568359375,
0.07763671875,
-0.012939453125,
-0.019287109375,
-0.10498046875,
-0.072265625,
0.0234375,
0.03515625,
0.08056640625,
0.047607421875,
0.03955078125,
0.0203857421875,
0.05908203125,
-0.064453125,
0.06494140625,
-0.08544921875,
-0.00002825260162353515... | 16,156 | 16156 | |
A true or false about an inner product
March 2nd 2009, 09:11 AM
arbolis
A true or false about an inner product
Hi MHF,
I did badly (failed) in the final exam on linear algebra (4.4/10) and so I must retake the exam in late June or early July. I'm still stuck on some exam questions :
Tell whether this is ... | 5 | [
-0.09521484375,
-0.046142578125,
0.031982421875,
-0.02685546875,
-0.041015625,
-0.057861328125,
0.068359375,
-0.052001953125,
0.021728515625,
0.00921630859375,
0.021484375,
0.0123291015625,
-0.0233154296875,
0.044921875,
0.0211181640625,
0.0390625,
0.0164794921875,
0.021240234375,
... | 16,157 | 16157 | |
Differentiation problem
Quote:
Originally Posted by xpi0t0s
> Now, when you differentiate f(x) : [[ D(h(x)) = Derivative of h(x) w.r.t. x ]]
> you do it like f'(x) = D(x) + D(x) + ..(x times).. + D(x) which is invalid.
Why is it invalid? According to
http://mathworld.wolfram.com/Derivative.h... | 4 | [
-0.10205078125,
-0.0498046875,
0.049072265625,
0.0115966796875,
-0.01373291015625,
-0.0087890625,
0.05224609375,
-0.04296875,
0.0306396484375,
0.0299072265625,
0.06640625,
0.02294921875,
0.0234375,
0.040771484375,
-0.008544921875,
-0.0020599365234375,
-0.07275390625,
0.064453125,
... | 16,158 | 16158 | |
Boolean algebra / venn diagrams
October 23rd 2009, 12:12 AM #1
Member
Joined
Sep 2008
Posts
239
Boolean algebra / venn diagrams
For any two subsets A and B of some set S,
$(A \cup B) - (A \cap B) = (A - B) \cup (B - A)$
where $X-Y = X \cap Y'$
Show that this is true by using a) Venn diagra... | 4 | [
0.08642578125,
-0.01226806640625,
0.0125732421875,
-0.056640625,
-0.01177978515625,
-0.00482177734375,
0.138671875,
-0.04052734375,
-0.05078125,
0.00445556640625,
-0.0184326171875,
-0.07763671875,
0.033447265625,
0.031005859375,
0.0458984375,
0.06005859375,
-0.0283203125,
-0.030517... | 16,159 | 16159 | |
MathGroup Archive: May 2009 [00287]
[Date Index] [Thread Index] [Author Index]
Re: derivative of a well-behaved function
• To: mathgroup at smc.vnet.net
• Subject: [mg99529] Re: [mg99466] derivative of a well-behaved function
• From: ... | 4 | [
-0.138671875,
0.0284423828125,
0.035400390625,
0.09326171875,
0.032470703125,
-0.099609375,
0.0703125,
0.058837890625,
0.0052490234375,
0.0125732421875,
0.07080078125,
0.07373046875,
0.0625,
0.031982421875,
-0.09375,
-0.012939453125,
-0.040283203125,
-0.0311279296875,
-0.05615234... | 16,160 | 16160 | |
planes, lines and points type of question.
August 14th 2006, 11:18 PM #1
Junior Member
Joined
Feb 2006
From
Victoria, Australia
Posts
36
planes, lines and points type of question.
I need help with this, do i use gaussian elimination or something else.
Three planes have eqn's given by:
x+3y-... | 4 | [
-0.01416015625,
0.001708984375,
-0.042724609375,
-0.0052490234375,
0.048828125,
0.052490234375,
0.0693359375,
-0.0274658203125,
-0.06298828125,
0.0244140625,
0.044189453125,
-0.029541015625,
0.02978515625,
0.026611328125,
-0.044677734375,
0.0517578125,
-0.08203125,
-0.126953125,
... | 16,161 | 16161 | |
Measuring the distance of a convex set from a ball (Nikodym distance)
up vote 2 down vote favorite
Assume we have a centrally symmetric convex set $K \subset \mathbb{R}^n$ such that Vol(K)=1. In addition, assume that for every direction $u$ we know that $Vol(K \Delta R_u(K)) < \epsilon$, where $A
\Delta B$ is the symm... | 5 | [
0.02783203125,
-0.004791259765625,
-0.036376953125,
-0.15234375,
-0.05224609375,
0.0164794921875,
0.08642578125,
-0.02490234375,
0.0234375,
-0.01031494140625,
-0.03662109375,
0.004119873046875,
-0.0108642578125,
0.0179443359375,
-0.0108642578125,
-0.0791015625,
0.1142578125,
-0.012... | 16,162 | 16162 | |
The Maximal Subspace for Generation of
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 683021, 14 pages
http://dx.doi.org/10.1155/2012/683021
Research Article
The Maximal Subspace for Generation of -Regularized Families
^1Facultad de Ciencias Básicas, Universidad Tecnológica de Bolívar, Cartagena, Colo... | 4 | [
-0.04150390625,
0.009765625,
0.0223388671875,
0.009033203125,
0.015380859375,
0.0703125,
0.0247802734375,
-0.05224609375,
-0.0245361328125,
-0.01953125,
0.0223388671875,
0.0283203125,
0.0164794921875,
-0.05126953125,
-0.047607421875,
0.0263671875,
-0.00089263916015625,
-0.004791259... | 16,163 | 16163 | |
Some Fuzzy-Wavelet-Like Operators and Their Convergence
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 832831, 10 pages
http://dx.doi.org/10.1155/2013/832831
Research Article
Some Fuzzy-Wavelet-Like Operators and Their Convergence
Department of Mathematics, Karaj Branch, Islamic Azad University,... | 5 | [
-0.05615234375,
-0.06201171875,
-0.006866455078125,
-0.0576171875,
-0.07080078125,
0.0277099609375,
0.08154296875,
-0.05322265625,
-0.005126953125,
-0.00872802734375,
0.07861328125,
0.058837890625,
0.00872802734375,
0.017578125,
-0.058349609375,
0.0159912109375,
-0.007720947265625,
... | 16,164 | 16164 | |
Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer with Kerr Nonlinearity
Advances in Mathematical Physics
Volume 2012 (2012), Article ID 609765, 21 pages
http://dx.doi.org/10.1155/2012/609765
Research Article
Nonlinear Effects of Electromagnetic TM Wave Propagation in Anisotropic Layer wit... | 4 | [
-0.0732421875,
0.0242919921875,
0.06982421875,
0.033447265625,
-0.0157470703125,
-0.037841796875,
-0.0126953125,
-0.049072265625,
-0.0223388671875,
0.00567626953125,
0.10595703125,
0.050048828125,
-0.00823974609375,
-0.0115966796875,
0.0084228515625,
0.036865234375,
-0.00222778320312... | 16,165 | 16165 | |
Help on continuity
December 16th 2006, 03:51 AM #1
Senior Member
Joined
Jul 2006
From
Shabu City
Posts
381
Help on continuity
Determine the number at which the function is discontinuous, and show why definition 1.8.1 isnt satisfied at this number
Def 1.8.1
1.) $f(a)$ exists
2.) $\lim_{x \... | 4 | [
-0.01385498046875,
-0.0038299560546875,
0.02197265625,
-0.042724609375,
0.028076171875,
0.041015625,
0.050048828125,
0.06591796875,
-0.0267333984375,
-0.05419921875,
0.11572265625,
-0.041015625,
0.005523681640625,
-0.0283203125,
-0.010986328125,
0.006256103515625,
-0.006011962890625,... | 16,166 | 16166 | |
Euclidean algorithm gcd lcm help..
August 10th 2006, 04:50 AM
kodirl
Euclidean algorithm gcd lcm help..
Use the euclidean algorithm to find the gcd of 2232 and 3828 and find the lcm of 2232 and 3828.
I'm not expecting an answer maybe just a quick and easy example of how to solve the sum quickly..thanks
Aug... | 4 | [
0.003997802734375,
-0.033447265625,
-0.09375,
-0.0966796875,
0.0291748046875,
-0.00025177001953125,
-0.01300048828125,
0.0311279296875,
-0.068359375,
0.017333984375,
0.0238037109375,
0.06787109375,
0.06591796875,
-0.10546875,
0.016357421875,
0.005096435546875,
-0.0390625,
0.0397949... | 16,167 | 16167 | |
Summation proof
I have conjectured that $\sum^{n}_{i=m}i = \sum^{n}_{i=m}( n+m-i).$ How would one go about constructing a proof for this? Cheers.
Split the right hand side into $\sum^{n}_{i=m}(n+m)- \sum^{n}_{i=m}(i)$ And note that $\sum^{n}_{i=m}(i)= \sum^{n}_{i=1}(i)-\sum^{m}_{i=1}(i)$ You should know how to sum int... | 4 | [
-0.004913330078125,
0.022216796875,
0.076171875,
0.004058837890625,
0.004608154296875,
-0.0361328125,
0.0390625,
0.017578125,
-0.06787109375,
0.01397705078125,
-0.023681640625,
-0.01397705078125,
0.10693359375,
-0.01007080078125,
0.01495361328125,
0.0703125,
0.09912109375,
0.103515... | 16,168 | 16168 | |
[SOLVED] Integration by Substitution
February 11th 2009, 01:03 PM #1
Newbie
Joined
Feb 2009
Posts
10
[SOLVED] Integration by Substitution
I am trying to integrate the equation sin (x) * cos(cos (x)), I assume it is best done through integration by U-substitution but I cannot seem to come up with the U. A... | 4 | [
-0.08154296875,
0.0030364990234375,
0.03857421875,
-0.03466796875,
-0.02099609375,
-0.0025634765625,
0.046142578125,
-0.033447265625,
-0.08740234375,
-0.03125,
0.06591796875,
-0.033447265625,
0.036865234375,
0.018798828125,
0.052001953125,
-0.057373046875,
0.0693359375,
0.029907226... | 16,169 | 16169 | |
equation of tangent
October 11th 2010, 04:37 AM #1
Member
Joined
Oct 2009
Posts
202
equation of tangent
The normal to the curve $y=x^2 - 6x + 1$ at the point $p$ is parallel to the straight line.Find the equation of the $2y = x + 3$ tangent to the curve at the point $p$
If this is how your post shou... | 4 | [
-0.0164794921875,
-0.035400390625,
0.0185546875,
0.0084228515625,
0.048583984375,
0.11328125,
0.004058837890625,
0.1220703125,
-0.013427734375,
0.05712890625,
0.054931640625,
-0.0142822265625,
-0.028076171875,
-0.00701904296875,
-0.000843048095703125,
0.010986328125,
-0.1396484375,
... | 16,170 | 16170 | |
Simplifying product of to sum of in likelihood equation
December 1st 2009, 11:06 AM #1
Newbie
Joined
Nov 2009
Posts
13
Hi, I'm having problems with the veru bsics so I cant get any further on my questions. When given a function f(xlt). to find the likelihood you have to do the product of it. I dont unders... | 4 | [
-0.044189453125,
-0.0576171875,
0.09130859375,
-0.0869140625,
0.06201171875,
-0.0751953125,
0.1435546875,
0.0869140625,
0.049560546875,
0.01904296875,
0.06689453125,
-0.019775390625,
0.09912109375,
-0.029052734375,
0.022216796875,
0.09521484375,
-0.0302734375,
0.039794921875,
-0.... | 16,171 | 16171 | |
Sufficient Efficiency Conditions for Vector Ratio Problem on the Second-Order Jet Bundle
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 713765, 9 pages
http://dx.doi.org/10.1155/2012/713765
Research Article
Sufficient Efficiency Conditions for Vector Ratio Problem on the Second-Order Jet Bundle
Faculty... | 5 | [
-0.06298828125,
0.06298828125,
0.0213623046875,
0.031982421875,
0.04736328125,
0.0537109375,
-0.027587890625,
0.0125732421875,
-0.02294921875,
-0.047607421875,
0.007537841796875,
0.12255859375,
-0.040283203125,
0.040771484375,
-0.017333984375,
0.053955078125,
0.030029296875,
0.0478... | 16,172 | 16172 | |
Patent US7899652 - Linear programming support vector regression with wavelet kernel
FIELD OF THE INVENTION
The present invention relates to nonlinear dynamical systems identification and modeling, in particular using linear programming support vector regression (LP-SVR) with wavelet kernel.
BACKGROUND OF THE INVENTIO... | 4 | [
-0.14453125,
-0.049072265625,
0.004119873046875,
-0.044189453125,
0.0024566650390625,
-0.029052734375,
-0.028076171875,
0.050537109375,
-0.0240478515625,
-0.01055908203125,
-0.0771484375,
0.1025390625,
-0.0194091796875,
-0.0595703125,
-0.055908203125,
0.00836181640625,
-0.01135253906... | 16,173 | 16173 | |
quick solution required for DE of TanX*TanY=C?
i am very much thankful to the one who show quick solution for DE of TanX*TanY=C?
If I undestand correctly You require the DE the solution of which is, in implicit form,... $\tan x\cdot \tan\ y = c$ (1) In that case we first separe the variables... $\tan y= c\cdot \cot x$... | 5 | [
-0.030029296875,
-0.00009059906005859375,
0.04541015625,
0.041259765625,
0.0213623046875,
0.044921875,
0.03271484375,
-0.00836181640625,
0.007293701171875,
0.0084228515625,
0.087890625,
-0.043701171875,
-0.06103515625,
0.05517578125,
0.040283203125,
-0.00469970703125,
-0.07568359375,... | 16,174 | 16174 | |
general soltn by using mthd of characteristic
May 7th 2010, 12:55 AM #1
Newbie
Joined
Dec 2008
Posts
18
u_xx + 10u_xy + 9u_yy = y
how can we find this equation's general solution by using the method of characteristics? ı m new in this field.
First we will determine the type. Then general form of... | 5 | [
-0.0167236328125,
0.051025390625,
0.056396484375,
-0.04296875,
0.016357421875,
0.1162109375,
-0.0478515625,
0.01470947265625,
-0.07177734375,
-0.0306396484375,
0.072265625,
-0.0233154296875,
-0.032470703125,
0.02880859375,
0.05517578125,
0.0024261474609375,
-0.038330078125,
-0.0388... | 16,175 | 16175 | |
Exact Equation
September 11th 2010, 09:49 PM #1
Exact Equation
$(e^x \sin{y} -3x^2) \,dx +(e^x \cos{y} + \frac{y^{-2/3}}{3}) \, dy = 0$
$(e^x \sin{y} -3x^2) +(e^x \cos{y} + \frac{y^{-2/3}}{3}) \frac{dy}{dx} = 0<br />$
$M = e^x \sin{y} -3x^2 \,, N = e^x \cos{y} + \frac{y^{-2/3}}{3}$
$\frac{\partial ... | 5 | [
-0.05517578125,
0.014404296875,
-0.059814453125,
0.04345703125,
-0.007049560546875,
0.0213623046875,
-0.0162353515625,
-0.00049591064453125,
-0.0380859375,
-0.039794921875,
0.087890625,
-0.07421875,
-0.0028076171875,
-0.07666015625,
0.10400390625,
-0.045654296875,
-0.0194091796875,
... | 16,176 | 16176 | |
Area of a rose petal using Green's Theorem
February 22nd 2010, 09:02 PM #1
Member
Joined
Nov 2008
Posts
76
Area of a rose petal using Green's Theorem
Use Green's theorem to compute the area of one petal of the 16-leafed rose defined by r = 13sin(8t).
It may be useful for recall that the area of a re... | 4 | [
-0.0771484375,
0.049072265625,
-0.0113525390625,
-0.03857421875,
0.02978515625,
0.00811767578125,
-0.055908203125,
0.109375,
0.033935546875,
-0.047607421875,
0.043212890625,
-0.0038909912109375,
-0.02685546875,
0.00138092041015625,
0.023193359375,
0.026123046875,
-0.146484375,
-0.0... | 16,177 | 16177 | |
Patent US6381624 - Faster multiply/accumulator
BACKGROUND OF THE INVENTION
A multiply/accumulator (MAC) is a circuit that accepts three numerical input values A,B and C, and produces therefrom the arithmetic result A*B±C. Often, A, B and C are signed floating point 5 binary
numbers expressed in the format described by... | 4 | [
-0.04345703125,
-0.015380859375,
-0.099609375,
-0.029052734375,
-0.08984375,
-0.07275390625,
-0.0213623046875,
0.0291748046875,
0.01422119140625,
0.034423828125,
0.04296875,
-0.076171875,
0.0028533935546875,
-0.00104522705078125,
-0.033935546875,
0.0101318359375,
-0.054931640625,
0... | 16,178 | 16178 | |
Linear combinations of random variable
November 7th 2006, 04:09 PM #1
Junior Member
Joined
May 2006
Posts
37
Linear combinations of random variable
I have no idea what I did wrong, please help!
Small packets of nails are advertised as having average weight 500 g, and large packets as having average ... | 5 | [
0.0042724609375,
0.072265625,
0.045654296875,
-0.08203125,
0.0106201171875,
-0.1083984375,
0.05615234375,
0.0732421875,
-0.08935546875,
0.061279296875,
0.038818359375,
0.018310546875,
0.024658203125,
0.021728515625,
-0.017333984375,
-0.009033203125,
0.09228515625,
-0.00311279296875... | 16,179 | 16179 | |
Calc 2 : Integrals
February 18th 2009, 11:09 AM #1
Calc 2 : Integrals
Hey,
It's most likely my poor Algebra, but I'm having an issue with this problem:
Solve the integral: $\int{\frac{x-1}{x^2-4x+5}}dx$
$\int{\frac{x-1}{x^2-4x+5}}dx \Longrightarrow \int{\frac{x-1}{(x-2)^2+(3)^2}}dx$
$\Longright... | 5 | [
-0.055419921875,
-0.02783203125,
0.057373046875,
-0.0162353515625,
0.083984375,
0.0146484375,
-0.1025390625,
-0.004669189453125,
0.0034637451171875,
-0.05029296875,
0.038818359375,
-0.0791015625,
-0.072265625,
0.054931640625,
-0.0888671875,
-0.04443359375,
0.04296875,
-0.0607910156... | 16,180 | 16180 | |
maximum value
Given that 2u+3v+4x is equal to 12. Then find the maximum value of u^2×v^3×x^5.
Hey geniusgarvil. If you perform a trinomial expansion on your 2u+4x+4x, you will be able to get a term in regards to u^2*v^3*x^5 if you raise it to the power of (2+3+5) = 10. If you assume that the
highest term contains all ... | 5 | [
0.05126953125,
0.0147705078125,
-0.0732421875,
-0.055908203125,
-0.033203125,
0.00726318359375,
0.009765625,
-0.049072265625,
-0.0419921875,
0.00628662109375,
-0.0003070831298828125,
0.00225830078125,
-0.06689453125,
0.07080078125,
0.032958984375,
0.0262451171875,
0.06640625,
0.062... | 16,181 | 16181 | |
[SOLVED] Exponential Functions
April 20th 2009, 01:20 AM #1
Junior Member
Joined
Jan 2009
Posts
74
I need help with 2 problems, please. I'm not sure how to solve them.
#1:
$<br /> 4x^{2}(2^{x}) - 9(2^{x}) = 0<br />$
#2:
$<br /> \frac{(x+4)10^{x}}{x-3} = 2x(10^{x})<br />$
Thanks for ... | 4 | [
-0.01446533203125,
-0.0179443359375,
0.0093994140625,
0.037353515625,
0.0250244140625,
0.0291748046875,
0.01336669921875,
0.02587890625,
-0.035888671875,
-0.034423828125,
0.09521484375,
-0.1044921875,
0.07177734375,
0.053955078125,
0.037109375,
0.053955078125,
-0.01275634765625,
-0... | 16,182 | 16182 | |
need help.. related rates
November 5th 2006, 10:51 AM #1
Member
Joined
Sep 2005
Posts
136
need help.. related rates
A small boy standing in a flat field watches a balloon ise at a distance.The ballon leaves the ground 500m away from the boy and rises vertically at a rate of 14m/ minute.At what rate is th... | 5 | [
-0.0169677734375,
0.0869140625,
0.0026702880859375,
-0.04150390625,
0.06640625,
0.02294921875,
-0.042724609375,
0.068359375,
-0.0150146484375,
0.003662109375,
0.09619140625,
0.00616455078125,
-0.035400390625,
0.11669921875,
0.00750732421875,
0.06787109375,
0.015625,
0.0130615234375... | 16,183 | 16183 | |
T
TRIGONOMETRY
© Department of Physics, University of Guelph
C is a right angle and the angle at A we will call θ. The lengths of the sides of the triangle we will denote as p, q and r. From your elementary geometry, you know several things about this
Panel triangle. For example, you know ... | 4 | [
-0.09521484375,
0.031982421875,
-0.0732421875,
-0.03515625,
-0.076171875,
0.00921630859375,
-0.0030364990234375,
0.0177001953125,
0.10693359375,
0.039794921875,
0.044921875,
-0.01068115234375,
0.0185546875,
0.09765625,
0.04736328125,
-0.09765625,
-0.10107421875,
0.03515625,
-0.01... | 16,184 | 16184 | |
Vectors - help needed
Last edited by wiseguy; August 6th 2010 at 10:29 AM.
a) You will need vector addition, which is just adding vectors componentwise. b) Use the law of cosines c) Use the formula $\frac{1}{2}|\vec{a} \times \vec{b}|$ where $\times$ is the cross-product
and $|\qquad|$ is the magnitude. d) Use the for... | 5 | [
-0.058349609375,
-0.06494140625,
-0.0810546875,
-0.12890625,
0.05810546875,
0.056884765625,
0.00823974609375,
0.03369140625,
-0.06494140625,
0.126953125,
0.030517578125,
-0.00836181640625,
0.0341796875,
0.0185546875,
0.0023345947265625,
0.0830078125,
-0.05322265625,
0.0008735656738... | 16,185 | 16185 | |
Mapping Iterative Medical Imaging Algorithm on Cell Accelerator
International Journal of Biomedical Imaging
Volume 2011 (2011), Article ID 843924, 11 pages
http://dx.doi.org/10.1155/2011/843924
Research Article
Mapping Iterative Medical Imaging Algorithm on Cell Accelerator
Department of Computer Science, University... | 4 | [
-0.05517578125,
0.062255859375,
-0.03564453125,
-0.09375,
-0.11083984375,
-0.08837890625,
-0.033935546875,
0.060302734375,
0.0120849609375,
0.007110595703125,
-0.025390625,
0.09521484375,
0.052978515625,
0.0198974609375,
-0.087890625,
-0.05859375,
-0.048095703125,
0.083984375,
0.... | 16,186 | 16186 | |
Help with basic Geometry proof
September 12th 2009, 05:55 PM #1
Newbie
Joined
Sep 2009
Posts
2
Help with basic Geometry proof
I've been having a bit of trouble with geometry proofs. I'm really trying to learn and figure this one out myself, but I could use a little guidance. I'm not sure if I'm missing s... | 4 | [
-0.095703125,
0.09716796875,
0.07861328125,
-0.033203125,
0.00128936767578125,
0.004547119140625,
0.022705078125,
0.061767578125,
-0.01458740234375,
0.056884765625,
0.02294921875,
-0.115234375,
0.0361328125,
-0.004425048828125,
0.038818359375,
0.00994873046875,
-0.0115966796875,
0.... | 16,187 | 16187 | |
Cramer's Rule Computation Help
March 27th 2012, 10:12 AM
renolovexoxo
Cramer's Rule Computation Help
Let D(x,y) denote the determinant of the 2x2 matrix with rows x and y. Assume the vectors v1,v2, v3 in R2 are pairwise linearly independent. Prove that D(v2, v3)v1 + D(v3, v1) v2 + D(v1, v2)v3=0.
(Hint: write... | 4 | [
-0.03125,
-0.048095703125,
-0.068359375,
-0.0908203125,
0.07421875,
-0.00897216796875,
0.003509521484375,
-0.09423828125,
-0.068359375,
0.06787109375,
-0.035888671875,
0.04345703125,
-0.028564453125,
0.0267333984375,
-0.00347900390625,
0.064453125,
-0.042236328125,
0.068359375,
0... | 16,188 | 16188 | |
Inverse of a 3 by 3 matrix
September 13th 2009, 01:00 PM #1
Junior Member
Joined
Sep 2009
Posts
61
Inverse of a 3 by 3 matrix
i am having trouble with this problem. its been almost an hour and i still only get part of the answer. i dont know what i am doing wrong.
the question is find the inverse of... | 5 | [
-0.052001953125,
-0.05322265625,
0.018310546875,
-0.041259765625,
0.019775390625,
-0.1064453125,
-0.027587890625,
-0.04248046875,
-0.00116729736328125,
0.051025390625,
0.04345703125,
-0.01055908203125,
0.0238037109375,
-0.056640625,
-0.059814453125,
0.068359375,
-0.044677734375,
0.... | 16,189 | 16189 | |
Patent US5859912 - Digital information privacy system
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to electronic communication of messages, and more particularly, to security of these messages.
2. Description of Related Art
Systems for creating random number have been used in ... | 4 | [
-0.11083984375,
0.06103515625,
-0.08837890625,
-0.049560546875,
-0.087890625,
0.0267333984375,
0.125,
0.01434326171875,
0.09375,
0.010986328125,
-0.0203857421875,
0.1318359375,
0.091796875,
-0.057861328125,
-0.037109375,
-0.06201171875,
0.0341796875,
-0.0205078125,
-0.00030899047... | 16,190 | 16190 | |
box item problem
May 16th 2010, 10:37 PM #1
Member
Joined
Apr 2010
From
dfsdfdf
Posts
160
Dear Sir,
I need help some help with the below problem and would appreciate very much if can offer some help.
thanks
Kingman
John has 5 items, one each to be named P,Q, R,S and T. Each item is pl... | 5 | [
0.0113525390625,
0.050537109375,
0.029541015625,
-0.037109375,
-0.011474609375,
0.0191650390625,
0.0849609375,
-0.0118408203125,
-0.0023956298828125,
0.076171875,
0.01171875,
-0.006591796875,
0.06591796875,
0.0791015625,
-0.0263671875,
-0.00107574462890625,
-0.0274658203125,
-0.009... | 16,191 | 16191 | |
Compute Perimeter & Area
October 23rd 2006, 06:22 AM
TreeMoney
Compute Perimeter & Area
Consider the region in the plane enclosed by y = x^2 and y = 4.
a) Compute it's perimeter P and area A, and the ratio Q = A / P^2. (By squaring the perimeter we make this ratio independent of the unit length chosen to mea... | 5 | [
0.07373046875,
0.09619140625,
0.00286865234375,
0.00457763671875,
0.033935546875,
-0.04833984375,
0.0238037109375,
0.035400390625,
0.0654296875,
-0.00921630859375,
0.0108642578125,
0.0048828125,
0.044189453125,
0.11083984375,
0.060791015625,
0.054443359375,
0.00921630859375,
-0.042... | 16,192 | 16192 | |
Solving triangle ABC using given measurements
May 4th 2008, 11:25 AM
emmahlav
Solving triangle ABC using given measurements
I was not paying attention in class when this was taught and now I'm completely lost
right triangle ABC
B=40 degrees
side a=14
what do I do next?
May 4th 2008, 11:29 AM
... | 4 | [
-0.061767578125,
0.130859375,
-0.002044677734375,
0.00958251953125,
-0.03369140625,
0.059814453125,
-0.031005859375,
0.0205078125,
-0.000720977783203125,
0.0478515625,
0.08447265625,
-0.06494140625,
0.059814453125,
0.08251953125,
0.0693359375,
0.0025634765625,
-0.1142578125,
0.0250... | 16,193 | 16193 | |
Series solution, second order diff. eq.
Hi there. I have this differential equation: [tex]x^4y''+2x^3y'-y=0[/tex]
And I have to find one solution of the form: [tex]\sum_0^{\infty}a_nx^{-n},x>0[/tex]
So I have:
[tex]y(x)=\sum_0^{\infty}a_n x^{-n}[/tex]
[tex]y'(x)=\sum_1^{\infty}(-n) a_n x^{-n-1}[/tex]
[tex]y''(x)=\... | 5 | [
-0.119140625,
-0.044921875,
0.080078125,
0.0712890625,
-0.014892578125,
0.01287841796875,
-0.036376953125,
-0.036865234375,
0.03564453125,
-0.04296875,
0.09912109375,
0.011962890625,
-0.007110595703125,
-0.042724609375,
-0.037109375,
0.04833984375,
0.004425048828125,
-0.02844238281... | 16,194 | 16194 | |
Math Help
November 12th 2008, 04:38 AM #1
Tests
I've done these questions but I would like them to be checked.
Let $w=e^{\frac{2i\pi}{3}}$. Then $iw$ is an n-th root of unity where n is:
a). 12
b). 7
c). 4
d). 3
My answer is c).
Suppose that u, v and w are unit vectors in $\Re ^... | 5 | [
-0.06005859375,
0.0390625,
-0.06298828125,
-0.039794921875,
-0.02880859375,
0.052490234375,
0.08447265625,
-0.037109375,
-0.038330078125,
-0.009033203125,
0.115234375,
-0.015380859375,
-0.04248046875,
-0.0250244140625,
-0.0654296875,
-0.0245361328125,
-0.052001953125,
-0.0859375,
... | 16,195 | 16195 | |
Lorentz force law equation
Use magnetic lorentz force on a charged particle equation. And you can prove
F=BqvsinΘ.(Magnitude only).
so B= F/qvsinΘ
So, the unit of B is N/C(ms^(-1))
multiply s on both numerator and denominator,
so the unit is Ns/Cm
But F = BILsinΘ (Force on current carrying wire)
Unit of RHS is th... | 4 | [
-0.11767578125,
0.02197265625,
-0.0118408203125,
0.046630859375,
-0.0625,
0.0478515625,
0.046630859375,
-0.034423828125,
0.022216796875,
0.041259765625,
0.078125,
-0.1142578125,
0.050048828125,
0.091796875,
-0.08349609375,
0.0810546875,
-0.031982421875,
0.0703125,
-0.09375,
0.0... | 16,196 | 16196 | |
Outer product on operators?
First of all, I think that the formula should be J = L[itex]\otimes[/itex]1 + 1[itex]\otimes[/itex]S . About it's meaning, when you have two operators (say A and B) which operate on two, in general
different, Hilbert spaces (say H[A] and H[B]), then you can create a new Hilbert space by the ... | 4 | [
-0.0751953125,
-0.10791015625,
0.05078125,
-0.0751953125,
-0.059326171875,
0.0859375,
0.078125,
-0.03173828125,
-0.046875,
-0.06005859375,
-0.010986328125,
-0.00341796875,
-0.0111083984375,
-0.028564453125,
0.016845703125,
0.1376953125,
-0.0247802734375,
0.007110595703125,
-0.102... | 16,197 | 16197 | |
Algorithms Explained
0
Tags:
encryption server advanced
Encryption has become a part and parcel of our lives and we have accepted the fact that data is going to encrypted and decrypted at various stages. However, there is not a single encryption algorithm
followed everywhere. There are a number of algorithms existin... | 4 | [
-0.04638671875,
0.06201171875,
0.00665283203125,
-0.04541015625,
-0.04443359375,
-0.078125,
-0.053955078125,
0.0255126953125,
0.060302734375,
0.059814453125,
-0.057373046875,
0.06591796875,
-0.005401611328125,
-0.060791015625,
-0.0225830078125,
-0.034423828125,
-0.05322265625,
-0.0... | 16,198 | 16198 | |
Learn about Senior Chemistry: Energetics 9
Male Speaker: Okay, so its not the most exciting lab to do in the world but you know it has one of the most important and impressive types of calculations to be able to do and here is the thing about
the ice cube lab that's pretty much standard lab that we do everywhere as che... | 4 | [
-0.046875,
0.037841796875,
0.0294189453125,
0.057861328125,
0.005889892578125,
-0.03173828125,
0.007232666015625,
0.0771484375,
0.001251220703125,
-0.0284423828125,
-0.10400390625,
-0.072265625,
0.024169921875,
-0.0196533203125,
0.053955078125,
-0.01116943359375,
-0.0033111572265625,... | 16,199 | 16199 |