Wikipedia:Reference desk/Archives/Mathematics/2008 May 10
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May 10
[edit]Nodes of Vibrating Plate
[edit]I've seen this video [1] and others like it many times, but I can't find what shape those curves are - a maathematical description of them. Can anyone point me in the right direction? Black Carrot (talk) 02:32, 10 May 2008 (UTC)
- Those are Chladni plate interference surfaces
- They have a *LOT* of applications in the design of wood saw blades to reduce noise. 71.193.2.115 (talk) 14:10, 10 May 2008 (UTC)
Parabolas and Lines
[edit]Hello. One of my students (I am a mathetmatics tutor) has a problem which I am unable to help them with. They need to do the following:
Given the parabola, y=X^2
- write an equation of the line through a point P (a,a^2) with slope m.
- Write a quadratic equation involving x and m that must be satisfied by all points of intersection of any line through point P and the parabola.
- Find the slope of a tangent line m, in terms of a. (Hint: The tangent line to a parabola intersects the graph only once.)
—Preceding unsigned comment added by 64.26.98.90 (talk) 20:39, 10 May 2008 (UTC)
- fixed format of original question -- Meni Rosenfeld (talk) 20:45, 10 May 2008 (UTC)
- 1 is a standard "find a line with a given slope through a point" exercise. For 2 - you have found the equation of a general line through P. Now you just need to equate it to the parabola. For 3 - use the hint. -- Meni Rosenfeld (talk) 20:45, 10 May 2008 (UTC)
- Seems to me that calculus could be used to find the answer to question 3. Zrs 12 (talk) 21:45, 10 May 2008 (UTC)
- No need for that - you already have a way of finding the points of intersection of a line through P with the curve, the tangent to the curve at P is the line that intersects the curve at only P (with multiplicity two). That's easy enough to find (I won't say more). --Tango (talk) 22:01, 10 May 2008 (UTC)
- Presumably, the question was posed to a class which hasn't studied calculus yet, or was supposed to demonstrate that there are some things you could do even without calculus. I think it does the latter rather nicely. -- Meni Rosenfeld (talk) 22:35, 10 May 2008 (UTC)
- I agree - it's a nice question. --Tango (talk) 23:55, 10 May 2008 (UTC)
Number of unique outcomes for 5 dice
[edit]How many unique outcomes are there if 5 dice are rolled simultaneously?
1 2 3 4 5 and 2 3 4 5 1 should be considered the same outcome, since they have the same combination of numbers.
Similar problems for 5 dice:
a) What is the probability of three 1's on a single throw?
b) What is the probability of throwing three 1's and two 5's on a single throw?
c) What is the probability of rolling the dice from 1 through 5?
Can you show me the technique for solving these problems?
—Preceding unsigned comment added by 68.99.185.240 (talk) 22:49, 10 May 2008 (UTC)
- Take a look at our article combinatorics, and pick up a book on the subject if you want to know more. The first question is a problem of combinations with repetitions, with 5 draws out of a pool of 6 objects. Thus the answer is . -- Meni Rosenfeld (talk) 23:11, 10 May 2008 (UTC)
- For part (a), it matters if you want exactly, or at least 3 1’s. Exactly three 1’s would be 5C3 * 1/6^3 * (5/6)^2. 5C3 to choose the three dice that are 1’s. 1/6 for each of the 1’s, and 5/6 for each of the not-1’s. The method for many problems of this sort, involves multiplying the probability for each of the different events that occur simultaneously (in this case the rolling of the 5 dice), and how many ways it can occur. (the 5C3 above, for the number of ways of choosing 3 dice of the 5). GromXXVII (talk) 23:25, 10 May 2008 (UTC)
- If by (c) you mean rolling a one, a two, a three, a four, and a five in any order, then it's fairly simple to calculate it intuitively by comsidering what would happen if you rolled each die individually. The first one could be any of those five numbers (probability, 5/6) . The second could be any number except for six or the number on the first die (prob. 4/6)the third could be any number except six and the two numbers already rolled (prob. 3/6) and so on. The prrobabiolity of rolling a 1, a 2, a 3, a 4, and a 5 in any order is thus (5/6)*(4/6)*(3/6)*(2/6)*(1/6) = 5!/(6^5) = 5/324 = 0.0154 = 1 in 64.8 Grutness...wha? 00:45, 11 May 2008 (UTC)