Activity for JRN
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #286926 |
Do they have to be first order ordinary differential equations? (more) |
— | over 1 year ago |
| Edit | Post #286612 | Initial revision | — | almost 2 years ago |
| Question | — |
Notation for nested exponents An expression such as $a^{b^c}$ is usually interpreted as $a^{(b^c)}$ and not as ${(a^b)}^c$. (See, for example, the Wikipedia entry for double exponential function.) Is there a reputable source that states how an expression such as $a^{b^{c^{\cdots^n}}}$ is to be interpreted? (more) |
— | almost 2 years ago |
| Comment | Post #285983 |
The handwritten text that you show is not Xi, it is Xi divided by overline Xi (as shown in Peter Taylor's answer). (more) |
— | about 2 years ago |
| Edit | Post #285018 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Intuitively, why can $a, b$ cycle in ${\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$? "what's the intuition why a,b can swap places, whilst c remains in the numerator?" It's called the commutative property of multiplication. If $ab=c$ leads to $b=c/a$, then $ba=c$ leads to $a=c/b$. (more) |
— | over 2 years ago |
| Comment | Post #284723 |
"*In fact, subtracting the additive inverse of $b$ to $a$ still counts as using the addition operator.*" If so, then your proposed method "$(a\times b)-(b-a)$" would involve addition, because it is just $a\times b-b+a$. (more) |
— | over 2 years ago |
| Comment | Post #283252 |
From the words in the text "by putting the cutoff for a positive result at a very low level (purple dashed line), you may capture all positive samples, and so the test is very sensitive." and the words in the image "To increase sensitivity, shift to the left (blue line)," it can be concluded that the... (more) |
— | over 2 years ago |
| Comment | Post #283945 |
You say "Solve all operations" but it seems that you mean "perform all operations." Instead of "equation solving," it seems that you are interested in "expression evaluation." For example, when you evaluate the expression "4(3+2)" as "20," you are not solving any equations (the expression does not ... (more) |
— | over 2 years ago |
| Edit | Post #283388 |
Post edited: Fixed formatting |
— | over 2 years ago |
| Edit | Post #283638 | Post undeleted | — | over 2 years ago |
| Edit | Post #283638 |
Post edited: Fixed error |
— | over 2 years ago |
| Edit | Post #283638 |
Post edited: Fixed error |
— | over 2 years ago |
| Edit | Post #283638 | Post deleted | — | over 2 years ago |
| Edit | Post #283638 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Is $r \times \frac{d}{dt} mv=\frac{d}{dt} (r \times mv)$ In equations 1.9 and 1.10, the quantities $\mathbf{r}$, $\mathbf{F}$, $\mathbf{N}$, and $\mathbf{v}$ are vectors, and the symbol $\times$ denotes a vector cross product operation. The product rule of differential calculus also applies to the vector cross product. That is, $\frac{\mathrm{d}}{\ma... (more) |
— | over 2 years ago |
| Comment | Post #283633 |
What is the result of a vector crossed with itself? (more) |
— | over 2 years ago |
| Comment | Post #283593 |
@#53922 A function can be a continuous function and yet still have a discontinuity at a point, as long as that point is not in its domain. (more) |
— | over 2 years ago |
| Comment | Post #283593 |
The graph of Desmos is correct. But the function is still a continuous function. Desmos "doesn't say" it is a continuous function, but it "doesn't say" that it is not a continuous function, either. (more) |
— | over 2 years ago |
| Comment | Post #283593 |
More specifically, while $f(x)=\frac{1}{x-1}$ is discontinuous at $x=1$, it is a continuous function because of what @r~~ said. (more) |
— | over 2 years ago |
| Suggested Edit | Post #283388 |
Suggested edit: Fixed formatting (more) |
helpful | over 2 years ago |
| Comment | Post #283317 |
@#54138 means the exponent must be zero, so it should be k (which is equal to zero) and it should not be k+1 (which is equal to one). (more) |
— | over 2 years ago |
| Comment | Post #283281 |
A line has length but it has no thickness. When you say "measure a perimeter," that means measuring its length. You don't need to measure its "thickness" because the "thickness" of a line is zero. I suggest that you edit your question to say that you are interested in the "thickness" because the t... (more) |
— | over 2 years ago |
| Comment | Post #283281 |
Based on your comments, it seems that you are asking about the "thickness" of the perimeter, and not its length. Is that correct? Are you basically asking how "thick" a line is? (more) |
— | over 2 years ago |
| Edit | Post #282998 |
Post edited: OP says they meant to say "variable," not "function." |
— | over 2 years ago |
| Suggested Edit | Post #282998 |
Suggested edit: OP says they meant to say "variable," not "function." (more) |
helpful | over 2 years ago |
| Comment | Post #283086 |
This is the first link that comes up when I use DuckDuckGo to search for "integration under integral sign": https://mathworld.wolfram.com/IntegrationUndertheIntegralSign.html (more) |
— | over 2 years ago |
| Comment | Post #282998 |
Please edit your question to use the correct term. (more) |
— | over 2 years ago |
| Edit | Post #283023 | Initial revision | — | over 2 years ago |
| Answer | — |
A: What is a dummy variable (in an integral)? When integrating, a dummy variable is one that "disappears completely in the final result." For example, in the expression $\int x\ \mathrm{d}x$, $x$ is not a dummy variable because the expression is equivalent to $\frac{x^2}{2}+c$, that is, the $x$ hasn't "disappeared." If we had replaced $x$ wi... (more) |
— | over 2 years ago |
| Comment | Post #282998 |
Do you perhaps mean that $x$ is a dummy *variable*? (more) |
— | over 2 years ago |
| Edit | Post #282946 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Intuitively, why does A, B independent $\iff$ A, $B^C$ independent $\iff A^C, B^C$ independent? If events $A$ and $B$ are independent, then the probability that event $A$ happens is not affected by whether $B$ happens. If it isn't affected by whether $B$ happens, then it isn't affected by whether $B$ doesn't happen. (The rest of your statements can be shown to be true with the same reasoning.... (more) |
— | over 2 years ago |
| Comment | Post #282702 |
See, for example, https://pwg.gsfc.nasa.gov/stargaze/Strig5.htm (more) |
— | almost 3 years ago |
| Comment | Post #282623 |
Without context, it is difficult to answer your question. How are $f$ and $F$ related? Is $0\<\theta\<1$? Is $a\<b$? Is $h\>0$? (more) |
— | almost 3 years ago |
| Comment | Post #282623 |
I asked you to identify the book so I can look up the context, what was before and what was after the text you quoted. But your answer does not identify the book (you didn't state the author, publisher, or year of publication). Perhaps if you showed an image of the page of the book in question, the... (more) |
— | almost 3 years ago |
| Comment | Post #282623 |
From what book is this? (more) |
— | almost 3 years ago |
| Edit | Post #282620 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Why aren't the "21 possibilities here" NOT equally likely? If the $36$ ordered pairs are equally likely, then the probability of getting a cake cone with chocolate in the afternoon and a waffle cone with vanilla in the evening is $P($cakeC,waffleV$)=1/36$, and the probability of getting a waffle cone with vanilla in the afternoon and a cake cone with chocola... (more) |
— | almost 3 years ago |
| Comment | Post #282602 |
As it currently stands, your first question is inconsistent with what is in your image. (more) |
— | almost 3 years ago |
| Edit | Post #282610 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: "A occurred" vs. "something must happen" $A$ is a specific event, specified beforehand. Let's have an example. Let a random experiment be rolling a six-sided die and looking at what face lands up. The sample space is $S=\\{1,2,3,4,5,6\\}$. What is event $A$? Let's specify it before the experiment is done. Let $A$ be the event that... (more) |
— | almost 3 years ago |
| Comment | Post #282600 |
Also asked at https://matheducators.stackexchange.com/q/21150/77 (more) |
— | almost 3 years ago |
| Comment | Post #282013 |
Also asked at https://matheducators.stackexchange.com/q/20959/77 (more) |
— | almost 3 years ago |
| Edit | Post #282524 |
Post edited: |
— | almost 3 years ago |
| Edit | Post #282524 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: How can Abraham Wald's approach lead you to ignore crucial features of a problem? If we add 1000 g of ethanol to 18 g of ethanol, the result has a weight of 1018 g. If we add 1000 mL of water to 18 mL of water, the result has a volume of 1018 mL. A person who focuses on the abstract (and not the concrete) would only look at 1000+18=1018 (the "struts and nails"); the other de... (more) |
— | almost 3 years ago |
| Edit | Post #282478 | Initial revision | — | almost 3 years ago |
| Answer | — |
A: Why are you permitted to define $1 − 1 + 1 − 1 + . . .$? By definition, a positive real number is a real number greater than zero. That statement cannot be proved to be right; it cannot be proved to be wrong. We either reject it and use a different definition, or we accept it and move on. Consider the statement "$1-1+1-1+... = 0$." Here is a "proof... (more) |
— | almost 3 years ago |
| Edit | Post #282474 | Initial revision | — | almost 3 years ago |