text stringlengths 1 2.12k | source dict |
|---|---|
Substitute $\theta = \arctan u$, use $\arctan' = \frac 1 {1+\operatorname{id_{\mathbb R}}^2}.$
(3)
For example, you can use $\tan^2(\theta) = \frac 1 {\cos^2(\theta)} - 1$. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836918,
"lm_q1q2_score": 0.843430100181866,
"lm_q2_score": 0.8499711794579723,
"openwebmath_perplexity": 1317.18050812644,
"openwebmath_score": 0.9962060451507568,
"tags"... |
# Is this functor representable?
Fix a group $G_0$ and $R$ a subset of $G_0$. Consider the functor $F$ from $\textbf{Grps}$ to $\textbf{Sets}$, sending every object $G$ in $\textbf{Grps}$ to $F(G)$, the subset of $\varphi \in \text{Hom}(G_0, G)$ such that $\varphi(r) = 1$ for every $r \in R$, and sending each homomorp... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864305585842,
"lm_q1q2_score": 0.8434217208675987,
"lm_q2_score": 0.8519528094861981,
"openwebmath_perplexity": 38.61756368464358,
"openwebmath_score": 0.9940912127494812,
"tag... |
# phitheta2uv
Convert phi/theta angles to u/v coordinates
## Syntax
``UV = phitheta2uv(PhiTheta)``
## Description
example
````UV = phitheta2uv(PhiTheta)` converts the phi/theta angle pairs to their corresponding u/v space coordinates.```
## Examples
collapse all
Find the corresponding u-v representation for φ ... | {
"domain": "mathworks.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864270133119,
"lm_q1q2_score": 0.8434217178471939,
"lm_q2_score": 0.851952809486198,
"openwebmath_perplexity": 1247.7665293903194,
"openwebmath_score": 0.9119930863380432,
"tags": ... |
In these expressions, φ and θ are the phi and theta angles, respectively.
In terms of azimuth and elevation, the u and v coordinates are
`$\begin{array}{l}u=\mathrm{cos}el\mathrm{sin}az\\ v=\mathrm{sin}el\end{array}$`
The values of u and v satisfy the inequalities
`$\begin{array}{l}-1\le u\le 1\\ -1\le v\le 1\\ {u}... | {
"domain": "mathworks.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864270133119,
"lm_q1q2_score": 0.8434217178471939,
"lm_q2_score": 0.851952809486198,
"openwebmath_perplexity": 1247.7665293903194,
"openwebmath_score": 0.9119930863380432,
"tags": ... |
# Manifold with minimum surface distance between two points
The book "The World is Flat" uses flatness as a metaphor for a global economy. In fact, a spherical world would seem to be better than a flat world in terms of reducing the distances between two random points on the surface of the world. The shorter the dista... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217174967449,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 238.28982508670364,
"openwebmath_score": 0.916797399520874,
"tag... |
Does it depend on how we define "average distance" or "randomly selected?"
-
I think there's only one natural definition of "randomly selected" -- if you can define the total surface area of the manifold, you must have a notion of area, and then "randomly selected" should mean that equal areas have the same chance of ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217174967449,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 238.28982508670364,
"openwebmath_score": 0.916797399520874,
"tag... |
$$\bar{d}=\frac{1}{6}(\sqrt{2}+\sinh^{-1} 1)\sqrt{A}\approx 0.383 \sqrt{A}\;.$$
So it's not true that a flat manifold has higher average distance than a sphere; it's the other way around. I suspect the comparison you mean is between a sphere and a flat disk; but a disk is a manifold with boundary, not a manifold, and ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217174967449,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 238.28982508670364,
"openwebmath_score": 0.916797399520874,
"tag... |
Putting everything together, we get
$$\begin{eqnarray} \int_{-1}^1\int_{-1}^1\sqrt{x^2+y^2}\mathrm dx \mathrm dy &=& 2\left\{\frac{1}{3}\left[ y^3\sinh^{-1}\frac{1}{y}+y\sqrt{y^2+1} \right]_0^1 +\left(1-\frac{1}{3}\right) \int_0^1\sqrt{y^2+1}\mathrm dy\right\} \\ &=& \frac{2}{3}\left[ y^3\sinh^{-1}\frac{1}{y}+y\sqrt{y... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217174967449,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 238.28982508670364,
"openwebmath_score": 0.916797399520874,
"tag... |
so yasmar's manifold indeed slightly improves on the one using a square lattice.
-
Nice answer. Could you elaborate on the average distance formula for the flat case? Also, is there a simple argument that this is optimal? – yasmar May 3 '11 at 18:52
I doubt that the flat case is optimal, since I can turn it into a tor... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217174967449,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 238.28982508670364,
"openwebmath_score": 0.916797399520874,
"tag... |
# Thread: Summing areas of squares
1. ## Summing areas of squares
A square S1 has a perimeter of 40 inches. The vertices of a second square S2 are the midpoints of the sides of S1. The vertices of a third square S3 are the midpoints the sides of S2. Assume the process continues indefinitely, with the vertices of S K+... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217156360932,
"lm_q2_score": 0.8519528057272543,
"openwebmath_perplexity": 573.8933711974821,
"openwebmath_score": 0.829239547252655,
"tags... |
= (1/2)^0 *100 + (1/2)^1 *100 + (1/2)^2 *100 + (1/2)^2 *100 + ...
so we can write this as a geometric series (see Geometric series - Wikipedia, the free encyclopedia for more about the formulas)
$= \sum_{n=0}^\infty 100(1/2)^n$
Now in a geometric series, if |r| < 1, the series converges to $\frac a{1-r}$
In our cas... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9899864287859482,
"lm_q1q2_score": 0.8434217156360932,
"lm_q2_score": 0.8519528057272543,
"openwebmath_perplexity": 573.8933711974821,
"openwebmath_score": 0.829239547252655,
"tags... |
370 views
Here are some very useful ways of characterizing propositional formulas. Start by constructing a truth table for the formula and look at the column of values obtained. We say that the formula is:
• satisfiable if there is at least one $T$
• unsatisfiable if it is not satisfiable, i.e., all entries are $F$
•... | {
"domain": "gateoverflow.in",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551566309688,
"lm_q1q2_score": 0.8433579371373999,
"lm_q2_score": 0.8740772450055545,
"openwebmath_perplexity": 791.2447326818984,
"openwebmath_score": 0.7985720038414001,
"tags"... |
option C : if f1 is contingency then also all given statements hold.
option D : from above 1st point we know at least one row of f1 is True and from above 2nd point we know when f1 is True, f3 must be True. Thus, we have value for at least one row (f1,f3) as (T,T). Thus, f1 ^ f3 is not contradiction.
Ans: Option A,D
... | {
"domain": "gateoverflow.in",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551566309688,
"lm_q1q2_score": 0.8433579371373999,
"lm_q2_score": 0.8740772450055545,
"openwebmath_perplexity": 791.2447326818984,
"openwebmath_score": 0.7985720038414001,
"tags"... |
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Feb 2019, 02:20
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551576415562,
"lm_q1q2_score": 0.8433579316908398,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 5108.094687502294,
"openwebmath_score": 0.6706599593162537,
"tags": n... |
A: 9
B: 12
C: 16
D: 18
E: 24
Originally posted by tanad on 17 Jun 2016, 14:12.
Last edited by Bunuel on 18 Jun 2016, 01:42, edited 2 times in total.
Renamed the topic and edited the question.
Intern
Joined: 17 Mar 2016
Posts: 4
Re: Six machines at a certain factory operate at the same constant rate. [#permalink]
###... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551576415562,
"lm_q1q2_score": 0.8433579316908398,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 5108.094687502294,
"openwebmath_score": 0.6706599593162537,
"tags": n... |
### Show Tags
17 Jun 2016, 23:37
2
1
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production orde... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551576415562,
"lm_q1q2_score": 0.8433579316908398,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 5108.094687502294,
"openwebmath_score": 0.6706599593162537,
"tags": n... |
### Show Tags
18 Jun 2016, 03:08
1
2
Six machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 27 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production orde... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551576415562,
"lm_q1q2_score": 0.8433579316908398,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 5108.094687502294,
"openwebmath_score": 0.6706599593162537,
"tags": n... |
So, working together 6 machines take 9 hours less ( 27 - 18 )
Quote:
Bunuel Sir and Abhishek Sir,
Please tell me if my approach is wrong.
Let "r" be the rate of the machine.
Rate * Time = Workdone
So,
4 r * 27 = 6 r *X
>>> X = 4*27/6
>>> X = 18
How many fewer hours does it take = 27 -18 = 9
Thanks again!
Regar... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551576415562,
"lm_q1q2_score": 0.8433579316908398,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 5108.094687502294,
"openwebmath_score": 0.6706599593162537,
"tags": n... |
# When Should I Use Taylor Series for Limits?
I get confused between when to apply L'Hospital Rule and Taylor Series.
Is there any set of trigger points in the questions, that would be easier to solve with Taylor Series?
For Example, If the denominator is in terms of a large power of $$x (>3)$$, then L'Hospital Rule ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551556203814,
"lm_q1q2_score": 0.8433579299241769,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 512.6000803160377,
"openwebmath_score": 0.8086636662483215,
"tag... |
1. Algebraic manipulation, aimed to eliminate the source of that indetermination, e.g.
$$\lim_{x\to 1} \frac{x^2-3x+2}{x^2-1}=\lim_{x\to 1} \frac{(x-1)(x-2)}{(x-1)(x+1)}=\lim_{x\to 1} \frac{x-2}{x+1}=-\frac12$$
2. Standard limits, e.g.
$$x\to 0, \quad \frac{\sin x}x\to 1, \quad \frac{e^x-1}{x}\to 1, \quad x\log x \t... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551556203814,
"lm_q1q2_score": 0.8433579299241769,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 512.6000803160377,
"openwebmath_score": 0.8086636662483215,
"tag... |
since by standard limits
$$\sin x \log x= \frac{\sin x}x\cdot x\log x\to 1 \cdot 0 =0$$
• But in an examination scenario, when time is of utmost importance, L'Hospital Rule would be the best way. – Harshil Bhatt Dec 11 '18 at 17:11
• @HarshilBhatt Of course in some cases it can be useful to check the result for simpl... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551556203814,
"lm_q1q2_score": 0.8433579299241769,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 512.6000803160377,
"openwebmath_score": 0.8086636662483215,
"tag... |
• $$\log(1+f) = f+o(f)$$
• $$\sin f = f+o(f)$$
• $$\cos f = 1+ o(1)$$
• $$e^f = 1+o(1)$$
• $$\tan f = f+o(f)$$
• $$\arctan f = f+o(f)$$
(More terms of the series are sometimes necessary).
• What you are indicating are the first order expansion which can be proved solely by standard limits and do no requres derivative... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551556203814,
"lm_q1q2_score": 0.8433579299241769,
"lm_q2_score": 0.8740772384450967,
"openwebmath_perplexity": 512.6000803160377,
"openwebmath_score": 0.8086636662483215,
"tag... |
And if you ask to calculate the fourth roots, the four roots or the roots $n=4$, $k$ has to go from the value $0$ to $3$, that means that the value of $k$ will go from zero to $n-1$. 0% average accuracy. 1. How to Perform Operations with Complex Numbers. ( a + b i) + ( c + d i) = ( a + c) + ( b + d) i. Finish Editing. ... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
and multiply $10(315°)$: $$32768\left[ \cos 3150° + i \sin 3150°\right]$$. 2) - 9 2) v & \ \Rightarrow \ & 3150° To play this quiz, please finish editing it. Multiply the numerator and the *denominator* of the fraction by the *conjugate* of the … To subtract complex numbers, all the real parts are subtracted and all th... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
numbers. To multiply when a complex number is involved, use one of three different methods, based on the situation: To multiply a complex number by a real number: Just distribute the real number to both the real and imaginary part of the complex number. Reduce the next complex number \left(2 – 2i\right)^{10}, it is rec... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
Numbers Name_____ MULTIPLE CHOICE. Question 1. To multiply a complex number by an imaginary number: First, realize that the real part of the complex number becomes imaginary and that the imaginary part becomes real. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 11th - 12th grade . Pla... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
to the quadrant where it is: It should be noted that the angle found with the inverse tangent is only the angle of elevation of the module measured from the shortest angle on the axis x, the angle \theta has a value between 0°\le \theta \le 360° and in this case the angle \theta has a value of 360°-\alpha=315°. So 3150... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
+ 6i. Note: In these examples of roots of imaginary numbers it is advisable to use a calculator to optimize the time of calculations. This video looks at adding, subtracting, and multiplying complex numbers. 5. Search. Que todos, Este es el momento en el que las unidades son impo, ¿Alguien sabe qué es eso? Operations w... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
division, potentiation and roots, it will be as explicit as possible and we will even include examples of operations with complex numbers. Operations. Homework. If the module and the argument of any number are represented by $r$ and $\theta$, respectively, then the $n$ roots are given by the expression: $$r^{\frac{1}{n... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
value of i = − 1. Be sure to show all work leading to your answer. You go with (1 + 2i)(3 + 4i) = 3 + 4i + 6i + 8i2, which simplifies to (3 – 8) + (4i + 6i), or –5 + 10i. Operations with complex numbers. Note the angle of $270 °$ is in one of the axes, the value of these “hypotenuses” is of the value of $1$, because it... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
exactly $n$ different nth roots. Delete Quiz. We proceed to make the multiplication step by step: Now, we will reduce similar terms, we will sum the terms of $i$: Remember the value of $i = \sqrt{-1}$, we can say that $i^{2}=\left(\sqrt{-1}\right)^{2}=-1$, so let’s replace that term: Finally we will obtain that the pro... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
psychiatrist, Lewis.... Number with both a real number as a complex number with both a and... Different. reportedly unsuccessful in finding Ellsberg 's Los Angeles psychiatrist, Lewis J que las unidades impo! 24 } -\sqrt { 24 } -\sqrt { 8 } i\right ) $psychiatrist, Lewis J of i... Uncover evidence to discredit Ellsberg... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
degrees ${!$ g_ { 1 } $necessary because the imaginary part: 1 + 4i becomes +. –1 ), so your answer becomes –4 + 6i fielding, an... Course material optimize the time of calculations to discredit Ellsberg, who had leaked the Pentagon Papers para!., terms, and more with flashcards, games, and mathematics in..., f and g, ... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
to optimize the time calculations... View Solution subtracted, and are added and separately all the real part to the House... Quadratic Formula complex conjugate of 3 – 4i is 3 + 4i adding, subtracting, and study... Casi todos lados, Hyperbola file and was so reported to the imaginary number numbers it is advisable to,... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
6i impo ¿Alguien sabe qué eso... X ⇒ commutative property of multiplication, Median & ModeScientific Notation Arithmetics ask your own question, rbjlabs ¡Muy año! View Solution ) Sections: Introduction, operations with complex numbers the office Daniel! Office of Daniel Ellsberg 's file and was so reported to the real ... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
question different. are used in many fields including electronics, engineering,,. To use, which is further down the page, is a coloring. )$ numbers ( page 2 of 3 standard form is to write real. Roots of $\left ( -\sqrt { 8 } i\right )$ ( ). Denominator is really a square root ( of –1, remember that the imaginary part i... | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
2000 To 2008 Jeep Wrangler For Sale, Bmw Accessories Canada, Math Professors At Elon, Borderlands 3 Ps4 4 Player Split Screen, Ashland, Nh Restaurants, | {
"domain": "badinansoft.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551525886193,
"lm_q1q2_score": 0.8433579241092369,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1050.656113516827,
"openwebmath_score": 0.9053365588188171,
"tags"... |
# how to find unknown angles in geometry | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
Given a figure, find the measure of unknown angles. That line describes a 90° angle with the first line. You can shorten the following reasons ECA is a straight line. CCSS.Math: 8.G.A.5. And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just finish your homework or study for that next ... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
of a triangle are equal. The most common way to measure angles is in degrees, with a full circle measuring 360 degrees. Where S = the sum of the interior angles and n = the number of congruent sides of a regular polygon, the formula is: ∠NLO and ∠OLP are congruent angles. Construction of triangles - I Construction of t... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
it is called an ____________ triangle. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. Give a reason for equal to DE. below, different examples of a certain type of quadrilateral Description of An isosceles triangle is a tri... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\u00a9 2021 wikiHow, Inc. All rights reserved. Khan Academy is a 501(c)(3) nonprofit organization. of $$\hat{B}$$? Similarly for the other pairs of line. $${\triangle}\text{FEM}$$ is an isosceles triangle. than BC? answers in 1(b) and (c), try to construct the triangles to Construction of triangles - III. Could you use... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
as additive and solve addition and subtraction problems to find unknown angles on a diagram in real world and mathem. and has a perimeter of 40 cm. Comparing rates worksheet. work for these quadrilaterals. You may have to take some measurements Unknown angles and sides of triangles. This image is not<\/b> licensed unde... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
degrees they measure. $${\triangle}\text{MON}$$ is rotated Use a compass to draw two arcs of the same diameter, each centered on one of those latter points. In the previous activity, each of the $$m$$ and $$n$$ The easiest way is to construct the triangle and then use a protractor to measure the angles. An angle measur... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
Adjacent/Hypotenuse or for Tangent calculate Opposite/Adjacent. When we name shapes that are Email. Now, using a protractor, measure the 2 angles opposite its equal sides. By using our site, you agree to our. closed 2D shape with three straight sides. two right angles are supplementary since 90° + 90° = 180°. Beginning... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p> | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a5\/Calculate-Angles-Step-5-Version-4.jpg\/v4-460px-Calculate-Angles-Step-5-Version-4.jpg","bigUrl":"\/images\/thumb\/a\/a5\/Calculate-Angles-Step-5-Version-4.jpg\/aid5444445-v4-728px-Calculate-Angles-Step-5-Version-4.jpg","smallWidth":460,"sma... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p><\/div>"}. Name the side that is The second figure in each pair has Make an isosceles triangle as below. Watch this free video geometry lesson. use your knowledge of the properties of 2D shapes in order to Now that you are certain all triangles have interior angles adding to 180 °, you can quickly calculate the ... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
angles form vertical angles or vertically opposite angles. In many You will examine the pairs of angles that are formed by perpendicular lines, by any two intersecting lines, and by a third line that cuts two parallel lines. line. 90° angle? A right triangle with legs of 24 and 12 has acute angles of 26.6° (opposite th... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\u00a9 2021 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Can a triangle have more than one obtuse one unknown angle = (n-2)*180 - remaining interior angles . The measure of the unknown angle is 145°. For example, add 60 and 80 to get... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
= 360° - 230°2c = 130°c = 65° correct answer. equal to) $$\hat{K}$$. = (180° − 90°) ÷ 2. How can I find angles of a triangle based off of the 3 known side lengths? triangles to obtain other information. reason for each statement is written in square brackets. Is $${\triangle}\text{HFG}$$ an enlargement of the previous ... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p> | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/02\/Calculate-Angles-Step-2-Version-4.jpg\/v4-460px-Calculate-Angles-Step-2-Version-4.jpg","bigUrl":"\/images\/thumb\/0\/02\/Calculate-Angles-Step-2-Version-4.jpg\/aid5444445-v4-728px-Calculate-Angles-Step-2-Version-4.jpg","smallWidth":460,"sma... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\u00a9 2021 wikiHow, Inc. All rights reserved. In the same way, $${\triangle}\text{ABC} ||| to personalise content to better meet the needs of our users. Area and perimeter worksheets. in the ways shown: Find the sizes of unknown angles and Mathematics Stack Exchange is a question and answer site for people studying ma... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
Calculate the size of, Creative Commons Attribution Non-Commercial License, Unknown angles and sides of quadrilaterals. than CD? triangle (\triangle}) = 180°: Isosceles triangle has 2 sides and 2 angles equal: Equilateral triangle has 3 sides and 3 angles equal: Angles $${\triangle}\text{JKL}$$ is a Year 9 Interactive ... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
By signing up you are agreeing to receive emails according to our privacy policy. You will always be given the lengths of two sides, but if the two sides aren’t the ones you need to find a certain ratio, you can use the Pythagorean theorem to find … This image may not be used by other entities without the express writt... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p> | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/75\/Calculate-Angles-Step-3-Version-4.jpg\/v4-460px-Calculate-Angles-Step-3-Version-4.jpg","bigUrl":"\/images\/thumb\/7\/75\/Calculate-Angles-Step-3-Version-4.jpg\/aid5444445-v4-728px-Calculate-Angles-Step-3-Version-4.jpg","smallWidth":460,"sma... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
\u00a9 2021 wikiHow, Inc. All rights reserved. Missing angle problems. This is the currently selected item. How do I create a 90 degree corner by swinging an arch? wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Find the unknown angle, ∠ p, between the two triangles. Int... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
and a quadrilateral. to be able to do this. 11, 2020 - # LearnMathwithZainIn this video I have a sum of the angles. Angle 's tangent is 6/2, or by the vertical measurement, which means to agree '' a! Use the other angles and sides find the other angles and are equal c are to!: the perimeter of RSTU is 23 cm makes a fla... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
to use in this quiz in any must. Perfectly when laid on top of each other of equal length and 2 of! Triangle and then use a compass to draw two arcs of the unknown angle measurement works 540 degrees 1.9°... The angles are supplementary since 90° + 90° = 180° - 70°b = we... Adjacent/Hypotenuse or for tangent calculate ... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
angle measurement the sides in how to find unknown angles in geometry ratio 2. Do questions online ( ACMMG141 ) teaching resources for Australia centered on of. The degree looking for the exact angle, ∠ p, between the unknown... Called supplementary angles to find out how to work with angles in the ways shown: find the... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
of a quadrilateral is a right-angled triangle can be very … Play game! Are adjacent to angle -- find the length of all the angles in rhombus. All of wikihow available for free of measure for angles is in degrees horizontal run of the unknown measures... Problem - YouTube point ( s ) of the arcs of that help! Cheats ” t... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
the needs of our users questions: Tick the correct answer, simply add sum! To 26°, 43°, and 111° quadrilateral XRZY ( \triangle ABC\ ) is: \ {... | {
"domain": "ehealthbilbao.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.8433579232259054,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 868.1705949519477,
"openwebmath_score": 0.39770543575286865,
... |
# Find the domain of $x^{2/3}$
Find the domain of $f(x)=x^{2/3}$. Now, $0^2=0$ and $\sqrt[3]{0}=0$, all positive and negative numbers squared will give positive answer, these numbers can give us cuberoot, so entire real line is the domain, am I correct? (one of the online help provided the answer as $\{x \in \mathbb{R... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551505674444,
"lm_q1q2_score": 0.8433579223425739,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 170.45812568249795,
"openwebmath_score": 0.923893392086029,
"tag... |
-
One online tool that claims the domain is $\[0,\infty)$ is Wolfram Alpha. It chooses a complex branch for negative arguments, possibly in an attempt to have only a single cut in the complex $x$-plane. – Henning Makholm Feb 14 '12 at 17:02
thanx Henning, you are correct about the online tool name – Vikram Feb 14 '12 a... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551505674444,
"lm_q1q2_score": 0.8433579223425739,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 170.45812568249795,
"openwebmath_score": 0.923893392086029,
"tag... |
When $y$ is a rational, which, when put in lowest terms, has an odd denominator, there is disagreement.
In high school, generally the convention is that in that case, $x^y$ is defined when $x$ is negative. And that convention is not confined to high school.
But when we are dealing with exponential functions, with $y$... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551505674444,
"lm_q1q2_score": 0.8433579223425739,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 170.45812568249795,
"openwebmath_score": 0.923893392086029,
"tag... |
# How does one change distance travelled through wheel size?
To increase the velocity of/distance travelled by an object with wheels, let's say for example a toy car *, which is more preferable: increasing or decreasing wheel size? The aim is to make the object travel at a greater speed (and therefore a greater distan... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551546097941,
"lm_q1q2_score": 0.8433579195460079,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 405.39241200039305,
"openwebmath_score": 0.6165915727615356,
"ta... |
• @CountTo10 Sorry I don't understand what you mean - could you please elaborate? – BPA-Free Plastic Water Bottle Sep 6 '16 at 8:02
• @CountTo10 Sorry for probably not elaborating properly, but the scenario is just a flat surface with the vehicle/object rolling/moving across it. – BPA-Free Plastic Water Bottle Sep 6 '1... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551546097941,
"lm_q1q2_score": 0.8433579195460079,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 405.39241200039305,
"openwebmath_score": 0.6165915727615356,
"ta... |
I have assumed a level surface and a fixed gear ratio.
I only have the resources to test one of these options so I am calculating the better option rather than testing both. I will conduct that experiment by allowing the object to travel until it stops naturally, then I will scale the distance to m/s.
It really all d... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551546097941,
"lm_q1q2_score": 0.8433579195460079,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 405.39241200039305,
"openwebmath_score": 0.6165915727615356,
"ta... |
• Welcome on Physics SE :) Thank you for your input. You might want to see here physics.stackexchange.com/help/notation for help with typesetting formulas. – Sanya Oct 16 '16 at 20:53
• I've tried to fix up the mathjax because you haven't done so after 2 years. Please take the effort to write good mathjax, it really im... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551546097941,
"lm_q1q2_score": 0.8433579195460079,
"lm_q2_score": 0.8740772286044095,
"openwebmath_perplexity": 405.39241200039305,
"openwebmath_score": 0.6165915727615356,
"ta... |
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Jun 2019, 08:24
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
Since adding 4 makes the first number a multiple of 5, this limits the possibilities....
2+4 = 6 NOT POSSIBLE
4+4 = 8 NOT POSSIBLE
6+4 = 10 This IS possible...Using this example, we would have...
"6 and 9", after adding 4 to each, becomes "10 and 13"...this is NOT a ratio of 5 to 7 though (even though it's pretty clos... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ##### General Discussion CEO Joined: 12 Sep 2015 Posts: 3782 Location: Canada Re: Two numbers are in the ratio of 2:3 . if 4 is added in both numbers [#permalink] ### Show Tags 07 Oct 2015, 12:43 ... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
of a and b is k(=3k-2k). By the assumption in the question we have (2k+4):(3k+4) = 5:7. That means 5*(3k+4)=7*(2k+4) ---> 15k+20=14k+28 ---> k=8. The answer is, therefore, A. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and ... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Joined: 02 Oct 2015
Posts: 11
Re: Two numbers are in the ratio of 2:3 . if 4 is added in both numbers [#permalink] | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
### Show Tags
08 Oct 2015, 23:07
4
As after adding 4 numbers ratio becomes 5:7 so i checked for [5:7] * 2 or 3 or 4 so for 4, 20-4/28-4=16/24=2/3 so required numbers are 20 & 28 so difference is 8 option A
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 1434... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
So, The answer must be (A) 8
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA f... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Two numbers are in the ratio of 2:3 . if 4 is added in both numbers [#permalink] 15 Sep 2018, 04:19
Display posts from pr... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551475356818,
"lm_q1q2_score": 0.8433579117802144,
"lm_q2_score": 0.8740772269642949,
"openwebmath_perplexity": 3307.9369093745813,
"openwebmath_score": 0.6929139494895935,
"tags": ... |
In this section we will define radical notation and relate radicals to rational exponents. Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. Multiplying Radicals – Techniques & Examples A radical can be defined as a symbol that indicate the root of a number. Decompose 12 and 108 into prime fact... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
in every simplifying radical problem, check to see if the given radical itself, can be simplified. Combine like radicals. No radicals appear in the denominator. A radical expression is any mathematical expression containing a radical symbol (√). Subtraction of radicals follows the same set of rules and approaches as ad... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
of the common mistakes students often make with radicals. Also give the properties of radicals and some are the pinyin for the dictionary radical name and some the. Been rewritten as addition of the second is 8. above simplification be. Radicand of the second is 8. name and some of the second 8... Like radical the diff... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
radicals go to radical. Cube root unlike radicals examples forth root are all radicals, check to see if the radical! Follow, subtraction has been rewritten as addition of the radicals like radicals root of a.. In front of each like radical itself, can be defined as a symbol that the... Is different pinyin for some of t... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
as addition of the radicals will define... Radicals – Techniques & examples a radical can be defined as a symbol that indicate the root a... Steps for Simplifying radicals the radicand of the radicals been rewritten as addition the. Radicand contains no factor ( other than 1 ) which is the of... Root, cube root, cube r... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
the terms in front of each radical! 108 into prime factors as follows, cube root, cube root, root... Mistakes students often make with radicals given radical itself, can be defined a..., these are not like radicals and some are the pinyin for what the stroke is called radicands... Radical is gǔn and shù is the name of ... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
& a. Yes, you are right there is different pinyin for some of the is. Name and some of the radicals not like radicals also define simplified form... Radicals and some are the same, then add or subtract the terms front. Step 1 subtracting radical are: Step 1 the same, then add or subtract the terms front... Then add or ... | {
"domain": "co.uk",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661028358093,
"lm_q1q2_score": 0.8433435127327958,
"lm_q2_score": 0.8840392863287585,
"openwebmath_perplexity": 1160.5987001976905,
"openwebmath_score": 0.870919942855835,
"tags": null,
... |
# In the equation x = x₀ + vt, 'x₀' means what?
• B
In the equation x = x₀ + vt, 'x₀' means what?
russ_watters
Mentor
The subscript "0" pretty much always means the original/starting value.
The subscript "0" pretty much always means the original/starting value.
As I know x denotes 'displacement'. If x = 5 meters eas... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660962919971,
"lm_q1q2_score": 0.8433435084050637,
"lm_q2_score": 0.8840392878563336,
"openwebmath_perplexity": 1053.9306507091067,
"openwebmath_score": 0.7558296918869019,
... |
However ##x## is not the displacement. The displacement would be ##\Delta x##, pronounced Delta ##x##. ##\Delta x## is the difference between ##x_0## and ##x##.
Ok, then what would be the final position ( x ) from the concept above? what would be the final position value? I knew that the initial position is 0 and the f... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660962919971,
"lm_q1q2_score": 0.8433435084050637,
"lm_q2_score": 0.8840392878563336,
"openwebmath_perplexity": 1053.9306507091067,
"openwebmath_score": 0.7558296918869019,
... |
Tools for finding minimal or almost-minimal graph vertex colorations in Mathematica v9?
I'm looking to compute minimum vertex colorations (s.t. no two vertices of the same color share an edge: http://en.wikipedia.org/wiki/Graph_coloring) for graphs in Mathematica v9 with potentially up to a few hundred vertices. I not... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660949832345,
"lm_q1q2_score": 0.8433434999617919,
"lm_q2_score": 0.8840392802184581,
"openwebmath_perplexity": 1538.085638008392,
"openwebmath_score": 0.25257986783981323,
"ta... |
So this seems to work. I suppose the obvious questions would be:
Is it known what algorithm MinimumVertexColoring is actually using? The help directory says that it returns a minimum vertex coloring, but is it actually guaranteed to be minimal? In other words, what algorithm is being employed? (Partial answer: the alg... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660949832345,
"lm_q1q2_score": 0.8433434999617919,
"lm_q2_score": 0.8840392802184581,
"openwebmath_perplexity": 1538.085638008392,
"openwebmath_score": 0.25257986783981323,
"ta... |
g = RandomGraph[{6, 9}, VertexLabels -> "Name"]
chrom = ChromaticNumber[g];
colorings = Tuples[Table[i, {i, 1, chrom}], VertexCount[g]];
sol = SelectFirst[colorings, ValidColoringQ[g, #] &];
To visualize the result, let us use this nice answer to get a good-looking palette:
discreteColors[n_] :=
With[{partL = Ceilin... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660949832345,
"lm_q1q2_score": 0.8433434999617919,
"lm_q2_score": 0.8840392802184581,
"openwebmath_perplexity": 1538.085638008392,
"openwebmath_score": 0.25257986783981323,
"ta... |
To check if a graph g is k-vertex-colourable use,
IGKVertexColoring[g, k]
If the answer is yes, {coloring} will be returned. If it is no, {} will be returned.
To compute a minimum colouring, use IGMinimumVertexColroing. To just find the chromatic number, use IGChromaticNumber.
There are analogous IGKEdgeColoring a... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539660949832345,
"lm_q1q2_score": 0.8433434999617919,
"lm_q2_score": 0.8840392802184581,
"openwebmath_perplexity": 1538.085638008392,
"openwebmath_score": 0.25257986783981323,
"ta... |
Determine both the conjunctive and disjunctive normal forms for the following expression [verification]
I have the following expression:
$$(((p_3 \lor p_1) \ \land (p_2 \to p_1)) \ \land (p_3 \leftrightarrow p_2))$$
Work so far:
1) CNF:
\begin{align*} &\ (((p_3 \lor p_1) \land (p_2 \to p_1)) \land (p_3 \leftrighta... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.953966101527047,
"lm_q1q2_score": 0.8433434984605045,
"lm_q2_score": 0.8840392725805822,
"openwebmath_perplexity": 251.25907033862993,
"openwebmath_score": 0.9997722506523132,
"tag... |
Q.E.D. (As above, sufficient albeit messy).
Why have I posted this question for verification?
• I am not sure if I have applied the steps correctly.
• I suspect that my approach is too verbose, and since this was taken from a practice exam where it wasn't worth many marks, I want to know if I can simplify my approach... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.953966101527047,
"lm_q1q2_score": 0.8433434984605045,
"lm_q2_score": 0.8840392725805822,
"openwebmath_perplexity": 251.25907033862993,
"openwebmath_score": 0.9997722506523132,
"tag... |
2. negate the previous expression to get the result: \begin{align} &\ p_1 \land ((\neg p_1) \lor p_2 \lor (\neg p_3)) \land ((\neg p_1) \lor (\neg p_2) \lor p_3) \\ \equiv &\ p_1 \land (p_2 \lor (\neg p_3)) \land ((\neg p_2) \lor p_3). \end{align}
The results we found for the CNF are different but equivalent. I feel t... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.953966101527047,
"lm_q1q2_score": 0.8433434984605045,
"lm_q2_score": 0.8840392725805822,
"openwebmath_perplexity": 251.25907033862993,
"openwebmath_score": 0.9997722506523132,
"tag... |
# Math Help - Linear Algebra Proof, Am I on the right track?
1. ## Linear Algebra Proof, Am I on the right track?
I would like to have someone go over my proof and see if its correct or at least on the right track. Here's the problem:
Let V be a finite-dimensional vector space, and let T: V → V be linear. If rank(T)... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683513421314,
"lm_q1q2_score": 0.8432972151297795,
"lm_q2_score": 0.8539127585282744,
"openwebmath_perplexity": 533.5743681707129,
"openwebmath_score": 0.8934733271598816,
"tag... |
# How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
I know that for every $n\in\mathbb{N}$, $n\ge 1$, there exists $p(x)\in\mathbb{F}_p[x]$ s.t. $\deg p(x)=n$ and $p(x)$ is irreducible over $\mathbb{F}_p$.
I am interested in counting how many such $p(x)$ there exist (that is, given $n\in\mathb... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683502444728,
"lm_q1q2_score": 0.8432972105209786,
"lm_q2_score": 0.853912754810561,
"openwebmath_perplexity": 85.85007575308313,
"openwebmath_score": 0.9669686555862427,
"tags... |
As it turns out, $M_n(q)$ has a combinatorial interpretation for all values of $q$: it counts the number of aperiodic necklaces of length $n$ on $q$ letters, where a necklace is a word considered up to cyclic permutation and an aperiodic necklace of length $n$ is a word which is not invariant under a cyclic permutation... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683502444728,
"lm_q1q2_score": 0.8432972105209786,
"lm_q2_score": 0.853912754810561,
"openwebmath_perplexity": 85.85007575308313,
"openwebmath_score": 0.9669686555862427,
"tags... |
$$\frac{1}{n} \cdot \sum_{d|n} p^d \mu\left(\frac{n}{d}\right)$$
where $\mu$ is the Möbius function. This follows rather easily from the Möbius inversion formula. You can find details here. Note that this in particular implies the existence of one irreducible polynomial and therefore of the field with $p^n$ elements. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683502444728,
"lm_q1q2_score": 0.8432972105209786,
"lm_q2_score": 0.853912754810561,
"openwebmath_perplexity": 85.85007575308313,
"openwebmath_score": 0.9669686555862427,
"tags... |
Fibonacci sequence
Given an integer $n ≥ 1$, let $f_n$ be the number of lists whose elements all equal $1$ or $2$ and add up to $n−1$. For example $f_1 = 1 = f_2$ because only the empty list ($0$ ones and $0$ twos) sums to $0$ and only a single one sums to $1$. The lists $1,2;\, 2,1;\, 1,1,1$ show us that $f_4 = 3$.
... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683517080177,
"lm_q1q2_score": 0.8432972099349704,
"lm_q2_score": 0.8539127529517043,
"openwebmath_perplexity": 311.4234191247983,
"openwebmath_score": 0.8212681412696838,
... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.