• Yesterday, 13:38
Well, let's see...the characteristic equation is: r-2=0\implies r=2 And thus, the closed form will take the form: a_k=c_12^k Now, we must...
11 replies | 158 view(s)
• Yesterday, 13:13
Typically, when you solve a recurrence relation (difference equation), you turn the relationship between successive values of the recurrence into a...
11 replies | 158 view(s)
• Yesterday, 13:04
I agree that: a_k=2a_{k-1} My reasoning would be: a_k=(\text{number of color choices})\cdot a_{k-1} Each time we add a tile, we have 2...
11 replies | 158 view(s)
• Yesterday, 12:50
If we assume the dominoes are 1 X 2, and we assume there will be no blank spaces (i.e. the chart is completely filled), then we must assume $n$ is...
11 replies | 158 view(s)
• Yesterday, 11:53
In my opinion, this is the most poorly constructed problem I've seen in quite some time (shame on whoever assigned this to students). Why were...
11 replies | 158 view(s)
• Yesterday, 02:04
Hi MHB, sorry for missing one week of high school's POTW, I guess I can make it up by posting two POTWs this week.(Blush) Here is this week's...
0 replies | 53 view(s)
• Yesterday, 00:16
Yes, now it makes sense to me the think of the "worst case scenario" for $n$ cards (let's call this $W_n$) to be: ...
9 replies | 171 view(s)
• April 22nd, 2017, 21:09
Only when the roots of the characteristic equation are imaginary do you typically express the homogeneous solution as a sinusoid. For example, if the...
5 replies | 116 view(s)
• April 22nd, 2017, 19:59
What I used to like to do as a student, when presented with a batch of similar problems, is to generalize to get a formula I could use. Suppose we...
5 replies | 116 view(s)
• April 22nd, 2017, 19:01
This problem is almost identical to the previous. What is your homogeneous solution $y_h$?
5 replies | 116 view(s)
• April 22nd, 2017, 16:22
Hello and welcome to MHB! (Wave) Using a thread title of "probability and statistics" in our forum titled "Basic Probability and Statistics" is...
1 replies | 45 view(s)
• April 22nd, 2017, 16:01
I didn't notice before, but your characteristic roots are incorrect...we actually have: r\in\{-2,0\} And so the general solution is: ...
7 replies | 118 view(s)
• April 22nd, 2017, 13:29
The dimensions are length $\ell$, width $w$ and height $h$. Suppose we know $\ell$ and $w$ to be 6 and 2 respectively. A rectangular prism (cuboid)...
3 replies | 75 view(s)
• April 22nd, 2017, 13:15
Here is this week's POTW: ----- In a triangle $ABC$, $\tan A:\tan B: \tan C=1:2:3$. Find $\dfrac{AC}{AB}$. ----- Remember to read the...
0 replies | 43 view(s)
• April 22nd, 2017, 13:12
Congratulations to the following members for their correct solution::) 1. Opalg 2. kaliprasad Solution from Opalg: Let $f(x) = x^2 + \pi x +... 1 replies | 122 view(s) • April 22nd, 2017, 12:32 I also thought that might be the intended problem. :D 6 replies | 128 view(s) • April 22nd, 2017, 12:26 Interesting...I also thought 60 would be the maximum number too. (Thinking) 9 replies | 171 view(s) • April 22nd, 2017, 11:31 I don't have a proof yet, but I'm convinced that the answer for n cards is n(n+3)/2-1. So for n=10, the answer is 64. If I can come up with a... 9 replies | 171 view(s) • April 21st, 2017, 22:24 I've moved the thread, and will wait until someone more proficient at probability to chime in. :D 6 replies | 128 view(s) • April 21st, 2017, 22:15 I think to begin, I would imagine that Randi has the cards arranged in the same order she will seek them...for example suppose she will seek them in... 9 replies | 171 view(s) • April 21st, 2017, 21:25 Suppose$x\ne0$and you divide both sides by$x^6$...what do you get? 6 replies | 128 view(s) • April 21st, 2017, 19:33 I was getting ready to reply that you need another initial condition, but you've fixed that. Also, I moved the thread to "Differential Equations" as... 7 replies | 118 view(s) • April 21st, 2017, 00:15 MarkFL replied to a thread Average value derivation in Calculus Yes...that's good. :D 5 replies | 81 view(s) • April 20th, 2017, 23:42 MarkFL replied to a thread Average value derivation in Calculus Well, think of it this way: Consider first only from$x=0$to$x=\pi$. The area$A_1$under the curve is equal to the area of the rectangle with... 5 replies | 81 view(s) • April 20th, 2017, 22:37 Let's look at the region over which we are to integrate: If we use horizontal strips, we see they are bounded on the left by$x=-\sqrt{4-y^2}$... 4 replies | 74 view(s) • April 20th, 2017, 21:50 Let's first look at the region$D$over which we are directed to integrate: Now if we use horizontal strips, then we see they are bound on the... 5 replies | 77 view(s) • April 20th, 2017, 15:55 MarkFL replied to a thread Average value derivation in Calculus The average value$M$of a function$f(x)$over some interval$$where$a<b$is given by: M=\frac{1}{b-a}\int_a^b f(x)\,dx Suppose we use a... 5 replies | 81 view(s) • April 20th, 2017, 10:35 From the region$D$...in this case it is a rectangular region bounded by the lines x=-\pi,\,x=\pi,\,y=0,\,y=\frac{\pi}{2}. 6 replies | 86 view(s) • April 20th, 2017, 10:31 That's where the sketch of the region$D$comes in...for example when using horizontal strips, we see they are bounded on the left by the line$x=0\$...
4 replies | 63 view(s)
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37 Visitor Messages

1. Happy birthday, caffeinemachine!
2. Yes caffeinemachine, I have a different solution of my own. I would have posted it along with johng's yesterday, but I was in a hurry, as I needed to get other things done. I might post it later today.
3. Thank you! It's been a bit hectic, what with moving to Kansas, and all. But I did have a great birthday.
4. Hi caffeinemachine. Very sorry that this is happening. Could you make a thread in our feedback forum describing what is happening when you get a moment? We will try to fix it ASAP.
5. My interests lie in dispersive wave equations and geometric analysis. You have a pretty interesting combination: combinatorics and geometry. So will you do combinatorial geometry or geometric combinatorics?
6. Hi caffeinemachine! I just wanted to wish you a happy birthday, and I hope you're having a great time.
7. Hey, just wanted to thank you. I didn't know the command \widehat existed until I saw you using it in your question about modules. Hope you get an answer, haha.

Best wishes.
8. Happy Birthday, my friend!
9. Hi AK,

I wish you luck, happiness, health and safety today, tomorrow and beyond...

As you look back on yesterday, may your memories be warm ones. As you celebrate today, may your heart be filled with happiness and joy. As you look ahead to tomorrow, may your deepest hopes and dreams come true for you!

I wish that for every extra candle on your cake, you receive an extra reason to smile. Happy Birthday to you!
10. Hi, I'm currently traveling but will get back to you later today. Thank you for your patience!
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Basic Information

Date of Birth
April 13, 1991 (26)
Biography:
I obtained a master's degree in mechanical engineering in May 2014.
Then I went on to join a master's programme in mathematics and obtained a master's degree in July 2016. I am currently a first year PhD student in mathematics. I love fountain pens and am a die hard fan of the Prince of Persia 2008 video game.
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