Wikipedia:Reference desk/Archives/Mathematics/2018 March 4

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

March 4

A design wind is defined as a 50-year wind (p=0.02)

The rest of the question, the answer and my attempt follow.[1] I don't understand why my attempt is wrong. Thank you in advance as always. 151.202.5.26 (talk) 01:15, 4 March 2018 (UTC)

But you're not wrong. There can be more than one way to enumerate the possible outcomes, which is what happened here. Hint: it might be a good idea to double check the book's computation of the numerical approximation. –Deacon Vorbis (carbon • videos) 02:14, 4 March 2018 (UTC)

I've performed the two calculations many times. The book's answer gives 1.24E-4, while mine gives 7.76E-5. The professor didn't want to go into details, perhaps because he hadn't covered it, but he said that my method calculates a different scenario. 151.202.5.26 (talk) 02:43, 4 March 2018 (UTC)

No, if you plug p = 0.02 into the book's answer, you get the same value that you're getting for your answer too. The book's answer is right, but its computation of an approximate value for that answer was wrong. I don't know where that number is coming from, but everything else is otherwise in agreement. The book's solution is only counting up to the 3rd success, whereas yours is counting all possibilities within the first 5 trials (or rather you're actually counting the complementary probability and subtracting from 1, but that doesn't really save you anything for this problem). But both approaches are correct and give the same answer. –Deacon Vorbis (carbon • videos) 02:53, 4 March 2018 (UTC)

The book's final answer is not an estimation, just a rounding.[2] 151.202.5.26 (talk) 03:00, 4 March 2018 (UTC)

Oh, the book forgot to divide 4*3 by 2 as I did? Thank you. 151.202.5.26 (talk) 03:04, 4 March 2018 (UTC)

The two expressions are equal for all p. So if the book gives a different value then either they are using a different value of p to start with, hard to tell without the first part of the problem, or they simply made a mistake in calculation. I get 7.76192E-5 for the expression when p=.02. --RDBury (talk) 04:00, 4 March 2018 (UTC)

What is the solution of this circuit by using thevenin theorem?

Here is a QUESTION — Preceding unsigned comment added by 39.40.141.28 (talk) 11:14, 4 March 2018 (UTC)

I don't know what thevenin theorem is, but basic circuit analysis gave me 63/13 mA and 108/13 V, no guarantee of correctness however.→31.53.2.226 (talk) 12:51, 4 March 2018 (UTC)

As 31.53.2.226 suggests, the problem can also be worked via basic circuit analysis, but they seem to have made a mistake in their calculation and their numerical answer is incorrect. To work this problem via Thévenin's theorem, you are to consider the points where the load attaches above and below R₂ to be terminals A and B. The easiest way to determine the source's equivalent voltage and resistance is to consider the two extremes of R_L=∞Ω and R_L=0Ω. In the first (open circuit) case all the current in the actual circuit passes through R₂ and it is easy to calculate the voltage across the A-B terminals. Since there would be no current in the equivalent circuit under this condition, that voltage must be V_Th. In the second (short circuit) case, no current in the actual circuit passes through R₂, so it is easy to determine the current through the shorted load. Since R_Th is all that is limiting current in the equivalent circuit under this condition, that resistance must be V_Th divided by the current you calculated. Now consider the equivalent V_Th/R_Th/A-B circuit with your given load R_L=4kΩ and determine the load's current and voltage. Once you have done that you may wish to verify your work by basic circuit analysis, showing that the answers (which are not what 31.53.2.226 gave) match. That should get you going, and you will learn more if you can work this problem through on your own, but let us know if you need more help. While it took some time to explain how to apply Thévenin's theorem, it is quicker and easier (for me, at least) to do the calculation that way than via basic circuit analysis, and it is particular useful if you wish to know the current and voltage for a variable load. But remember that it only tells you what is happening with the load, not with the actual source. -- ToE 14:27, 4 March 2018 (UTC)

The current through the system is $36/(6+3*4/(3+4))=14/3$ mA. The voltage at the load is $36-14/3*6=8$ V. Then the load current is $8/4=2$ mA. Ruslik_Zero 20:36, 4 March 2018 (UTC)