• October 15th, 2017, 22:29
MarkFL replied to a thread Show AB = BC in Pre-Calculus
It tells you the three points are collinear...now, is point $B$ the midpoint of $\overline{AC}$ ?
9 replies | 92 view(s)
• October 15th, 2017, 22:00
MarkFL replied to a thread Show AB = BC in Pre-Calculus
Please attach the images inline...otherwise they won't show up in the "Topic Review" and having them show up there can be helpful when replying to a...
9 replies | 92 view(s)
• October 15th, 2017, 21:51
MarkFL replied to a thread Show AB = BC in Pre-Calculus
In order for three points to be collinear, we can pick any two distinct sets of two points from the set of three to form two line segments, and those...
9 replies | 92 view(s)
• October 15th, 2017, 16:11
Hello, MHB Community! (Wave) Those of you active in this forum have likely noticed some new thread prefixes associated with a few of the threads...
2 replies | 1870 view(s)
• October 15th, 2017, 04:16
Unsolved Challenge
Evaluate ∠APR in Challenge Questions and Puzzles
As soon as you know that $x = 1/\sqrt2$, it follows (by looking at the triangle $PNA$) that $\overline{AP} = 1$. So $Q,P,R$ all lie on a circle...
3 replies | 113 view(s)
• October 15th, 2017, 00:20
Unsolved Challenge
Prove √(sinx)>sin√(x) in Challenge Questions and Puzzles
Prove that $\sqrt{\sin x}>\sin \sqrt{x}$ for $0<x<\dfrac{\pi}{2}$.
0 replies | 54 view(s)
• October 14th, 2017, 22:40
Unsolved Challenge
Evaluate ∠APR in Challenge Questions and Puzzles
Hi Opalg! I can't tell you enough how much I appreciate your participation to the two unsolved challenges of mine...and you definitely are on a...
3 replies | 113 view(s)
• October 14th, 2017, 19:42
MarkFL replied to a thread Isosceles Triangle in Pre-Calculus
Yes, the distance formula would be a good way to proceed, but recall, an equilateral triangle is a special case of an isosceles triangle...so, you...
2 replies | 48 view(s)
• October 14th, 2017, 19:39
MarkFL replied to a thread Show AB + BC = AC in Pre-Calculus
Yes, and if this is true, then what must be true of the 3 points?
2 replies | 45 view(s)
• October 14th, 2017, 19:36
When doing synthetic division, the actual root $r$ or zero of the polynomial is put out to the left. Thus we know: f(r)=0 And the polynomial...
1 replies | 42 view(s)
• October 14th, 2017, 19:26
I am assuming the volume is the cubic polynomial: V(x)=2x^3+9x^2+4x-15 We are told the depth is $x-1$, so we know $1$ is a zero of the...
1 replies | 40 view(s)
• October 14th, 2017, 19:18
MarkFL replied to a thread Show AB = BC in Pre-Calculus
Yes, the distance formula would work, or if you can show the 3 points are collinear, then you could use the mid-point formula. :)
9 replies | 92 view(s)
• October 14th, 2017, 19:14
When I plug in the numbers, I get choice C). W|A - 40000(0.11/12)/(1-(1+0.11/12)^(-30*12))
2 replies | 58 view(s)
• October 14th, 2017, 16:09
Unsolved Challenge
Evaluate ∠APR in Challenge Questions and Puzzles
\coordinate (Q) at (-5,0) ; \coordinate (P) at (-3.5,3.5) ; \coordinate (R) at (5,0) ; \coordinate (A) at (0,0) ; \coordinate (N) at...
3 replies | 113 view(s)
• October 14th, 2017, 12:24
Unsolved Challenge
Prove ∠A≤60°. in Challenge Questions and Puzzles
I can only say thank you, Opalg, for your so insightful and intelligent solution! (Sun)(Cool)
2 replies | 116 view(s)
• October 14th, 2017, 06:05
Unsolved Challenge
Prove ∠A≤60°. in Challenge Questions and Puzzles
Start with a bit of calculus. If $0<b\leqslant c$ and $f(x) = x(b+c-x)$, then $f(x) \geqslant bc$ whenever $b\leqslant x\leqslant c.$ The reason for...
2 replies | 116 view(s)
• October 14th, 2017, 02:19
Unsolved Challenge
Evaluate ∠APR in Challenge Questions and Puzzles
Let $A$ be the midpoint of the side $QR$ on a triangle $PQR$. Given that $\angle APQ=3\angle APR$ and $\angle PAQ=45^\circ$, evaluate $\angle APR$.
3 replies | 113 view(s)
• October 13th, 2017, 12:28
Unsolved Challenge
Prove ∠A≤60°. in Challenge Questions and Puzzles
Hello MHB, This is the first of our "Unsolved challenge" threads, it is a challenge which I found pretty interesting but yet I still couldn't...
2 replies | 116 view(s)
• October 13th, 2017, 12:14
Here is this week's POTW: ----- Consider the sequence $\{a_k\}_{k\ge 1}$ is defined by $a_1=1$, $a_2=\dfrac{1}{2}$ and...
0 replies | 57 view(s)
• October 13th, 2017, 12:05
Congratulations to the following members for their correct solution: 1. MarkFL 2. lfdahl Solution from MarkFL: By cyclic symmetry, we know...
1 replies | 99 view(s)
• October 13th, 2017, 07:04
If $z\in A\cap U^*$ (which is a nonempty set) then $z\notin A \cap U^*\cap V^*$ (because $A \cap U^*\cap V^*$ is empty). In particular, $z\notin... 2 replies | 52 view(s) • October 13th, 2017, 04:04 Starting from the fact that$e^t \to \infty$as$t\to\infty$, it follows that$\lim_{t\to\infty}e^{-t} = \lim_{t\to\infty}\dfrac1{e^t} =...
2 replies | 38 view(s)
• October 13th, 2017, 02:54
Let's let $D$ be the amount of the end of year deposits, and $i$ be the annual interest rate. So, the amount of the account at the end of year $n$...
2 replies | 46 view(s)
• October 12th, 2017, 09:29
MarkFL replied to a thread New here in Introductions
Hello and welcome to MHB, Johny! (Wave)
3 replies | 157 view(s)
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### 14 Visitor Messages

1. Thanks, you are doing a great job. I went through your Laplace transform tutorial. It is a good practice to try the Laplace transform of some new functions, and it is fun as well.
2. Er, DW, your .sig seem to be getting out of the separator of every post, so sometimes they are almost unreadable. Can you do something about it?
3. Wow, thanks for the new tutorial DW, it's just what I needed, a brief series of values of polygamma function and a closed formula in general. Thanks again! (To reply Visitor Messages, first click on "View Conversation" then reply to it)
4. Thanks for the tip, Balarka!! I've corrected it now... Was referencing a paper on arXiv.
5. DW, in your #3 post in "Generalized Log-Trig series related to the Hurwitz Zeta", shouldn't the Dirichlet characters be defined over $\mathbb{Z}/8\mathbb{Z}$ instead of what is given? $\mathbb{Z}/8$ is a weird beast...
6. DW, you should post those special value of Clausen function you have found out on the wiki article. It's nearly stub, I wonder why they didn't add that tag to it.
7. Not a bad idea, but it takes all the fun out of it...

It is pretty funny, mind... Folks join up, can get their heads around mind-bending equations, but fall foul of basic forum software. Oh dear!
8. Some have even humorously suggested we need to present a User's Manual to people when they join due to all the features we have here. Perhaps someday I will write such a manual...hehehe.
9. Thanks Mark! Just been toying around a bit and found out where to go. Cheers for your help!
10. Hey Gethin,

Here is a link to a topic explaining how to respond to visitor messages so that it gets posted on the recipient's wall:

http://mathhelpboards.com/questions-...hlight=message

Best Regards,

Mark.
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Conjecture: Life is ridiculous.

Proof: $\displaystyle X-Factor \in \{Life\}$, and $\displaystyle X-Factor \in \{ridiculousness\}$

$\displaystyle \therefore\, \{ Life \} \cap \{ ridiculousness \} \ne \varnothing \quad Q.E.D.\, \Box$

$\displaystyle {\color{Blue}\mathscr{H}\mathfrak{e} }{\color{Fuchsia}\, = \, } {\color{RedViolet} \mathcal{MC}} ^{\color{OrangeRed}\mathsf{\, Scared !!}}$

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