Rillchritty's Posts
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MindHacker9009:You were taking square root! Edit: I just noticed you made the exact same mistake in evaluating the fourth root of 40x^2. Somehow , you seem to be mixing up fourth root (power of 1/4) and square root (power of 1/2). Why not try a bunch of numbers (apart from 0 and 1) on a calculator to see if your simplified expression matches the original?
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Connoisseur:You seem to have misinterpreted the information about the time taken for the return journey—it is not 2 hours; rather 2 hours more than the time taken for the forward journey. |
MindHacker9009:You made a mistake while evaluating the 4th root of x^6 |
rtdCivilservant:You can simplify it further. Also, a caveat needs to be added: the expression is only valid for non-zero values of x.
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SolarEngr:Hi. You forgot the quadratic term when multiplying the terms in the brackets.
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Thabothabo101:Yeah, I used latex with the Verbtex app, a latex editor for Android (https://play.google.com/store/apps/details?id=verbosus.verbtex). This is the latex source file: \documentclass{article} % Allow the usage of UTF-8 characters \usepackage[utf8]{inputenc} % Allow the usage of graphics (.png, .jpg) \usepackage{graphicx} \newcommand{\num}{8\times 10^{67}} % Start the document \begin{document} % Create a new 1st level heading \section*{} The main idea is to observe that $\num$ is a large number and then use limit. It is known that $\lim\limits_{x\to \infty} \left(1-\frac{1}{x}\right)^x = \frac{1}{e}$. Hence, the expression $1 - \left(1-\frac{1}{\num}\right)^{\num} \approx 1-\frac{1}{e} \approx 0.632$. Note that commonly available calculators cannot accurately evaluate the given expression. Due to their limited numerical precision, they evaluate $\frac{1}{\num}$ as zero, thus incorrectly giving the final answer as 0. To correctly evaluate the expression numerically, one may use MATLAB, Octave, or any other computational software that supports variable-precision arithmetic. The one-line code in MATLAB or Octave is: \\ \\ vpa(1 - (1-1/sym(8e67))\^{}sym(8e67), 64) \\ The second argument (\textbf{64}) passed to the \textbf{vpa} function is the number of significant digits in the final answer. Setting it too low will result in inaccurate evaluation. % Uncomment the following two lines if you want to have a bibliography %\bibliographystyle{alpha} %\bibliography{document} \end{document} |
GABRIEL6036:That's exactly the answer I already gave in my original reply! And for goodness sake, format your post properly; it is hardly readable. |
sunsweet33:It depends on the level of precision required in the application. If your application involves computation with numbers as large as 8*10^67, then surely, the precision offered by common calculators is going to be inadequate. |
Light78:The approximation in your second step is not precise enough. Check my reply to @GABRIEL6036's post above. |
GABRIEL6036:Careful with your assumptions! For a large number x, although 1/x is close to zero, the expression (1 - 1/x)^x is NOT close to 1. Its value is approximately 1/e, where e is Euler's number (e = 2.71828). To understand why that is so, read about limits in any introductory calculus textbook. If you are not convinced, try to evaluate (1 - 1/x)^x for a set of increasingly large numbers that your calculator can handle, say, x = 8*10^16, 8*10^17, 8*10^18,... What you will notice is that the answer keeps getting closer and closer to 0.36787944117144, and when you get to about 8*10^31, you suddenly start getting 0 (showing that the numerical precision of the calculator is no longer enough for accurate evaluation of the expression). To avoid this, one must use variable precision arithmetic instead (MATLAB and Octave support that functionality). |
sunsweet33:Yes, I can authoritatively say that they are all wrong! I explained in my original reply why a calculator that does not have capacity for variable precision arithmetic CANNOT correctly evaluate the expression. |
Winterhaven:I have modified my reply above to include the logic of the solution. |
The answer is approximately 1-1/e = 0.632. I will upload the workings when I get to my laptop. Edit: See the attached image for the evaluation
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Jewessgratitud3:As I already said, the long 'I' and the short 'i' are NOT variants of the same sound. Being termed 'long' and 'short' does not mean that they are distinguished by duration only. They sound completely different when correctly pronounced. Listen carefully to the British (and American) pronunciation of 'seen' (https://dictionary.cambridge.org/pronunciation/english/seen) and 'sin' (https://dictionary.cambridge.org/pronunciation/english/sin). |
Rexymania: |
KanielOutis92:The words 'porn' and 'pun' are not homophones; their phonetic representations are /pɔːn/ and /pʌn/. Most Nigerians incorrectly pronounce the short vowel /ʌ/ either as short 'o' (as in 'lot') or as the long vowel sound /ɔ:/ (as in 'lord'). Actually, it is closer to the schwa sound than any of these two. My post assumes British English. |
poshestmina:In addition to what others have highlighted, 'seen' and 'sin' are not homophones; they do NOT sound the same at all. The former has the long 'I' sound, whereas the latter has the short 'i' sound. Note that these two vowel sounds are phonetically distinct and require different lip opening and tongue positions to pronounce. Unfortunately, Nigerian students are not taught to properly distinguish them. Another example is 'sheep' and 'ship'. The words 'save' and 'safe' feature two different consonants: 'v' and 'f', respectively. |
Verbtips:Island, perhaps? The former is surrounded by the latter. |
Verbtips:Of course, the exercise is not intended to test mathematical prowess. However, ability to understand the different possible patterns in which valid answers could be constructed is a good 'small reasoning' skill. After all, innovative solutions to real-world problems are sometimes inspired by trivial questions like this one. |
Assuming each expression is independent of the preceding expressions, the general rule is a + b = a * (b+1). Hence, 5 + 11 = 5 * (11+1) = 60. Conversely, if an expression depends on the one immediately preceding it, then the answer by @snowball11 is also correct. The general rule in this case is c(n) = a+b = c(n-1)+a+b, so c(4) = 5+11 = c(3)+5+11 = 24+5+11 = 40. (edit) It turns out there is another possible answer (see @Panda7's post below). The structure of each expression is c(n) = a(n+2) + b(n+2), where a(n+2) is the (n+2)th Fibonacci number, and b(n+2) is the (n+2)th arithmetic integer. The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, .... [1], while the arithmetic integer sequence is 1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22,... [2]. The general rule is c(n) = a(n+2) + b(n+2) = a(n+2) + n*b(n+2). Hence, c(4) = a(6)+b(6) = 5+4*11 = 49. This last approach, inspired by @Panda7's answer, perhaps overcomplicates the solution, but it explicitly shows how the terms of the expressions are constructed. It is more general and mathematically sound than the other two approaches already listed. In fact, one may construct subsequent expressions independent of preceding expressions, for example, the next expression is c(5) = 8 + 13. References: [1] https://en.m.wikipedia.org/wiki/Fibonacci_sequence [2] https://en.m.wikipedia.org/wiki/Arithmetic_number |
The radius of the smaller ball is 2 times cube root of 3 (i.e., cube root of 24). See the attached image.
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ntrukpum:Find the solution in the attached images. The first method uses substitution to solve the two simultaneous equations resulting from the matrix and vector multiplication, while the second method approaches the problem as an eigenvalue decomposition problem (you can read about eigenvalue decomposition in any introductory textbook on linear algebra).
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Hi. Please, at what bus stop or place do I need to alight when travelling to Shasha Road Akowonjo (either De Santos Hotel or GIGM terminal) from Oshodi? I know that buses go directly from Oshodi to Egbeda-Akowonjo area, but I don't know where to alight. Please help. Thank you in advance. |
It costs about 60k naira at B.Y. Mafit (https://www.gregmattoeflnigeria.com/toeflcentresinnigeria/). The official cost is $195 (https://www.ets.org/toefl/ibt/about/fees/). |
Kylekent59:Your expansion of the right-hand term is wrong!!
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Only two per state, apart from Benue and Kano States. No special treatment for oil producing states. I was expecting up to five from each state. |
Lekzen:Hi, unfortunately, I didn't make it to the interview then. However, they just rescheduled me again for next week. According to them, it is going to be a practical interview, in which you show them what you can do. |
The woman (No 3) is the culprit. Reasons - 1. it is women's toilet (a man entering a ladies room would certainly raise suspicions). 2. the surprise on the waiter's face on seeing another woman at the table (the now deceased woman must have been sitting there before). 3. the woman was stabbed in the back (implying her back was turned towards the culprit, while she was using the washroom; were a man the killer, the victim would probably be facing him, possibly screaming too, the moment he enters). Of course there's a little case against No 4 (missing table knife, stain (blood??) on the neck). However, the case against No 3 is stronger. |
Hi. What are the subfields of photonics (applied or fundamental), which are currently the subject of active academic research? I have long been inclined towards optical fiber sensing, toyed a little with the idea of researching multiplexing techniques. However, the more I read research papers, the more I feel that there is no gap left. Quite frustrating! Semiconductor photonics seems to be an interesting research subfield, but I cannot come up with any original research ideas. Please, if anyone could point me in a good direction, I would very much appreciate it. Thanks |
josefayo:I got rejection email on 4th July |
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