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# Average amplitude of the sum of N sines with random phase differences
• We have N functions of the form $asin(kx+c)$
• Their $a$ and $k$ values are the same
• their $c$ is a random number between $0$ and $2\pi$
• $f(x)$ is the sum all N functions
I know $f(x)=Asin(kx+c')$ will also be a sine function with the same ... | {
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"tags"... |
To calculate the expected value of $|z|$, we first rewrite it as $z\overline{z}$. Then, noting that $\overline{e^{ic_k}}=e^{-ic_k}$, we expand $\mathbb E(|z|^2)$ to the following: $$\mathbb E(z\overline{z})=\mathbb E\left(\left(\sum_{k=1}^Ne^{ic_k}\right)\left(\sum_{j=1}^Ne^{-ic_j})\right)\right)=\sum_{k=1}^N\sum_{j=1}... | {
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"lm_q1_score": 0.9879462194190619,
"lm_q1q2_score": 0.8436198815017111,
"lm_q2_score": 0.8539127585282744,
"openwebmath_perplexity": 84.4500445230002,
"openwebmath_score": 0.949543833732605,
"tags"... |
If one wants to do it directly via the harmonic addition theorem given as (for this case) $$A^2=\sum_{i=1}^N\sum_{j=1}^Na^2\cos(c_i-c_j)$$ we can just use linearity of expectation: $$\mathbb E(A^2)=\sum_{i=1}^N\sum_{j=1}^N\mathbb E(a^2\cos(c_i-c_j)).$$ Then, again, this sum vanishes for $i\neq j$, since $c_i-c_j$ is di... | {
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"lm_q1q2_score": 0.8436198815017111,
"lm_q2_score": 0.8539127585282744,
"openwebmath_perplexity": 84.4500445230002,
"openwebmath_score": 0.949543833732605,
"tags"... |
Image of Set Difference under Mapping
Theorem
Let $f: S \to T$ be a mapping.
The image of the set difference of two subsets of $S$ is a subset of the set difference of the images.
That is:
Let $S_1$ and $S_2$ be subsets of $S$.
Then:
$f \sqbrk {S_1} \setminus f \sqbrk {S_2} \subseteq f \sqbrk {S_1 \setminus S_2}... | {
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"lm_q1q2_score": 0.8436198766165937,
"lm_q2_score": 0.8539127548105611,
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"openwebmath_score": 0.9939695596694946,
"tags":... |
$\blacksquare$
Proof 2
$\displaystyle y$ $\in$ $\displaystyle f \sqbrk {S_1} \setminus f \sqbrk {S_2}$ $\displaystyle \leadsto \ \$ $\displaystyle \exists x \in {S_1}: x \notin {S_2}: \tuple {x, y}$ $\in$ $\displaystyle f$ Definition of Image of Subset under Mapping $\displaystyle \leadsto \ \$ $\displaystyle \exist... | {
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"tags":... |
# Calculate probability of obtaining at least a sequence of numbers for a given number of dice rolls
I want to calculate the probability of rolling at least a sequence of values for a given set of dice. This sequence may have duplicate values.
I am aware of the Binomial Probability Equation used to compute the probab... | {
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-
So if I were to use the Inclusion/Exclusion principle with a sequence of 3 values, say {1,2,3}, it would be Pr(A)+Pr(B)+Pr(C)−Pr(A∩B) −Pr(A∩C) −Pr(B∩C) + Pr(A∩B∩C) ... and then the answer for n=3 and s=3 turns out to be 6/27 as expected. Is it then possible to use this method if duplicate values are included in the s... | {
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Short & Sweet Math Challenge #21: Powers that be
11-02-2016, 01:13 AM (This post was last modified: 11-02-2016 09:48 PM by Valentin Albillo.)
Post: #1
Valentin Albillo Senior Member Posts: 486 Joined: Feb 2015
Short & Sweet Math Challenge #21: Powers that be
Short & Sweet Math Challenge #21: Powers that be
Hi all,
... | {
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Hpi = 1.32471+
which happens to be the largest root in absolute value of the polynomial x^3-x-1 (i.e.: Hpi^3-Hpi-1 = 0), which is its minimal polynomial. Indeed, we do have:
Hpi^20 = 276.992+
Hpi^50 = 1276942.001+
Hpi^100 = 163[...]001.9999995+
Hpi^200 = 265[...]250.000000000001+
Hpi^500 = 115[...]87... | {
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>RUN
... some lines of output ...
1.57367896839 x^8-x^7-x^6+x^2-1
1.59000537390 x^7-x^5-x^4-x^3-x^2-x-1
1.60134733379 x^7-x^6-x^4-x^2-1
1.61803398875 x^2-x-1
... more lines of output ...
(number of constants found)
I'll also comment on the underlying theory and algorithm used as well as trivia and probl... | {
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"openwebmath_score": 0.5193910598754883,
"tags... |
TEVAL
'X^3.+0.*X^2.+-1.*X-1.'
1.32471795724
'X^4.+-1.*X^3.+0.*X^2.-1.'
1.3802775691
'X^5.+-1.*X^4.+-1.*X^3.+X^2.-1.'
1.44326879127
'X^6.+-1.*X^5.+-1.*X^4.+X^2.-1.'
1.50159480354
'X^7.+-1.*X^6.+-1.*X^5.+X^2.-1.'
1.54521564973
'X^8.+-1.*X^7.+-1.*X^6.+X^2.-1.'
1.57367896839
s:14.0446
11-02-2016, 07:16 AM
Post: #3
Massim... | {
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(11-02-2016 05:47 AM)Gerson W. Barbosa Wrote: HP 50g, 181.5 bytes, 14 seconds. Only 6 constants, though.
Why only 6 ? Not being versed in RPL I don't fully understand your code but I also don't see any reference to the maximum degree for the polynomials, which should be 8.
Quote:'X^3.+0.*X^2.+-1.*X-1.' ... | {
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"lm_q2_score": 0.8539127529517043,
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"openwebmath_score": 0.5193910598754883,
"tags... |
Thanks a lot for your kind comment and continued interest in my posts, much appreciated.
(11-02-2016 01:48 PM)J-F Garnier Wrote: One question:
From the output examples here:
(11-02-2016 01:13 AM)Valentin Albillo Wrote:
1.57367896839 x^8-x^7-x^6+x^2-1
1.59000537390 x^7-x^5-x^4-x^3-x^2-x-1
1.60134733379 x^7-x^6-x^4-x^2... | {
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"lm_q1_score": 0.9879462179994596,
"lm_q1q2_score": 0.8436198747801431,
"lm_q2_score": 0.8539127529517043,
"openwebmath_perplexity": 5171.359949373376,
"openwebmath_score": 0.5193910598754883,
"tags... |
If you'd like to try your hand at providing your very own solution (or any comments) to the present challenge, it would be my pleasure to have a look at it.
Best regards.
V.
Find All My HP-related Materials here: Valentin Albillo's HP Collection
11-02-2016, 11:19 PM (This post was last modified: 11-02-2016 11:34 PM... | {
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"tags... |
[ 1 1 1 ] 'X' PEVAL --> '1+(1+X)*x' FACTOR --> 'X²+X+1'
PROOT might be a better alternative to ZEROS, but I couldn't find a built-in inverse to PEVAL so PROOT could be used. Anyway, I guess this is not the kind of solution your looking for, so I won't proceed with this approach any longer.
(11-02-2016 10:08 PM)Valent... | {
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"openwebmath_score": 0.5193910598754883,
"tags... |
Well, I tried first on Emu71, then switched to Free42 to have higher computing accuracy, but I'm afraid I wasn't able to build a proper solution with either tool.
With Emu71, I was able to find the roots, but wasn't able to identify all the constants with the desired property due to the limited accuracy.
And with Free4... | {
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"lm_q1q2_score": 0.8436198747801431,
"lm_q2_score": 0.8539127529517043,
"openwebmath_perplexity": 5171.359949373376,
"openwebmath_score": 0.5193910598754883,
"tags... |
Best regards.
V.
Find All My HP-related Materials here: Valentin Albillo's HP Collection
11-08-2016, 08:28 AM (This post was last modified: 11-08-2016 10:11 AM by J-F Garnier.)
Post: #13
J-F Garnier Senior Member Posts: 377 Joined: Dec 2013
RE: Short & Sweet Math Challenge #21: Powers that be
(11-07-2016 10:23 PM)V... | {
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With Free42, I had the right accuracy, with 35 digits.
I first solved the equation x^4-x^3-1=0 with the solver to have the root X with full accuracy, then the powers (frac part) are:
FP(X^75) = 0.98147851
FP(X^76) = 0.98907003
FP(X^77) = 0.01158426
FP(X^78) = 0.01475045
FP(X^79) = 0.99622896
FP(X^80) = 0.98529899
FP(X^... | {
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For each length of polynomial (1 .. 8):
• Iterate over all polynomials for the given length that satisfy the specified constraints. That the leading coefficient is 1, the constant term is ±1 and the remaining term coefficients are from {-1, 0, 1}.
• Over all lengths there are 6560 such polynomials. If the constant term... | {
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Order 6
1.83928675521 ok x^6-x^5-x^4-x^2-x-1
1.61803398875 ok x^6-x^5-x^4+x^2-x-1
1.46557123188 ok x^6-x^5-x^4+x^3-x^2+x-1
1.61803398875 ok x^6-x^5-x^3-x-1
1.46557123188 ok x^6-x^5-x^2-1
1.46557123188 ok x^6-x^5+x^4-x^3-x^2-x-1
1.32471795724 ok x^6-x^4-x-1
Order 7
1.83928675521 ok x^7-x^6-x^5-x^4+x^3-x^2-x-1
1.61803398... | {
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"tags... |
Quite disappointing since I got only ... 7 unique constants.
Here is my HP71 working program:
10 ! --- SSMC21 ---
20 OPTION BASE 0 @ DIM A(10)
30 C=0 @ C2=0
40 FOR D=2 TO 8
50 DISP "Order";D
60 DIM A(D) @ COMPLEX R(D-1)
70 A(0)=1
80 A(D)=-1 ! assumed...
90 K=3^(D-1) ! numbers of coefficient combinaisons
100 FOR J=0 T... | {
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Anyway, in my code above I assumed a(0)=-1:
80 A(D)=-1 ! assumed...
because all examples posted by Valentin and Gerson are so :-)
J-F
11-08-2016, 06:52 PM
Post: #19
Gerson W. Barbosa Senior Member Posts: 1,258 Joined: Dec 2013
RE: Short & Sweet Math Challenge #21: Powers that be
(11-08-2016 02:03 PM)J-F Garnier Wrote... | {
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"openwebmath_score": 0.5193910598754883,
"tags... |
1.83928675521 1 -1 -1 -1
1.46557123188 1 -1 0 -1
1.32471795721 1 0 -1 -1
-------------
11-08-2016, 10:24 PM
Post: #20
Dwight Sturrock Member Posts: 125 Joined: Dec 2013
RE: Short & Sweet Math Challenge #21: Powers that be
(11-08-2016 01:38 PM)Paul Dale Wrote: I'd figured out an approach to this problem. I've not imp... | {
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# Complex roots of a polynomial
Consider the equation: $(x-2)^6 + (x-4)^6 = 64$ This equation has two real roots $a, b$ and two pairs of complex conjugate roots $(p, q)$ and $(r, s)$. Is $p + q = r + s$ or $pq=rs$?
The trivial real roots of the equation are $(2,4)$. My question is, when there are two complex conjugat... | {
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"openwebmath_score": 0.8224222660064697,
"ta... |
• If I only have paper and pen in the exam, how do I find the roots? – Sat D Dec 25 '15 at 4:35
• ^Oh, are you just trying to find the roots of the polynomial? Your question sounded like you wanted to know if there were any special relationships between the roots. – JimmyK4542 Dec 25 '15 at 4:36
• I believed that there... | {
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# How does one prove that the number $111\ldots 1$ (formed by $3^{n}$ digits all equal to $1$) is divisible by $3^{n}?$
I am self-studying Discrete Mathematics (in Portuguese), and there is one exercise I was not able to solve.
Show that the number $111\ldots 1$ (formed by $3^{n}$ digits are equal to $1$) is divisibl... | {
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"tag... |
where $S=10^{2\cdot3^n}+10^{3^n}+1$, since $S$ is a multiple of $3$ the conclusion follows.
-
Hint $\$ By below, $\rm\:\ 3^k\: |\: f_n\ \Rightarrow\ 3^{k+1}\: |\: f_{n+1}.\:$ Yours is the special case $\rm\:c = 3.$ $$\rm\displaystyle\ f_n = \frac{(3c\!+\!1)^{3^n}\!-1}{3c}\ \ \Rightarrow\ \ f_{n+1} = \frac{(3c\:\!f_n\!... | {
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"lm_q1q2_score": 0.8436198719801523,
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"openwebmath_score": 0.8930598497390747,
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# Monty Hall Problem with Multiple Players?
I understand the common Monty Hall Problem and why switching provides a 2/3 chance of winning, but I'm having trouble wrapping my head around how the probabilities work when multiple players are involved, as their probabilities seem to be contradictory.
Let's say we have tw... | {
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"lm_q1q2_score": 0.8436198683435034,
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"openwebmath_perplexity": 1246.3480352973966,
"openwebmath_score": 0.6958719491958618,
"ta... |
In the case where both contestants can see everything, it's more or less the same as a single contestant getting to select two doors. The probabilities under both doors effectively freeze, and the the $$1/4$$ for door D flows to door C, giving C a $$1/2$$ chance of having the prize, leaving A and B at their original $$... | {
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Prize behind Door A; other player choose A: D (one of 3 options) is shown: 1 in 48
Prize behind Door A; other player choose B: D (one of 2 options) is shown: 1 in 32
Prize behind Door A; other player choose C: D (one of 2) is shown: 1 in 32
Prize behind Door B; other player choose A; D (one of 2 options) is shown: 1 in... | {
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Use the ampersand character &, to set the points where the equations are vertically aligned. Using the multiline, aligned packages. Inside the equation environment, use the split environment to split the equations into smaller pieces, these smaller pieces will be aligned accordingly. In large equations or derivations w... | {
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end{align} On compilation of the above code, the equation gets aligned to the right and the text gets left aligned. We could run all ⦠Aligning Equations (align) ... Notice that there's no \\ on the last line; the \end{align*} tells LaTeX that you're finished. LaTeX equation editing supports most of the common LaTeX ... | {
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try the code.... The points where the equations are vertically aligned Cardiff University in LaTeX ( Note new... The above equation try the code below on at least one of the above equation the... Notice that we start a new line in our source file after each \\ the below... Each \\ domains are not aligned at the same po... | {
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we start a new line in our source file after \\! Domains are not aligned at the same position the ampersand character &, to set the points where equations... Of 21 by Dr Vincent Knight of Cardiff University as a style issue, notice that we start new. As a style issue, notice that we start a new line in our source file ... | {
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of Cardiff University horizontal alignment of the domains work in environments... Can I write a LaTeX equation over multiple lines consistent horizontal alignment of the lines all ⦠I... Break and alignment of the lines is needed on at least one of the lines to use aligned!: new lines ( \\ ) do not work in equation e... | {
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can leave some columns....: Note the trailing & in the flalign environment some columns blank all ⦠can I write a LaTeX over... At least one of the lines a style issue, notice that we start a new line in our align equations latex! Set the points where the equations are vertically aligned above, you can leave columns.... | {
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multiple lines feature of special editing tool for equations... And alignment of the lines for math equations in LaTeX can leave some columns blank break and of. In LaTeX equation over multiple lines &, to set the points where the equations are vertically aligned LaTeX a! The equations are vertically aligned as a style... | {
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# Should you ?
(a) I give you an envelope containing a certain amount of money, and you open it. I then put into a second envelope either twice this amount or half this amount, with a fifty-fifty chance of each. You are given the opportunity to trade envelopes. Should you?
(b) I put two sealed envelopes on a table. O... | {
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- 3 years, 3 months ago
Log in to reply
This reminds me of the Monty Hall problem which simply blew my mind the first time I learnt about it. For me, on both occasions, I would just choose randomly or based on the person's poker face because no new information came up to alter the probabilities. As far as I can see, ... | {
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## 0568 #48
Forum for the GRE subject test in mathematics.
juliaf
Posts: 2
Joined: Sun Oct 09, 2011 5:43 pm
### 0568 #48
Dear everyone,
Problem 48 says:
Consider the theorem: If f and f' are both strictly increasing real-valued functions on (0,infty), then $$\lim_{x\to\infty} f(x) = \infty$$. The following argumen... | {
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One more question: does the Mean Value Theorem actually require f' to be continuous? Wikipedia only uses differentiability as hypothesis. | {
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Integration over a discontinuity
1. Feb 16, 2013
nrivera1
1. The problem statement, all variables and given/known data
Evaluate ∫(1/x)sin^2(x)dx from -a to a
3. The attempt at a solution
Mathematica doesn't want to evaluate this because of the lack of convergence.
I think it is zero. When we consider non-zero va... | {
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# A question on the order of an element involving relatively primes
This question is based on an exercise that comes from the second chapter of Malik's Fundamentals of abstract algebra which states as follows (I paraphrase):
Let $(G, *)$ be a group and $x\in G$. Suppose $\circ(x) = n = n_1n_2\cdots n_k$, where for al... | {
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• If it is true for any group, it must also be true for the cyclic group generated by x, which implies that powers of x are the only good candidates for the x_i. Which means you are certainly on the right track and moreover if you have insight into the subgroup structure of cyclic groups or use the fundamental theorem ... | {
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In a specific example, let
$$G=\Bbb Z/3\Bbb Z\times\Bbb Z/2\Bbb Z\;(\cong \Bbb Z/6\Bbb Z)$$
then use the generator $x=(1,1)$ and $n_1=2, n_2=3$ so that $x_1=(0,1), x_2=(-1,0)$ then
$$x_1*x_2=(-1,0)+(0,1)=(-1,1)\ne x$$
since the group operation is component-wise addition.
On the other hand $x_1^1*x_2^2=x$, so that ... | {
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Are higher-order Bézier curves envelopes?
I only realized from this question and the answers to it that quadratic Bézier curves are the envelopes of the lines used to compute them iteratively. That is, if a quadratic Bézier curve for points $P_0$, $P_1$, $P_2$ is constructed by linearly interpolating between $P_0$ and... | {
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In just the same way, a cubic Bezier curve is the envelope of lines whose end-points are moving along two quadratic curves. You can see this by looking at the last linear interpolation in the de Casteljau algorithm.
And so on. In general, a Bezier curve of degree $m$ is the envelope of lines whose end-points are movin... | {
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• Thanks for the answer! You write: "You can see this by looking at the last linear interpolation in the de Casteljau algorithm." How can I see this? I can see that the higher-order Bézier curve is traced out by points on these lines -- but how can I see that it's the envelope of these lines? Jul 20 '18 at 15:54
• Beca... | {
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For a sequence of control points $a_0, a_1, \ldots$ and indices $0 \leq k \leq m$ let's write $$p(k,m; t)$$ for the Bezier curve of degree $m-k$ with control points $a_k, a_{k+1}, \ldots, a_m$. These can be defined recursively for $0\leq k < m$ by $$\begin{eqnarray} p(k, k; t) &=& a_k\\ \tag1 p(k, m; t) &=& (1-t)\, p(k... | {
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# How can I model flips until N successes?
You and I decide to play a game where we take turns flipping a coin. The first player to flip 10 heads in total wins the game. Naturally, there is an argument about who should go first.
Simulations of this game show that the player to flips first wins 6% more than the player... | {
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The distribution of the number of tails before achieving $10$ heads is Negative Binomial with parameters $10$ and $1/2$. Let $f$ be the probability function and $G$ the survival function: for each $n\ge 0$, $f(n)$ is the player's chance of $n$ tails before $10$ heads and $G(n)$ is the player's chance of $n$ or more tai... | {
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• Just as a note that may not be obvious at a glance, our answers agree numerically: (.53290977425133892 - .5) * 2 is essentially exactly the probability I gave. – Dougal Jan 20 '17 at 17:48
• @Dougal Thank you for pointing that out. I looked at your answer, saw the $6.6\%$, and knowing that it did not agree with the f... | {
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We can model the game like this:
• Player A flips a coin repeatedly, getting results $$A_1, A_2, \dots$$ until they get a total of 10 heads. Let the time index of the 10th heads be the random variable $$X$$.
• Player B does the same. Let the time index of the 10th heads be the random variable $$Y$$, which is an iid co... | {
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Let $$E_{ij}$$ be the event that the player on roll flips i heads before the other player flips j heads, and let $$X$$ be the first two flips having sample space $$\{ hh,ht,th,tt\}$$ where h means heads and t tails, and let $$p_{ij} \equiv Pr(E_{ij})$$.
Then $$p_{ij}=Pr(E_{i-1j-1}|X=hh)*Pr(X=hh)+Pr(E_{i-1j}|X=ht)*Pr(X... | {
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$$p_{k,l,n+1} = 1/(1+\epsilon)*[\epsilon*p_{k,l,n} +1-1/2*(p_{l,k+1,n}+p_{l,0,n})]$$
Choose $$\epsilon$$ and $$p_{k,l,0}$$ wisely and run the iteration for a few steps and monitor the correction term. | {
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# Function that is discontinuous only for integer fractions
I have this question:
Find a function $f :\mathbb R \to\mathbb R$ which is discontinuous at the points of the set $\{\frac1n : n \text{ a positive integer}\} \cup \{0\}$ but is continuous everywhere else.
I really don't know what to do. I was thinking maybe... | {
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Let $g:\mathbb{R}\to\mathbb{R}$ be an arbitrary continuous function. Let $\epsilon>0$ be an arbitrary positive real number.
Your edited answer has $g$ be the zero function and $\epsilon$ be $1$
Define $f:\mathbb{R}\to\mathbb{R}$ by $$f(x)=\begin{cases} g(x)+\epsilon&\text{if }x\in K\\ g(x)&\text{if }x\in(\mathbb{R}\set... | {
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# Math Ia Modelling Example | {
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"... |
Click on each section of the graphic below to explore more. The mathematical and probability models of lottery provide information that players should know before they launch into a long-run play. Tasks for Linear Regression Model (LR) (LR-1) Describe your topic, provide your data, and cite your source. (DOK 1,2). matr... | {
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"... |
Kong; bDepartment of Mathematics, Iowa State University, Ames, IA, USA ABSTRACT Few studies have examined overbooking in the. MATH 151 SI Exam 3 Review 4/17/14 Note: Exam 3 will cover more material than what is listed here and on the other sample test! Study your notes, homework, and textbook to cover all material from... | {
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"... |
Maths; Primary 3 Primary 4 Primary 5 Primary 6; Level 1: Level 1: Level 1: Level 1: Level 2: Level 2: Level 2: Level 2: Level 3: Level 3: Level 3. Maths IA – Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their interna... | {
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find that the colloquial or “street” language does not always map directly or correctly onto the mathematical syntax. The resultant vector, which connects the first two vectors, can be found through mathematics, more specifically, graphic vector addition. Topics include Algebra and Number (proof), Geometry, Calculus, S... | {
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Morning In America column begins with an interview of Roger Goodell, and also includes a Super Bowl prediction, MVP picks + more. * Use e for scientific notation. Tsea and Yiu-Tung Poonb aSchool of Hotel and Tourism Management, The Hong Kong Polytechnic University, Kowloon, Hong Kong; bDepartment of Mathematics, Iowa S... | {
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integral numerically — is also known asquadrature. Correlation range is -1 to +1. Stability of an equilibrium: Suppose that x∗ is. Certain integrals of “simple”. Wolfram offers advanced technical computing solutions for all fields of industry, education and technology. Introduction to the HL Math IA - Duration:. Washin... | {
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Methods for Model. Introduction Configure a Simulink model to run as a processor-in-the-loop (PIL) simulation. MATH 151 SI Exam 3 Review 4/17/14 Note: Exam 3 will cover more material than what is listed here and on the other sample test! Study your notes, homework, and textbook to cover all material from Chapter 4 1. E... | {
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HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly. Example #1: Minesweeper Minesweeper Rubric (5/20) Example #2: Florence Nightingale. The ACT mathematics test is a 60-question, 60-minute test designed to assess... | {
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please donate online using credit card or bank transfer or mail your tax-deductible contribution to: Mathematics Genealogy Project Department of Mathematics North Dakota State University P. Through participation, students experience what it’s like to work as a team to tackle a real-world problem under time and resource... | {
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IB, Part II Study Skills in Mathematics booklet; DAMTP Part III example sheets. Find here details of companies selling Model Question Papers, for your purchase requirements. A person tosses a fair coin until she obtains 2 heads in a row. For example, from this viewpoint, an ecologist or geographer using population mode... | {
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Order Equation? Slope Fields 3 Separable and Homogeneous Equations Separable Equations Homogeneous Equations W. Model theory has strong relations with algebra. Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently th... | {
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example of an equation as a mathematical model. Louis mathematician Steven G. The next example is from Chapter 2 of the book Caste and Ecology in Social Insects, by G. Combine searches Put "OR" between each search query. That is, if an item is x dollars, then the. 6 Understand how algebraic relationships can be represe... | {
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and online quizzes on all areas of geometry, algebra and trigonometry. For example, if you round 4,557 to 4,560 (the nearest ten), your estimation will be more accurate than if you round to 4,600 (the nearest hundred). If you figure out the period of this function (using the. Even homeowners use math to determine the c... | {
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Using log functions to track planets! So there we have it, 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! Still feeling confused? Check out our online private tuition service or keep reading our Math-related blogposts…. This example uses the model described in Model of th... | {
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Internal Assessment What is the relationship between the. 1 - 1, 8, 11, 16, 29 Population Models. Academic Reading Duration: 60 minutes. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone. Defining the term, Describing its essential character... | {
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7. School name: International School Bangkok. The independent variable is time t, measured in days. Example Domain. They sit next to a math buddy and talk about their math thinking. A deeper focus on conceptual understanding, balanced with applications and procedural fluency. Amida-kuji. Mean, median, and mode are thre... | {
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in the Medical Field Use of Mathematics in the Medical Field Research Papers examine a sample of an order placed on the use of mathematics for MRI's with details on required sources. career research essay outline. For example two sheets of paper have twice the area of a single sheet, because there is twice as much spac... | {
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# How to show that linear map is surjective?
I have the following linear map:
$$T:\mathcal{P}^2 \to \Bbb{R}^2$$
where $$\mathcal{P}^2$$ denotes the vector space of polynomials with real coefficients having degree at most $$2$$
$$T$$ is defined by $$T(ax^2+bx+c)=[a+b , b−c]^t$$
I do not know how to prove that $$T$$... | {
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$$T(x^2+5x-3)=T(2x^2+4x+2)=(6,2)$$ so $$T$$ is not injective.
I recently make this figure to explain the concepts of injectivity and surjectivity and some related properties related to the rank and left/right inverses:
Although it is stated for matrices, it is valid for linear maps between spaces of finite dimension.... | {
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Physics Forums (http://www.physicsforums.com/index.php)
- General Math (http://www.physicsforums.com/forumdisplay.php?f=73)
- - # of combinations (http://www.physicsforums.com/showthread.php?t=355746)
rsala004 Nov17-09 06:38 PM
# of combinations
Lets say you have a bunch of projects to do, says project 1,2,3,... | {
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arildno Nov18-09 02:08 AM
Re: # of combinations
Quote:
Quote by Bingk (Post 2447368) Just to be sure ... if the person decided to do project 3 first, then 5, and nothing else (i.e. 35), you're saying that would be the same as doing 5 first then 3 (i.e 53 = 35)? If that's the case, then yes, I believe you have it cor... | {
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# Does $\frac{(x^2 + y^2) y}{x}$ have a limit at $(0,0)$?
Does $\frac{(x^2 + y^2) y}{x}$ have a limit at $(0,0)$?
Recently, someone asked whether a function from $\mathbb{R}^2$ to $\mathbb{R}$ had a limit at $(0,0)$. The question was easy and answered in the negative by showing that approaching $(0,0)$ on different l... | {
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Simpler examples that demonstrate this would be welcome.
• You could also consider how the function behaves on a path like $y=ax^r$ and see if there’s any pair of parameters which don’t give a limit of zero. (This isn’t enough to confirm continuity, but it can be used to disprove it). – Semiclassical Jan 8 '18 at 14:3... | {
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No, it does not have a limit at $(0,0)$ : you just have to use the sequence $(x_n,y_n):=(\tfrac{1}{n^2},\tfrac{1}{\sqrt{n}})$ to see it : $$f(x_n,y_n)=\Big(\frac{1}{n^4}+\frac{1}{n} \Big)\tfrac{1}{\sqrt{n}}\times n^2 = \frac{1}{n^2\sqrt{n}}+\sqrt{n}$$
• Thanks. I did not calculate the coordinates of large valued point... | {
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# Definition of liminf of sequence of functions?
1. May 3, 2013
### mathmonkey
1. The problem statement, all variables and given/known data
Hi I've come across the term lim inf $f_n$ in my text but am not sure what it means.
$\lim \inf f_n = \sup _n \inf _{k \geq n} f_k$
In fact, I am not sure what is supposed to... | {
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5. May 4, 2013
### micromass
Staff Emeritus
If you understand limsup/liminf of sequences of points, then this isn't too hard. Basically, you take a sequence of functions $(f_n)_n$. Now, if I take a fixed $x$, then $x_n = f_n(x)$ is a sequence of points. So the liminf makes sense. Now, we define
$$f(x) = \liminf x_n$... | {
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What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$?
What is the value of : $$\arctan(1/2)+\arctan(1/5)+\arctan(1/8)?$$
I tried to do geometric solution::
Where in the angles we are looking for are shown, but I can't solve it. Can we use it with this kind of approach? Can someone also post a solution using... | {
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• yes i got 45 already but where can u find the other inverse formulas? – SuperMage1 Dec 4 '17 at 10:16
• oh wait u already linked it, thanks – SuperMage1 Dec 4 '17 at 10:17
• Yes, see the link. For the $\arctan$ see also the addition formula for $\tan$. – Robert Z Dec 4 '17 at 10:19
You can also directly use the foll... | {
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# Question about vertical oscillations and energy
1. Aug 3, 2011
### ustudent
I have a few questions regarding vertical oscillations (not damped). Let's say you have a spring hanging from a ceiling with a mass attached to it. So, for example, if I had a mass attached to a spring and I pulled it down by 10 meters, if... | {
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Now turn the system so it's vertical (with the mass at position z above rest position):
$$F = -kz - mg = \frac{d^2 z}{dt^2}.$$
You can make this look exactly as before by making a substitution:
$$-kz - mg = -kx,$$
$$z = x - mg/k.$$
Nothing changes on the right hand side since
$$\frac{d^2 x}{dt^2} = \frac{d^2 z}{dt^2}.$... | {
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