• Yesterday, 11:10
Solution using complex analysis: Let $z = e^{i\theta}.$ Then $\sin\theta = \frac1{2i}(z - z^{-1})$, $1 - 2a\cos\theta + a^2 = (z-a)(z^{-1}-a)$ and...
2 replies | 77 view(s)
• Yesterday, 10:55
Ackbach replied to a thread [SOLVED] Complex Variables - Legendre Polynomial in Analysis
So, we have \begin{align*} \omega&= z+\sqrt{|z^2-1|} \, e^{i\theta} \\ \omega - z &=\sqrt{|z^2-1|} \, e^{i\theta} \\ d\omega &=\sqrt{|z^2-1|}...
2 replies | 49 view(s)
• November 18th, 2017, 13:51
On the right track! So here's our confidence interval formula: \overline{x} \pm t^{*} \frac{s}{\sqrt{n}}. Like you wrote, we just care about...
3 replies | 75 view(s)
• November 18th, 2017, 10:40
I think this question has to do with the lower bound of the confidence interval since the mean of the sample is above 100. What is the formula you've...
3 replies | 75 view(s)
• November 17th, 2017, 13:33
Different authors use different notations, but it's been my experience that those two notations mean the same thing on vectors. One caution: the...
2 replies | 74 view(s)
• November 17th, 2017, 13:22
I like Suppes myself.
1 replies | 33 view(s)
• November 17th, 2017, 13:21
Enderton is good.
1 replies | 24 view(s)
• November 17th, 2017, 13:18
Ackbach replied to a thread Firefox Quantum in Chat Room
Still not as fast as Vivaldi. I'm going to stick with Vivaldi for a while, even though BB codes behave weirdly on MHB during editing (always pushes...
3 replies | 102 view(s)
• November 17th, 2017, 08:20
Oh nice! My apologies, I think this didn't exist. I just checked the AdminCP and I think we are using 3.7.17. Does that help or make sense?
6 replies | 111 view(s)
• November 16th, 2017, 23:43
Hi MarkFL, I have an idea for vB4 product: limiting error emails to once per time frame. As you know when any database crashes or some other...
6 replies | 111 view(s)
• November 16th, 2017, 18:14
Here is this week's POTW: ----- Prove that every nonzero coefficient of the Taylor series of \ about $x=0$ is a rational number whose...
0 replies | 49 view(s)
• November 16th, 2017, 18:12
Congratulations to castor28 for his correct solution to the Putnam Archive Problem B-1 from 2007, which follows: Since $f$ has integer...
1 replies | 95 view(s)
• November 16th, 2017, 12:21
I thought this was rather ... epic. Enjoy!
1 replies | 51 view(s)
• November 16th, 2017, 10:17
If you have factorised $n^2 - 14n + 40$, then the only cases where this could represent a prime would be when one of the factors is $\pm1$ and the...
2 replies | 78 view(s)
• November 16th, 2017, 08:22
We don't know the standard deviation of the population, but we do know that SD of the sample. See this page. It looks like this isn't the way you are...
4 replies | 97 view(s)
• November 16th, 2017, 08:19
You may need to add an empty pair of braces before the superscript, like this: {}^{A}B. Otherwise, the superscript will attach itself to the previous...
3 replies | 85 view(s)
• November 15th, 2017, 23:21
Hi markosheehan, So this question basically comes down to finding a reasonable interval that we would expect the numbers to fluctuate between....
4 replies | 97 view(s)
• November 14th, 2017, 08:46
Hint: Factorise the quadratic expression $n^2 - 14n + 40.$
2 replies | 78 view(s)
• November 9th, 2017, 10:32
Here is this week's POTW: ----- Let $f$ be a polynomial with positive integer coefficients. Prove that if $n$ is a positive integer, then...
1 replies | 95 view(s)
• November 9th, 2017, 10:30
No one solved this week's POTW, which was B-6 from the 2015 Putnam archive. The solution, from artofproblemsolving.com, follows: ...
1 replies | 122 view(s)
• November 8th, 2017, 00:34
Hi RTCNTC, 1) There's no hard rule on how many values you should use. The more values you use the smoother/accurate the graph would be. 2)...
5 replies | 105 view(s)
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9 Visitor Messages

1. Hello and welcome back to MHB, Alexmahone!

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MarkFL.
2. Hello and welcome back to MHB, Alexmahone!

We are happy to see that you have returned, and we look forward to your continued participation here!

On Behalf Of MHB's Staff,

Ackbach.
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