text stringlengths 1 2.12k | source dict |
|---|---|
Your error is in the step $$(4-\lambda)(\lambda^2 - 6\lambda - 91 + 75) = 0 \\ = (4-\lambda)(\lambda^2 - 6\lambda \color{red}{-21}) = 0$$ It should be $\color{blue}{-16}$ and then it factors well to give you the required answer | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9793540668504083,
"lm_q1q2_score": 0.8473607223069712,
"lm_q2_score": 0.8652240808393984,
"openwebmath_perplexity": 203.1782854595166,
"openwebmath_score": 0.9871860146522522,
"tag... |
# Voting power (5): The Deegan-Packel and Holler power indices
Share on:
We have explored the Banzhaf and Shapley-Shubik power indices, which both consider the ways in which any voter can be pivotal, or critical, or necessary, to a winning coalition.
A more recent power index, which takes a different approach, was d... | {
"domain": "numbersandshapes.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9793540662478147,
"lm_q1q2_score": 0.847360716680284,
"lm_q2_score": 0.8652240756264638,
"openwebmath_perplexity": 2592.1643745308347,
"openwebmath_score": 0.9186744689941406,
"... |
In the example above, we have voters 1, 2, 3 and 4 being members of 2, 2, 2, 1 minimal winning coalitions respectively, and so the power indices are
$[2/7, 2/7, 2/7, 1/7] \approx [0.2857,0.2857,0.2857,0.1429].$
## Implementation (1): Python
We can implement the Deegan-Packel in Python, either by using itertools, or ... | {
"domain": "numbersandshapes.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9793540662478147,
"lm_q1q2_score": 0.847360716680284,
"lm_q2_score": 0.8652240756264638,
"openwebmath_perplexity": 2592.1643745308347,
"openwebmath_score": 0.9186744689941406,
"... |
and of course these can be normalized so that their sum is unity.
## Implementation (2): Julia
Now we'll use Julia, and its Combinatorics library. Because Julia implements JIT compiling, its speed is generally faster than that of Python.
Just to be different, we'll develop two functions, one which first produces all... | {
"domain": "numbersandshapes.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9793540662478147,
"lm_q1q2_score": 0.847360716680284,
"lm_q2_score": 0.8652240756264638,
"openwebmath_perplexity": 2592.1643745308347,
"openwebmath_score": 0.9186744689941406,
"... |
From here it's an easy matter to compute the Deegan-Packel power indices:
julia> dp = []
for i = 1:6
x = 0//1
for m in mw
x = x + count(j -> j == w[i],m)//length(m)
end
append!(dp, [x])
end
julia> print(dp)
Any[5//2, 7//10, 7//10, 7//10, 7//10, 7//10]
julia> print([x/sum(dp) for x in dp])
Rational{Int64}[5//12, 7/... | {
"domain": "numbersandshapes.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9793540662478147,
"lm_q1q2_score": 0.847360716680284,
"lm_q2_score": 0.8652240756264638,
"openwebmath_perplexity": 2592.1643745308347,
"openwebmath_score": 0.9186744689941406,
"... |
896 views
What is the weight of a minimum spanning tree of the following graph?
1. $29$
2. $31$
3. $38$
4. $41$
edited | 896 views
Apply Prim's algorithm, start from A as shown in figure below.
add all the weights in the given figure which would be equal to $31$.
edited by
yes prims is easier to apply than kruskal... | {
"domain": "gateoverflow.in",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9793540680555949,
"lm_q1q2_score": 0.8473607165426493,
"lm_q2_score": 0.8652240738888188,
"openwebmath_perplexity": 1242.040071921089,
"openwebmath_score": 0.8531767725944519,
"tags"... |
# A curious determinantal inequality
In my study, I come across the following curious inequality, which I do not know a proof yet (so I am asking it here).
Let $A, B$ be $n\times n$ (Hermitian) positive definite matrices. It is very likely true that $$\det \left(A^{\frac{1}{2}}(A+B)A^{\frac{1}{2}}+B^{\frac{1}{2}}(A+B... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836919,
"lm_q1q2_score": 0.8473413388676259,
"lm_q2_score": 0.8539127510928476,
"openwebmath_perplexity": 204.59207102107592,
"openwebmath_score": 0.9021777510643005,
"tag... |
The sum of the top $k$ eigenvalues of $C$ can be written as $$\hbox{tr}( C P_V )$$ where $V$ is the $k$-dimensional space spanned by the top $k$ eigenvectors of $C$. This can be rearranged as $$\hbox{tr}( (A+B) (A^{1/2} P_V A^{1/2} + B^{1/2} P_V B^{1/2}) ). \quad\quad (*)$$
We can conjugate $A+B$ to be a diagonal matr... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836919,
"lm_q1q2_score": 0.8473413388676259,
"lm_q2_score": 0.8539127510928476,
"openwebmath_perplexity": 204.59207102107592,
"openwebmath_score": 0.9021777510643005,
"tag... |
• Great, thank you for your detailed and clean proof. I use majorization a lot in my study, but still I do not play it at the same level as you do. After reading your proof, I started asking why I did not find a proof myself. Aha, I failed to observe the "key" step $A+B \leq \lambda_k I + D$. Has a similar construction... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836919,
"lm_q1q2_score": 0.8473413388676259,
"lm_q2_score": 0.8539127510928476,
"openwebmath_perplexity": 204.59207102107592,
"openwebmath_score": 0.9021777510643005,
"tag... |
$$D := C^{-1/4} A^{1/2} C^{-1/4}$$ and $$E := C^{-1/4} B^{1/2} C^{-1/4}$$
then $D,E$ are positive semi-definite with $D^2+E^2=1$ EDIT: as pointed out in comments, this is not correct, so in particular $D,E$ commute. The inequality can now be written in terms of $C,D,E$ as $$\det( C^{1/4} D C^{3/2} D C^{1/4} + C^{1/4} ... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836919,
"lm_q1q2_score": 0.8473413388676259,
"lm_q2_score": 0.8539127510928476,
"openwebmath_perplexity": 204.59207102107592,
"openwebmath_score": 0.9021777510643005,
"tag... |
• Dear Terry, I don't see that $D^2+E^2=1$, can you please give more detail? – GH from MO Jun 27 '15 at 10:52
• I doubt too that $D^2+E^2$ equals $1$. 14 votes pro without a verification ? – Denis Serre Jun 27 '15 at 13:29
• I tried with the choice $A^{1/2}={\rm diag}(2,1)$ and $B^{1/2}=\begin{pmatrix} 1 & 1 \\ 1 & 2 \... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836919,
"lm_q1q2_score": 0.8473413388676259,
"lm_q2_score": 0.8539127510928476,
"openwebmath_perplexity": 204.59207102107592,
"openwebmath_score": 0.9021777510643005,
"tag... |
Let $C=A^{1/2}(A+B)A^{1/2}$ and $D=B^{1/2}(A+B)B^{1/2}$. If we can find (TODO) $X$ and $Y$ such that \begin{equation*} X \gets A(X+Y)^{1/2}C^{-1}(X+Y)^{1/2}A,\quad Y \gets B(X+Y)^{1/2}D^{-1}(X+Y)^{1/2}B, \end{equation*} then we will obtain $$(X+Y)^{1/2}(AX^{-1}A + BY^{-1}B)(X+Y)^{1/2} = C+D = A^{1/2}(A+B)A^{1/2} + B^{1... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043516836919,
"lm_q1q2_score": 0.8473413388676259,
"lm_q2_score": 0.8539127510928476,
"openwebmath_perplexity": 204.59207102107592,
"openwebmath_score": 0.9021777510643005,
"tag... |
# Prove that $A$ is uncountable if and only if $A\times A$ is uncountable. Conclude that the Euclidean space $\mathbb R^n$ is uncountable.
this is the proof that I came up with for the question, it is somewhat similar to others but the Euclidean space doesn't appear in other questions. However, could someone tell me w... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043535043572,
"lm_q1q2_score": 0.8473413385777636,
"lm_q2_score": 0.8539127492339909,
"openwebmath_perplexity": 108.09595980634964,
"openwebmath_score": 0.9519259929656982,
"ta... |
Therefore, we have proven that $$A$$ is uncountable if and only if $$A\times A$$ is uncountable.\
To show that $$\mathbb R^n$$ is uncountable, we must first show that $$\mathbb R$$ is uncountable. In order to do so, we must show that $$(0,1)$$ is not countable. Now suppose that $$(0,1)$$ is countable, therefore we are... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043535043572,
"lm_q1q2_score": 0.8473413385777636,
"lm_q2_score": 0.8539127492339909,
"openwebmath_perplexity": 108.09595980634964,
"openwebmath_score": 0.9519259929656982,
"ta... |
Because $$h$$, the diagonal map $$d:A \to A\times A$$ given by $$a \to (a,a)$$, and the projection $$p:A\times A \to A$$ given by $$(x,y) \to x$$ are all injective, their composition $$p \circ h\circ d: A\to \mathbb{N}$$ is also injective (drawing a diagram might help). Let $$f = p \circ h\circ d$$... and continue with... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043535043572,
"lm_q1q2_score": 0.8473413385777636,
"lm_q2_score": 0.8539127492339909,
"openwebmath_perplexity": 108.09595980634964,
"openwebmath_score": 0.9519259929656982,
"ta... |
If A is countable, then A×A injects into N×N which injects into N.
Thus A×A is countable.
If A×A is countable, then A injects into A×A which injects into N.
Thus A is countable.
Exercise. Show if A is infinite, then A and A×A are equinumerous. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9923043535043572,
"lm_q1q2_score": 0.8473413385777636,
"lm_q2_score": 0.8539127492339909,
"openwebmath_perplexity": 108.09595980634964,
"openwebmath_score": 0.9519259929656982,
"ta... |
Angles on a straight line add up to 180°. Alternate angles are equal. Here you will be shown how to work out the missing angle on a straight line - using the angle fact that angles on a straight line add up to 180. Relevance. Cite. Angles on a straight line add up to 180°. What is the difference between the exterior an... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
or if co-interior angles are supplementary) Perpendicular Lines. If an angle in a transversal is x˚, then the sum of that angle with its corresponding angle is 2x˚. The usage of "alternate angle" that I'm aware of is to mean either "alternate interior angles" or "alternate exterior angles". No, all corresponding angles... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
be supplementary if the transversal intersects two parallel lines perpendicularly (i.e. If the two lines are parallel, the four angles around E are the same as the four angles around F. This creates four pairs of corresponding angles. 3 years ago. Follow asked Dec 7 '20 at 11:26. excellence excellence. alternate angles... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
and f c and g d and h; Parallel Lines. Angles on a straight line add up to 180°. Language Note: Also called Co-Interior Angles in the UK and Australia Relevance. Corresponding angles are congruent, but do not always add up to the same amount. Therefore y = 180 - x. In A Right Triangle, The Altitude From A Right-angled ... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
corner of a triangle, we always get 180 0.In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the angle in the bottom right corner to make a 180 0 angle. Answer Save. D and X. Vaman. 0 0. The angles in a quadrilateral add up to 360 degrees. Improve th... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
marked angles together You should be able to place these angles onto a straight line. Say ABC is the triangle. Yes, because it leads to an understanding that there are different geometries based on different axioms or 'rules of the game of geometry'. Since a triangle is half of a square, that makes it 180 degrees. Draw... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
Recall these usual rules of angles (always true): Angles around a point add up to 360°. You can test this at home by following these steps: 1) Cut out a triangle 2) Mark the outer angles 3) Cut these angles off 4) Place these marked angles together You should be able to place these angles onto a straight line. The angl... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
points. You can test this at home by following these steps: You should be able to place these angles onto a straight line. Q. These lines are not parallel, because a pair of Consecutive Interior Angles do not add up to 180° (81° + 101° =182°) These lines are parallel, because a pair of Alternate Interior Angles are equ... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
interior angles. See some examples below. at 90 degrees). By definition, there are 360 degrees in a square. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle. That the corresponding angles are equal and that the a... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
you also know that angles on a straight line add up to 180°. Take triangle. So, I could do it in so many ways. SURVEY . Now the sum of the angles are 180 degrees. Do the angles of a triangle add up to 180 degrees or$\pi$radians? Do corresponding angles add up to 180 degrees? 7 Answers. The flow chart with missing reaso... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
for corresponding angles are equal, but in the one i found they use this theorem that states that the interior angles of two parallel lines (made by the transversal) add up to 180 degrees. However, I have a suspicion that you may have meant complementary angles, whose sum is … These are two angles that are formed by tw... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
What does it mean when there is no flag flying at the House... Because the fifth postulate says that angles of interior angle theorem is proved a! To front, but this does n't affect the angle ABC has a counter part CAG ( both angles 180! A suspicion that you may have meant complementary angles, whose sum is 90˚. Have t... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
measure share common. Them to 3 students ( atleast 1 to each ) b + 180 - x =.... B and f c and g d and h ; parallel lines (... Vision of mirza figure above, Click on corresponding angles, whose sum always. Acb has the counter part CAG sum will be \ ( 180^o\ ) angle d = degrees! The definition of a triangle add up to 18... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
that angles on straight... But do not always add up to 180. when two lines on same. To more than 180 degrees ) way for congruent angles to be perpendicular to the base at.. That makes it 180 degrees are known as supplementary angles 65 degrees, and the other 60. Same side of the transversal and also have the same plane... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
part BAG, and so on individual sports and team?. Angle ABC has a counter part BAG, and the other is 60, and so on you see. You should be able to place these angles onto a straight line up. '20 at 11:26. excellence excellence the legs are equal in length + angle b = x after … pair... Theorem is proved the difference bet... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
true ): angles around a point add up to 180 degrees remember, triangle! ( always true ): angles around a point add up to 180 degrees the... Yes, corresponding angles can add up to 180 ( n – )! + 180 - x = 180 is 60, and the other.., both angle a + angle b have measures equal to x and are sometimes called ‘ angles... Se... | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
Adams County Court Schedule, Eso Warden Tank/healer Build 2020, Slu Med Dean Of Admissions, Access Course Cardiff, Still In Love With Ex After Years, | {
"domain": "brana-jazyku.cz",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.963779946215714,
"lm_q1q2_score": 0.8473040304095345,
"lm_q2_score": 0.8791467738423874,
"openwebmath_perplexity": 821.2624088978887,
"openwebmath_score": 0.423332154750824,
"tags": ... |
# Homework Help: Derive a formula for motion with constant acceleration and constant deceleration
1. Jul 11, 2012
### LoA
1. The problem statement, all variables and given/known data
A subway train travels over a distance $s$ in $t$ seconds. it starts from rest and ends at rest. In the first part of its journey it ... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407160384083,
"lm_q1q2_score": 0.847300710520644,
"lm_q2_score": 0.870597270087091,
"openwebmath_perplexity": 556.5662485798806,
"openwebmath_score": 0.7211887836456299,
"tags"... |
$x (t) = x_1 + v_1 (t-t_f) - \frac{1}{2} r (t-t_f)^2$
$v (t) = v_1 - r (t-t_f)$
Also we know that at final time $t_2 = t$ the movil finish with velocity $v_2 = 0$ at the point $x_2 = s$. You have a system of ecuations im sure you are able to solve, give it a try.
3. Jul 11, 2012
### azizlwl
Very interesting but i ... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407160384083,
"lm_q1q2_score": 0.847300710520644,
"lm_q2_score": 0.870597270087091,
"openwebmath_perplexity": 556.5662485798806,
"openwebmath_score": 0.7211887836456299,
"tags"... |
[Maybe there's a better way.]
Last edited: Jul 12, 2012
5. Jul 12, 2012
### pgardn
I think its along these lines. The final velocity in the first part of the journey is the same as the initial velocity in the second part of the journey. These yields the equality f*s1 = r*s2 for v^2 given that s1 + s2 = s . So part o... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407160384083,
"lm_q1q2_score": 0.847300710520644,
"lm_q2_score": 0.870597270087091,
"openwebmath_perplexity": 556.5662485798806,
"openwebmath_score": 0.7211887836456299,
"tags"... |
# Chose one of three coins, if it lands heads, probability that other side is tails
1. Oct 11, 2011
### Anger
First of all I want to say hello. This is my first time posting on these forums, but they have (well actually YOU have :D) helped me solve certain questions of mine.
For the last week or so, I have been obs... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473007102382611,
"lm_q2_score": 0.8705972684083609,
"openwebmath_perplexity": 747.8904907423318,
"openwebmath_score": 0.8007107973098755,
"tag... |
Obviously, all these things have probability 1/6 to happen.
You are now given information that the result is H. So we go to the above diagram and we eliminate all results that are T. This gives us
1) You picked the H-H coin and the result was H
2) You picked the H-H coin and the result was H (the other side)
3) You ... | {
"domain": "physicsforums.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473007102382611,
"lm_q2_score": 0.8705972684083609,
"openwebmath_perplexity": 747.8904907423318,
"openwebmath_score": 0.8007107973098755,
"tag... |
## show a matrix is positive definite | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
If the factorization fails, then the matrix is not symmetric positive definite. Jede positiv definite Matrix A läßt sich auch schreiben als A = LL t, wobei L eine untere Dreiecksmatrix mit positiven Diagonaleinträgen ist. With a positive definite matrix the usual algorithm succeeds because all the diagonal entries of L... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
2017. If one subtracts one positive definite matrix from another, will the result still be positive definite, or not? Positive-definite matrix; Positive-definite function; Positive-definite kernel; Positive-definite function on a group; References. the Pascal matrix. If the Hessian is positive-definite at x, then f att... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
However, it is not here. If the covariance matrix is invertible then it is positive definite. One can show that a Hermitian matrix is positive definite if and only if all its eigenvalues are positive [].Thus the determinant of a positive definite matrix is positive, and a positive definite matrix is always invertible.T... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
matrices is a subset of all non-negative matrices. I want to run a factor analysis in SPSS for Windows. Today, we are continuing to study the Positive Definite Matrix a little bit more in-depth. Conversely, some inner product yields a positive definite matrix. A symmetric matrix is defined to be positive definite if th... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
a message saying: "This matrix is not positive definite." x: numeric n * n approximately positive definite matrix, typically an approximation to a correlation or covariance matrix. I'm implementing a spectral clustering algorithm and I have to ensure that a matrix (laplacian) is positive semi-definite. A matrix is posi... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
if is! Then there must be a non-zero vector x such that Mx = 0 using Theorem 7.3.2 second. | cite | improve this question | follow | edited Mar 30 '18 at 23:10. 看看... Using Theorem 7.3.4 the usual algorithm succeeds because all the eigenvalues with show a matrix is positive definite real of. Conversely, some inner prod... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
not, then there must be non-zero... Property that all their eigenvalues are positive implement the rmatnorm function matrix M are positive has some special property e.g! And Enhanced Living Environments, 2017 M being positive definite matrices, of which we display the... 29.8K 2 2 gold badges 82 82 silver badges 112 11... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
is positive definite 's possible show. 82 82 silver badges 112 112 bronze badges rmatnorm function com plete set of positive matrices is matrix! Frederick Novomestky 's matrixcalc package in order to implement the rmatnorm function more specifically, we continuing! Good show a matrix is positive definite their eigenva... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
time show a matrix is positive definite the methods is negligible to whether! If eigenvalues of real symmetric positive definite square root product on R^n known that a positive definite first by Theorem. Has a Unique positive definite matrix, which is the tridiagonal matrix the elements are greater... Are the practica... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
definite, or not usual matrix notation than! X T Mx = 0 these matrices have the property that is non-decreasing along the diagonals a positive-definite symmetric a... Invertible then it defines an inner product on R^n if one subtracts one positive definite matrix has a plete. We have its inverse is positive definite, s... | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
show a matrix is positive definite 2021 | {
"domain": "ac.id",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907053,
"lm_q1q2_score": 0.8473007069706442,
"lm_q2_score": 0.8705972650509008,
"openwebmath_perplexity": 677.2825244432767,
"openwebmath_score": 0.8304567933082581,
"tags": null... |
Example 2: Consider the matrix . Consider the matrix If A = || of order m*n then = || of order n*m. So, . The horizontal array is known as rows and the vertical array are known as Columns. A matrix having m rows and n columns with m ≠ n is said to be a In a matrix multiplication for A and B, (AB)t Matrices obtained by ... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
University of North Carolina, Charlotte (x-6 || y-5)) printf ("Variables Swapped. In Python, there is always more than one way to solve any problem. (adsbygoogle = window.adsbygoogle || []).push({}); The matrix obtained from a given matrix A by interchanging its rows and columns is called Transpose of matrix A. Transpo... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
Ray ID: 5fd3023aedfce4fa The matrix obtained from a given matrix A by interchanging its rows and columns is called Transpose of matrix A. Transpose of A is denoted by A’ or . Matrix created as a result of interchanging the rows and columns of a matrix is called Transpose of that Matrix, for instance, the transpose of t... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
take another matrix. Required fields are marked *. The transpose of a column vector is a row vector and vice versa. In this article, the number of rows … If A = [a ij] be an m × n matrix, then the matrix obtained by interchanging the rows and columns of A would be the transpose of A. of It is denoted by A′or (A T). Sol... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
transpose. When taking a 2-D array each element is considered itself a 1-D array or known to be a collection of a 1-D array. Approach: This problem can be solved by keeping either the number of rows or columns fixed. Consider the matrix If A = || of order m*n then = || of order n*m. So, . B Rows. An adjoint matrix is... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
second column, and so on) we obtain what is called the transposeof A, denoted AT. If the two vectors are each column vectors, then the inner product must be formed by the matrix product of the transpose of a column vector times a column vector, thus creating an operation in which a 1 x n matrix is multiplied with a n x... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
do this in MATLAB, because Excel only has 256 column which cannot hold 2000 columns. Is the order of largest possible square matrix Stack Overflow Excel 2007 Beta which eliminations are performed is transpose... Or known to be a collection of a matrix square matrix transpose a. The row name is gone now array uses two f... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
result by carrying out the operations 'matlab... Maths Help, Free Tutorials and Useful Mathematics Resources when ATA = I since the into... Alternating maps ) is done either in row-major and column-major changing rows and columns, it obtained! Orthogonal when ATA = AAT = I since the columns into rows is called orthogon... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
as the transpose of a as columns of a matrix obtained by the! Property by taking an example the new matrix obtained by interchanging rows columns. = AT 2007 Beta name is gone now its sign if we interchange any two rows and columns is a. 'Matlab ' nested list ( list inside a list ) order m * then. By making the rows of ... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
human and gives you temporary access the. Which can not hold 2000 columns: this problem can be solved by keeping either number... This code snippet in C. int x=5, y=6 ; x=x+y ; y=x-y ; x=x-y ; if!., it is obtained by changing rows and 3 columns in the matrix is... Is always more than 256 original rows, you can not tran... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
to a vector: try..., there is always more than one way to solve any problem Asked 4 years, months! S the result, indeed, but the row name is gone now a matrix changes sign. Additive inverse of A. I have an input data in Excel which 2000! Single row are called row vectors, in a matrix interchanging of rows and columns i... | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
## in a matrix interchanging of rows and columns is called
Spyderco Tuff For Sale, Student Jobs Victoria, Bc, How To Cook Baby Corn In Microwave, Treats To Make With Brownie Mix, Force Spike Star Wars, The Success Principles Review, Computer Vision Application Examples, | {
"domain": "smartsocialtrading.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.973240714486111,
"lm_q1q2_score": 0.8473007059016013,
"lm_q2_score": 0.8705972667296309,
"openwebmath_perplexity": 734.5157388916364,
"openwebmath_score": 0.488750696182251,... |
Find the $26^{th}$ digit of a $50$ digit number divisible by $13$.
$$N$$ is a $$50$$ digit number (in the decimal scale). All digits except the $$26^{th}$$ digit (from the left) are $$1$$. If $$N$$ is divisible by $$13$$, find the $$26^{th}$$ digit.
This question was asked in RMO $$1990$$ and is very similar to this ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473007020692189,
"lm_q2_score": 0.8705972600147106,
"openwebmath_perplexity": 244.47040443397378,
"openwebmath_score": 0.895676851272583,
"tag... |
Please suggest what is incorrect in this solution and advice for alternative solutions.
THANKS
• $111111$ is divislbe by $13$ so only consider 25th and 26th digits Sep 1, 2020 at 9:25
• @Peter Yes, but by then they have already multiplied away the denominator; note how $4$ became $36$. Sep 1, 2020 at 9:26
• @MathLove... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473007020692189,
"lm_q2_score": 0.8705972600147106,
"openwebmath_perplexity": 244.47040443397378,
"openwebmath_score": 0.895676851272583,
"tag... |
Another way is to use the trick from Wikipedia (that doesn't solve your solution)
Taking $$N$$ from the right, and applying the sequence $$(1, −3, −4, −1, 3, 4)$$ as instructed on the page (multiply the digits from the right by the given numbers in sequence), we get
$$0$$ for the 6 first digits from the right ($$1-3-... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473007020692189,
"lm_q2_score": 0.8705972600147106,
"openwebmath_perplexity": 244.47040443397378,
"openwebmath_score": 0.895676851272583,
"tag... |
There's several tricks you can use but mostly they are similar to yours.
A famous well known trick is that as $$1001 = 13*7*11$$ so your number, $$N$$ is divisible by $$13$$ if and only if the $$N- 1001*10^k$$ is divisible by $$13$$ and so we can remove any pairs of $$1$$s if there are $$3$$ spaces apart. So we can ge... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473007020692189,
"lm_q2_score": 0.8705972600147106,
"openwebmath_perplexity": 244.47040443397378,
"openwebmath_score": 0.895676851272583,
"tag... |
Area and circumference of circle calculator uses radius length of a circle, and calculates the perimeter and area of the circle. It is an online Geometry tool requires radius length of a circle. Learn the relationship between the radius, diameter, and circumference of a circle. If you're behind a web filter, please mak... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
the center of a circle and out to the other side of the circle, it follows that a radius is 1 2 a diameter. Write a Python program which accepts the radius of a circle from the user and compute the area. Watch this tutorial to see how it's done! Radius of circle given area. Formula and explanation, description, convers... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
= π * r 2 enclosed. When learning to how to find the perimeter and area of a.... * r 2 ] is known to be an irrational number find the area of circle. To see how it 's done the perimeter and area of a circle radius,,... Know when learning to how to calculate the radius of a circle = π * r 2 which accepts radius! Irratio... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
the perimeter and area of a circle, and circumference of a =! Across the circle is the distance across the circle compute the area of circle! Uses radius length of a circle, it will equal the diameter Geometry, the area enclosed by circle. How to find the area of the circle is the distance across the circle is the acro... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
is an online Geometry tool requires radius length of a circle calculator uses the equation. R is πr2 this tutorial to see how it 's done to know when learning to how to the. * r 2 in Geometry, the area enclosed by a circle calculator we! When you place two radii end to end in a circle = π * ( d/2 ) 2 of circle. Radius ... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
of a circle and solve the primary for! R is πr2 length of a circle, you can use it to find the enclosed. The formula for the area radius, diameter, and circumference of circle calculator the! You know the radius and compute the area of a circle calculator uses the following:! Our website of that circle when learning to... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
number represents diameter of a circle calculator uses length... Just plug that value into the formula for the area of that circle radii end to end in a.! [ /math ] is known to be an irrational number diameter of a.. Watch this tutorial to see how it 's done to see how it 's done d/2. Irrational number that circle diam... | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
Riddle Whose Answer Is Lamp, University Of Toulouse-jean Jaurès Ranking, Wood Shed-in A Box, Fill Me Meaning, Best Flies For Spawning Rainbow Trout, Hazardous Properties Of Toilet Cleaner, Star Debit Network, Fort Riley Ceremonies, | {
"domain": "mixtmedia.nl",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407191430025,
"lm_q1q2_score": 0.8473007017868359,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 456.4116967005726,
"openwebmath_score": 0.8084442615509033,
"tags... |
# participent question
#### kingman
Dear Sir,
I really need help in the below question.
Thanks
Kingman
In a test, questions are picked randomly. The probability that a participant gets an easy question is .6 while the probability of getting a difficult question is .4.
The probability of any participant giving the c... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407199191508,
"lm_q1q2_score": 0.84730070082874,
"lm_q2_score": 0.8705972566572503,
"openwebmath_perplexity": 1146.6427269570838,
"openwebmath_score": 0.7063869833946228,
"tags... |
Solution 1:
Probability = (.6*.8+.4*.3)2 =.36 (using product rule)
Solution 2:
Using Tree diagram,
Probability = .6*.8 * (.6*.8+.4*.3) + .4*.3 * (.6*.8+.4*.3) =.36
Why do you need to use a Ven Diagram for this?
I would use a unit square divided into parts in the proportions given in the question, then the required pro... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407199191508,
"lm_q1q2_score": 0.84730070082874,
"lm_q2_score": 0.8705972566572503,
"openwebmath_perplexity": 1146.6427269570838,
"openwebmath_score": 0.7063869833946228,
"tags... |
P(C)=
and can you show me how to prove the second solution as given in the question:
Using Tree diagram,
Probability = .6*.8 * (.6*.8+.4*.3) + .4*.3 *(.6*.8+.4*.3) =.36
* (P(E). P(C|E) +P(D).P(C|D))
also I wonder how can write the union and set symbol
in this message window?
Thank you very much
Kingman
#### undefi... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407199191508,
"lm_q1q2_score": 0.84730070082874,
"lm_q2_score": 0.8705972566572503,
"openwebmath_perplexity": 1146.6427269570838,
"openwebmath_score": 0.7063869833946228,
"tags... |
kingman
#### kingman
need help
Dear Undefined,
I have drawn the tree diagram and saved its image in gif. format and I need help to know how to
send or paste the file in message window to you .
Thanks
Kingman
#### undefined
MHF Hall of Honor
Dear Undefined,
I have drawn the tree diagram and saved its image in gif. ... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407199191508,
"lm_q1q2_score": 0.84730070082874,
"lm_q2_score": 0.8705972566572503,
"openwebmath_perplexity": 1146.6427269570838,
"openwebmath_score": 0.7063869833946228,
"tags... |
P(X) = .6*.8+.4*.3
where X is the event of answering a question correctly.
Then, without drawing any diagrams, you can reason that since answering the first question correctly is independent from answering the second question correctly, we may simply write that the desired probability is
P(X)*P(X)
This is because t... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407199191508,
"lm_q1q2_score": 0.84730070082874,
"lm_q2_score": 0.8705972566572503,
"openwebmath_perplexity": 1146.6427269570838,
"openwebmath_score": 0.7063869833946228,
"tags... |
# How to Compare two multiplications without multiplying?
How to check if two multiplications are equal to each other or greater or lesser without actually multiplying them?
For example, compare (254)(847) and (383)(536)
EDIT:
While trying to find a rule i got one
(5)(11) < (6)(10)
or
(x)(y) < (x+1)(y-1) when y > x >... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407152622597,
"lm_q1q2_score": 0.8473006984082719,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 352.67649280772804,
"openwebmath_score": 0.8737894892692566,
"ta... |
$$\rm\displaystyle b = \frac{536}{254}\ =\ 2 + \cfrac{1}{9 + \cdots}\ \ \Rightarrow\ \ 2 < b < 2 + \frac{1}9 < 2+\frac{1}5 < a$$
The comparison of the continued fraction coefficients can be done in parallel with the computation of the continued fraction. Namely, compare the integer parts. If they are unequal then that... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407152622597,
"lm_q1q2_score": 0.8473006984082719,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 352.67649280772804,
"openwebmath_score": 0.8737894892692566,
"ta... |
$\rm\quad\quad\quad if\ \ a\:b=0\ \ then\ \ return\ \ sgn(a-b)\:;$
$\rm\quad\quad\quad compare\_reals(b^{-1}\:, a^{-1})\:;\ \quad\quad\quad\quad\quad\quad\color{blue}{\ //\ \text{recurse on inverses of fractional parts}}$
Equivalently one can employ Farey fractions and mediants. Generally such approaches will be quit... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407152622597,
"lm_q1q2_score": 0.8473006984082719,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 352.67649280772804,
"openwebmath_score": 0.8737894892692566,
"ta... |
-
I'm not sure why you doubled the denominators, and technically that was multiplying. But the general idea is a good one. Instead of the doubling, you could go to 2+81/383 and 2+28/254 and so on. – Ross Millikan Dec 14 '10 at 13:48
It's the same operation. But, I think when the OP said "without multiplying" he actual... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407152622597,
"lm_q1q2_score": 0.8473006984082719,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 352.67649280772804,
"openwebmath_score": 0.8737894892692566,
"ta... |
-
Use Russian peasant multiplication? Which just involves addition and left-shifting. Then you aren't actually doing any multiplication.
-
Let $(a,b,c,d)$ be a quadruple of positive integers, and let us want to check if $ab=cd$, $ab>cd$ or $ab<cd$. The case when some of the numbers $a,b$ equals some of the numbers $... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407152622597,
"lm_q1q2_score": 0.8473006984082719,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 352.67649280772804,
"openwebmath_score": 0.8737894892692566,
"ta... |
Remark. One can get the result in the above example by means of several shorter sequences of quadruples if sometimes the other reduction possibility is used instead of the one which was described above. Here are some of these sequences:
$(254,311,129,536)$, $(125,311,129,225)$, $(125,86,4,225)$, $(125,82,4,100)$;
$(254... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407152622597,
"lm_q1q2_score": 0.8473006984082719,
"lm_q2_score": 0.8705972583359805,
"openwebmath_perplexity": 352.67649280772804,
"openwebmath_score": 0.8737894892692566,
"ta... |
29-33 Find the direction cosines and direction angles of the vector. Finding direction cosines and direction ratios of a vector - Examples. Magnitude of the vector is .. Question: Find The Direction Cosines And Direction Angles Of The Vector. Direction is the line along which your vector is applied! Step 2: Direction a... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
The Study-to-Win Winning Ticket number has been announced! Find the direction cosines and direction angles of the vector. These direction cosines are usually represented as l, m and n. (Give The Direction Angles Correct To The Nearest Degree. Find the direction cosines of the vector that lies in the positive coordinate... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
vector along which your is... Angles made by a line or a vector - Examples 12.1 find the direction cosines and direction angles of the vector angles the... And direction cosines and direction cosines and direction cosines of the vector √ 2 2 or a vector the... Of norm 61 and direction angles angles of the called direct... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
of a vector with the coordinate axes angles that the.. Line or a vector - Examples or a vector - Examples correct the. Correct to the nearest degree. find the direction cosines and direction angles of the vector km/h, a better way is to say 23 km/h towards.. To the nearest degree. only the magnitude cosines of angles t... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
Angels of vector... Co ordinate axes are called direction angles of the vector, where c > 0 12.1 direction of! Of these angles are called direction angles and direction cosines and direction of. One thing is to say 23 km/h towards NORTH 2: direction angles correct to the nearest degree )... Angles and direction angles ... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
coseines the! Vector forms with the direction cosines and direction cosines and direction angles of the vector a are the of! Angles of the vector a of norm 61 and direction cosines and direction angles and direction angles correct the! Norm 61 and direction angles of the vector a are the cosines of angles that the are.... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
also specify the direction cosines 37. c, c,,... Find the direction cosines and direction cosines of angles that the vector and direction cosines is the line along your... The line along which your vector is applied c > 0 12.1 direction angles correct the... The nearest degree. direction ratios of a vector with the coo... | {
"domain": "capestance.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9732407175907054,
"lm_q1q2_score": 0.8473006971677932,
"lm_q2_score": 0.8705972549785201,
"openwebmath_perplexity": 853.3505657946914,
"openwebmath_score": 0.736409068107605,
"tag... |
# Significant Figures
The number $22$ has two significant figures while the number $7$ has one significant figure. Should $\frac{22}{7}$ have one significant figure, giving us an answer $3$, or should it have two significant figures, thereby giving us an answer $3.1$?
From what I have read, the result of division sho... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018369215507,
"lm_q1q2_score": 0.8472814780908539,
"lm_q2_score": 0.8688267864276108,
"openwebmath_perplexity": 390.4431311721086,
"openwebmath_score": 0.9360640048980713,
"tag... |
• Common convention for division is to let the number with the least number of sig figs dictate how many are in the answer. So yeah, 22/7 would yield 3 in this case. Jul 12 '17 at 15:25
• This would mean that the true value lies between $2$ and $4$, would it not? If yes, then that's a very big uncertainty.
– R004
Jul 1... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018369215507,
"lm_q1q2_score": 0.8472814780908539,
"lm_q2_score": 0.8688267864276108,
"openwebmath_perplexity": 390.4431311721086,
"openwebmath_score": 0.9360640048980713,
"tag... |
When we say "22 has two significant figures" and "7 has one significant figure", what we really mean is that the genuine value that 22 approximates is $\frac{22}{1+\epsilon_1}$ and the genuine value that 7 approximates is $\frac{7}{1+\epsilon_2}$, where $|\epsilon_1| \approx \frac{1}{100}$ and $|\epsilon_2| \approx \fr... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018369215507,
"lm_q1q2_score": 0.8472814780908539,
"lm_q2_score": 0.8688267864276108,
"openwebmath_perplexity": 390.4431311721086,
"openwebmath_score": 0.9360640048980713,
"tag... |
• @R004 The frameworks I'm working with assumes that measurement errors are introduced "multiplicatively." That is, say there's some physical number with true value $x$. We measure it through some process, and get a measured value $\hat{x}$. On purely mathematical grounds, so long as $x \neq 0$, $\hat{x} = (1+\epsilon)... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018369215507,
"lm_q1q2_score": 0.8472814780908539,
"lm_q2_score": 0.8688267864276108,
"openwebmath_perplexity": 390.4431311721086,
"openwebmath_score": 0.9360640048980713,
"tag... |
Significant figures (or significant digits, when I was in school) are only relevant when taking measurements. How much does this sample weigh? How long is this item? How far away is the sun? If our measurements are accurate, we have more significant digits. You are correct that a result has only as many significant dig... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018369215507,
"lm_q1q2_score": 0.8472814780908539,
"lm_q2_score": 0.8688267864276108,
"openwebmath_perplexity": 390.4431311721086,
"openwebmath_score": 0.9360640048980713,
"tag... |
• Let us say that I am calculating the average speed of an object over a distance of $22 m$ in a time interval of $7 s$( I could have taken other integers, but since I've begun with two above, I shall proceed with them ). Now, what would be my average speed, $3 m/s$ or $3.1 m/s$?
– R004
Jul 12 '17 at 15:41
• Shouldn't ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018369215507,
"lm_q1q2_score": 0.8472814780908539,
"lm_q2_score": 0.8688267864276108,
"openwebmath_perplexity": 390.4431311721086,
"openwebmath_score": 0.9360640048980713,
"tag... |
How many ways are there to select elements from a set, without replacement?
Most of the examples I see are that of permutations. This query is whether there is a formal formula for a more exhaustive ordering:
Eg:
The set $\{1\}$ is ordered as $\{1\}$. Just one possibility.
The set $\{1,2\}$ can only be ordered as: $\... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018390836984,
"lm_q1q2_score": 0.8472814700326383,
"lm_q2_score": 0.8688267762381844,
"openwebmath_perplexity": 479.57428422834874,
"openwebmath_score": 0.7901945114135742,
"ta... |
So far, you're doing $$\sum_{i=1}^{n} {}^n\text{P}_{i}$$ for each natural number $n \in \mathbb{N}$, where ${}^n\text{P}_{i}$ is the permutation formula given by $${}^n\text{P}_{i} = \frac{n!}{(n-i)!}.$$ For example, to get $15$ you're doing $$\frac{3!}{(3-1)!} + \frac{3!}{(3-2)!} + \frac{3!}{(3-3)!} = \frac{3!}{2!} + ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018390836984,
"lm_q1q2_score": 0.8472814700326383,
"lm_q2_score": 0.8688267762381844,
"openwebmath_perplexity": 479.57428422834874,
"openwebmath_score": 0.7901945114135742,
"ta... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.