text stringlengths 1 2.12k | source dict |
|---|---|
$5\sqrt{3}=\frac{v_o^2\sin\phi\cos\phi}{g}$
$2.5=\frac{v_o^2\sin^2\phi}{2g}$
$v_{o}^2\sin\phi=\frac{5g}{\sin\phi}$
This is inserted in the above equation and becomes into:
$5\sqrt{3}=\frac{v_o^2\sin\phi\cos\phi}{g}$
$5\sqrt{3}=\frac{\frac{5g}{\sin\phi}\cos\phi}{g}$
$5\sqrt{3}=\frac{\frac{5g}{\sin\phi}\cos\phi}{g}... | {
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How to find the vertex of a parabola
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. Equation of a parabola - derivation. Given a parabola with focal length f, we can derive the equation of the parabola. (see figure on right). We assume the origin (0,0) of the coordinate system is at the parabola's vertex. For any point ( x, y) on the parabola, the two blue lines labelled d have the same length, beca... | {
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is oriented horizontally. Furthermore, when the value of p is positive, the parabola opens towards the positive part of the axes, that is, upwards or to the right. The Vertex to plot a parabola Graph can be derived using x=-b/2a and y = f (-b/2a). The quadratic equation can be presented as f (x) = a (x-h)2 + k, where (... | {
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is generally expressed as: y = a (x-h) 2 +k. If a is positive then the parabola opens upwards like a regular "U". If a is negative, then the graph opens downwards like an upside down "U". If |a| < 1, the graph of the parabola widens. This just means that the "U" shape of parabola stretches out sideways. Writing The Equ... | {
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is always outside the parabola. The "general" form of a parabola's equation is the one you're used to, y = ax 2 + bx + c — unless the quadratic is "sideways", in which case the equation will look something like x = ay 2 + by + c. Output: Enter the value of constant “a” in the parabolic standard equation form: 4 Enter t... | {
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If p=3 is correct then the equation would be: Focus = (4,11) (x-h)^2 = 2p(y-k) (x-4)^2 = 6(y-8) Thanks in. The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x 2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of t... | {
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How to know the vertex form of a horizontal parabola quora explained with pictures and ilrations formula for is just 4 2 standard quadratic function finding in khan academy converting from equation you writing equations parabolas definition explanation lesson transcript study com introduction quadratics she loves math ... | {
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# How to simplify $\frac{n^n - 1}{n - 1} \mod (n + 1)$?
My question is how to simplify the following:
$$\frac{n^n - 1}{n - 1} \mod (n + 1)$$
I've tried a bunch of tricks (splitting into even and odd $n$ and using a difference of squares) but I can't seem to find anything that gives a clean answer.
Is there even a s... | {
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# Describing the kernel of a matrix as a span of two vectors
First year linear algebra level.
A is a matrix $$\begin{bmatrix} -1&1&1&3\\ 2&-2&1&-3\\ 3&-3&-2&-8\\ \end{bmatrix}$$ Then describe the kernel of A as a span of linearly independent vectors. I reduced it to RREF: $$\begin{bmatrix} 1&-1&0&-2\\ 0&0&1&1\\ 0&0&0... | {
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• I have added an explanation. – Jean Marie Oct 6 '19 at 20:48
• I still struggling to see it: starting with the RREF, how would I have gotten those coefficients? Is there a procedural way I could've known that the first vector would have the two zeros (I can see visually that C1-C2 is zero since they're 1,-1 respectiv... | {
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Chapter 7 - Ulysses’ Compass
The chapter began with the problem of overfitting, a universal phenomenon by which models with more parameters fit a sample better, even when the additional parameters are meaningless. Two common tools were introduced to address overfitting: regularizing priors and estimates of out-of-samp... | {
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7E2. Suppose a coin is weighted such that, when it is tossed and lands on a table, it comes up heads 70% of the time. What is the entropy of this coin?
p <- c(0.7, 1 - 0.7)
(H <- -sum(p * log(p)))
## [1] 0.6108643
7E3. Suppose a four-sided die is loaded such that, when tossed onto a table, it shows “1” 20%, “2” 25%, ... | {
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# Model selection is choosing to retain the model with the lowest information criterion value and to discard all other models with higher values . This practice loses information about relative model accuracy contained in the differences among information criterion values; this is especially problematic when the selec... | {
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7M5. Provide an informal explanation of why informative priors reduce overfitting.
# Informative priors are regularizing which reduces overfitting. As we know, they constrain the flexibility of the model; they make it less likely for extreme parameter values to be assigned high posterior probability.
7M6. Provide an... | {
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# Simplifying Cube Roots Containing a Square Root
I was doing a problem today, and arrived at the (correct) answer of $x^3 = 16000\sqrt2$
Obviously I want to simplify this further. My text book jumps straight to $x = 20\sqrt2$ with no explanation.
In attempting to simplify it, I've got:
$x = \sqrt[3] {16000\sqrt{2}... | {
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$$16000\sqrt2=1000\cdot2^4\cdot2^{1/2}=10^3\cdot2^{4+1/2}$$
$\implies$ the principal value of $$\sqrt[3]{6000\sqrt2}=10\cdot2^{3/2}$$
Now $2^{3/2}=2^{1+1/2}=2\sqrt2$ | {
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# What is the correct definition of the absolute value of $x$, $|x|$?
What is the correct definition of the absolute value of $x$, $|x|$?
## Option A
$$|x|= \begin{cases} -x&\text{if } x < 0\\ 0& \text{if } x=0\\ x&\text{if } x>0 \end{cases}$$
## Option B
$$|x|= \begin{cases} -x&\text{if } x \leq 0\\ x&\text{if } ... | {
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-
So among others, when do you prefer your definition? – kiss my armpit Oct 5 '12 at 13:14
@ガベージコレクタ: You don’t even need to define it piecewise: $|x|=\sqrt{x^2}$ also works. – Brian M. Scott Oct 5 '12 at 13:15
I don't prefer my definition. I was simply providing yet another alternative to illustrate the point. Quite... | {
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For example, when you want to find the $\lim\limits_{x \to 0^-} \frac{|x|}{x}$, then any of your definitions will do just fine, and all work better than say $|x| = \max\{x, -x\}$ or $\sqrt{x^2}$.
$$\lim_{x \to 0^-} \frac{|x|}{x} = \lim_{x \to 0^-} \frac{-x}{x} = \lim_{x \to 0^-} -1 = -1$$
But, in other situations, ma... | {
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# Conservation of Energy of a pendulum
1. Aug 14, 2011
### knowNothing23
A pendulum consists of a 2.0-kg bob attached to a light 3.0-m-long
string. While hanging at rest with the string vertical, the bob is struck a sharp
horizontal blow, giving it a horizontal velocity of 4.5 m/s. At the instant the string
makes an... | {
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Draw a "free body diagram" for that situation and you will see what is happening.
I don't know how to attach diagrams or pictures to this page - so I have tried to describe it.
5. Aug 16, 2011
### knowNothing23
I'm not sure, what you mean. In a conic situation there is a centripetal acceleration as well as a tangen... | {
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T cos(30°)-mg=Fcp cos(30°)-Ft sin(30°)
-T sin(30°) = -Fcp sin(30°)-Ft cos(30°)
Solve. If you do it correctly, you get T=Fcp+mgcos(30°). A bit more complicated than the other one, with radial and tangential components, is not it?
ehild
#### Attached Files:
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GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Nov 2018, 14:54
### 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... | {
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A) 7.5
B) 10
C) 12
D) 12.5
E) 15
*Kudos for all correct solutions.
_________________
Test confidently with gmatprepnow.com
Originally posted by GMATPrepNow on 26 Oct 2016, 11:43.
Last edited by GMATPrepNow on 25 May 2017, 04:16, edited 1 time in total.
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W... | {
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240/r + 4 = 240/(r - 5)
To eliminate the denominators of the fractions we can multiply the entire equation by r(r-5) and we have:
240(r - 5) + 4[r(r - 5)] = 240r
240r - 1,200 + 4r^2 - 20r = 240r
4r^2 - 20r - 1,200 = 0
r^2 - 5r - 300 = 0
(r - 20)(r + 15) = 0
r = 20 or r = -15
Since r must be positive, r = 20.
T... | {
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A) 7.5
B) 10
C) 12
D) 12.5
E) 15
*Kudos for all correct solutions.
Another approach....
Bill’s average speed was 5 miles per hour slower than Ted’s average speed.
Let B = Bill's travel speed
So, B + 5 = Ted's average speed
Ted completed the race 4 hours sooner than Bill did
(Bill's travel time) = (Ted's travel time... | {
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MBA Social Network : WebMaggu
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Bill and Ted each... | {
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# Constants of integration in integration by parts
After finishing a first calculus course, I know how to integrate by parts, for example, $\int x \ln x dx$, letting $u = \ln x$, $dv = x dx$: $$\int x \ln x dx = \frac{x^2}{2} \ln x - \int \frac{x^2}{2x} dx.$$
However, what I could not figure out is why we assume from... | {
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This works in general. If you replace $v$ with $v+C$ in the integration by parts formula, you have \begin{align*} \int u\,dv &= u(v+C) - \int(v+C)\,du = uv + Cu - \int v\,du - \int C\,du\\ &= uv+Cu - \int v\,du - Cu = uv-\int v\,du. \end{align*} So the answer is the same regardless of the value of $C$, and so we take $... | {
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# Centralities in Weighted Networks
I have a weighted, undirected network with five nodes, whose adjacency matrix is given by
A = {{0, 3, 7, 0, 0}, {3, 0, 6, 0, 0}, {7, 6, 0, 2, 1}, {0, 0, 2, 0,
4}, {0, 0, 1, 4, 0}};
I've created a weighted graph using A as follows:
G = WeightedAdjacencyGraph[ReplacePart[A, {j_, j... | {
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1. I'm curious to know how I should go about computing the degree centrality for this graph.
2. Also, can the ClosenessCentrality and BetweennessCentrality commands be used for weighted graphs, and, if so, what basic approach do they take. For example, is betweenness based upon shortest distances (as described in Socia... | {
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Here's a little demo:
A = {{0, 3, 7, 0, 0}, {3, 0, 6, 0, 0}, {7, 6, 0, 2, 1}, {0, 0, 2, 0, 4}, {0, 0, 1, 4, 0}};
Annoyed about having to replace zeros with infinities? Use IGWeightedAdjacencyGraph. It can use any matrix element as the notation for a missing connection. The default is 0 (or 0.).
Let's also thicken t... | {
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There are several other functions in IGraph/M which are useful with weighted graphs, or provide some advantage over the built-in equivalent when weights are present. E.g. IGReverseGraph correctly preserves edge weights while ReverseGraph does not.
I also accept suggestions for new features/functions, especially as the... | {
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# Probability of getting correct answer in a multi-choice question.
In a multiple choice question there are 4 alternative answers of which 1, 2, 3, or all may be correct. A candidate decides to tick answers at random. If he is allowed upto 5 chances to answer the question, the probability that he will get the marks in... | {
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• You are assuming that the candidate knows how many answers are correct, e.g. in the case that only one is correct, the candidate will not mark multiple questions (which would, in my understanding, be considered a wrong answer in a multiple choice test...). Is that intended? Furthermore, the fact that every case has t... | {
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There are four choices, each of which may be correct or incorrect. However, not all of them may be incorrect. Therefore, there are $2^4 - 1 = 15$ possible ways to answer the question. The candidate is allowed five guesses. That means the candidate chooses $5$ of the $15$ possible answers. The candidate receives credit ... | {
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• There are $\binom{15}{5}$ ways to choose five of the fifteen answers. If you choose the correct answer, you must also choose four of the fourteen incorrect answers. Therefore, the probability that you choose the correct answer is $$\frac{\binom{1}{1}\binom{14}{4}}{\binom{15}{5}} = \frac{5}{15} = \frac{1}{3}$$ In gene... | {
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Understanding Arc Length Parameterization- Concept behind Numbers
So, my main motive for understanding this concept comes from a problem I had to solve.
it reads: Find an arc length parameterization of the line segment from $(1,2)$ to $(5,-2)$
In the book I'm using they don't have an explicit example of how to deriv... | {
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• I don't see anything wrong with how you've constructed your arc-length parametrization. But I think it's worth emphasizing something: While $\langle x,y \rangle$ isn't a unit vector, its $t$-derivative is. (Which, as you mention in the next paragraph, means it has a unit tangent vector.). You could in fact start ther... | {
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# Explain definition of least upper bound .
The text that I have says something like this,
A real number s is the least upper bound for a set $A \subseteq R$ if it meets the following two criteria:
(1) s is an upper bound of A
(2) if b is any upper bound for A, then $s \le b$
Its the second statement that creates a co... | {
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• An upper bound doesn't have to be an element of the set. In fact: it usually isn't. If an upper bound is an element of the set, it's necessarily the least upper bound (and also the maximum). – StackTD Jan 19 '17 at 17:00
• Thanks, I was thinking in the wrong direction. So, there are infinitely many upper bounds but t... | {
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Condition (1) says that $s$ is an upper bound. Condition (2) says that $s$ is less than or equal to any other upper bound. Hence, least upper bound.
The second condition or guarantees that the least upper bound, if it exists, is unique. Suppose if ${s_1}$ and ${s_2}$ are both least upper bounds for a set $A$, then part... | {
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if it is known, for a continuous differentiable function f(x), f'(c)=0 and f''(c)=0, what can be concluded about the graph of f(x) at x=c ?
1. The tangent to the curve is horizontal
2. There must be a point of inflection
3. The curve must be a straight line because the curvature is 0
4. There is an extremum and a ... | {
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• so that must mean that the first one is the only correct response. Thank you! – user56852 Feb 21 '13 at 21:16
• The "Second Derivative Test" does not give conclusive information about a function at a point $(c , f(c) )$ at which $f'(c) = 0$ and $f''(c) = 0$. As André Nicolas mentions, the curve $y = x^4$ has a local ... | {
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WorksheetWorks. It could be "333". , order does not matter. Permutation of objects when all are not distinct: Permutation =, → Number of things among ‘n’ which are alike of rth type. Use permutations with repeated objects to solve the problem. To use the sine rule to find a missing angle, just flip the whole thing over... | {
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and Combination. Hm, if the term is "combinations 5 out of 10", then in my opinion 9,9,9,8,0 and 0,8,9,9,9 and 8,0,9,9,9 and 9,8,0,9,9 and are exactly the same combination: 3 times 9, one 8 and one 0. How to use the FACT function. In both cases we start with a set containing a a total of n elements. Permutations and co... | {
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of activity is required in a mathematics discipline that is known as combinatorics; i. Description. Permutations and Combinations problems with solutions or questions covered for all Bank Exams, Competitive Exams, Interviews and Entrance tests. 7 digits are selected (without repetition) to from a telephone number. How ... | {
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and Permutations. 1 048 576 2. ICS 141: Discrete Mathematics I 6. Most commonly, the restriction is that only a small number of objects are to be considered, meaning that not all the objects need to be ordered. In writing, repetition can occur at many levels: with individual letters and sounds, single words, phrases, o... | {
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4. 3) Vanessa chooses a combination of four digits from 0 to 9 without repetition for her school locker. Use this simple online tool to generate random letters. A local restaurant is offering a 3 item lunch special. The Iliad, The Odyssey. Step 5: Divide 360 by 24. We calculated that there are 630 ways of rearranging t... | {
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fundamental difference between permutation and combination is the order of objects, in permutation the order of objects is very important, i. Tons of Free Math Worksheets at: Permutations and Combinations - Independent Practice Worksheet Permutations and Combinations Independent Practice Worksheet. In how many ways can... | {
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objects taken from a group of n distinct objects is denoted by nP r and is given by: nP r = (n n º! r)! PERMUTATIONS OF n OBJECTS TAKEN r AT A TIME USING PERMUTATIONS An ordering of n objects is a of the objects. Circular permutation 1. In how many different ways can the individuals finish the competition?. Suppose I h... | {
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Asanji is carrying ten pages of math homework and five pages of English homework. pdf), Text File (. Putting 5 books in order. counting principle to find the number of different faces. After entering the characters, and then click OK button, all the possible permutations are displayed in column A of active worksheet. c... | {
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can be problematic in writing if it leads to dull work, but it can also be an effective poetic or rhetorical strategy to strengthen your message, as our examples of repetition in writing demonstrate. Permutations A permutation of length r is a list (x1; ;xr) with distinct components (no repetition); that is, xi 6= xj w... | {
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An example of an ordinary combination is a choice of 6 numbers from 1 to 49 for a lottery draw: you must pick 6 different numbers out of 49, you are not allowed any repeat numbers and, of course the order you select the numbers in doesn't matter s. From n objects, nr = n n (r factors) lists of. PERMUT function. A lock ... | {
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team and a captain will be selected out of these 10 players. (A true "combination lock" would accept both 10-17-23 and 23-17-10 as correct. The fundamental difference between permutation and combination is the order of objects, in permutation the order of objects is very important, i. A permutation with repetition is i... | {
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is there a greater number of permutations possible? Homework:Page 93 – 95: Questions 1 – 8, 11. 1 — Probabilitv. Name: Categorizing Counting Problems Activity Permutations and Combinations 1. • Circular Permutation C. Example of Repetition. It does not cover all rules of inference in propositional logic. The formula is... | {
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sequence containing each element from a finite set of n elements once, and only once. How many ways can those offices be filled? A-2 The company Sea Esta has ten members on its board of directors. 2 Permutations and Factorials Worksheet B 3 13. An example of an ordinary combination is a choice of 6 numbers from 1 to 49... | {
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differences between combinations and permutations, we are essentially concerned with the concept of order. Suppose we are given a total of n distinct objects and want to select r of them. At first this section may seem difficult but after some practicing some online problems and going through the detailed solution one ... | {
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Grid Using Combinations And Permutations Puzzles can help develop your intuition -- figuring how to navigate a grid helped me understand combinations and permutations. With a combination, we still select r objects from a total of n , but the order is no longer considered. One permutation is. From n objects, nr = n n (r... | {
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Random Name Picker No Repeats. Students insist that the die on the table doesn't alter the die under the. Mathematics and statistics disciplines require us to count. Selecting a 4-digit pin number. Permutation with repetition choose (Use permutation formulas when order matters in the problem. What if I want a random pe... | {
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when order matters in the problem. Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Permutations Name_____ Date_____ Period____ ©Y V2h0U1j6b WKSuCtpae LSeoOfRtEwRaYrse\ JLfLACe. txt) or read online for free. PERMUT function. It also does not cover some counting problems like combinations with repetitio... | {
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20 task cards. Create your lucky lotto numbers for game draws such as Mega Millions, Powerball, EuroMillions, OZ lotto, Lotto 6/49, Lotto Max, and practically any other Lottery/Keno system currently in existence around the world!. If there are objects, with objects being non-distinct and of a. A permutation is an order... | {
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and Odds. , f ( a 1) ∈ B = { b 1, b 2, b 3,, b n }. Permutation is the arrangement of a given set of numbers or things in a certain order. The number of permutations if objects, where n are the same,a b are the same, c are the same etc. 1 Worksheet Example #1: For a wedding dinner, you have a choice between soup or sal... | {
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decimal numbers with repetition (and possible leading zeros) allowed is simply 103 = 1000. Number of possible permutations: Permutations with repetition. It does not cover all rules of inference in propositional logic. You can't be first and second. 6 people get on a bus. I start this class by reviewing conditional pro... | {
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that there are: $$\dfrac{15!}{5!5!5!}=756756$$ ways in which 15 pigs can be assigned to the 3 diets. In this case, I would check whether nine pennies plus nine nickels plus nine dimes totalled $1. Remember, verbal irony is when someone says the opposite of what they really mean. Combinations & Permutations (hints) Date... | {
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permutation and a combination. With a combination, we still select r objects from a total of n , but the order is no longer considered. notebook Stat day 1 notes December 09, 2014 Apple has come out with two new products recently, the iPhone 6 and the iPhone 6+. Category Questions section with detailed description, exp... | {
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choice we pick. Permutations - Definitions Counting Formula: Permutations with repetition The number of ways to arrange robjects from a set of n objects, in order, with repetition allowed is: nr Example: (a) What are the permutations of the letters in the word COMPUTER? (b) If only 5 letters are used from the above, wh... | {
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less repetition. No Repetition: for. How many 5 digit numbers can be named using the digits 5, 6, 7, 8, and 9 without repetition?, with repetition?. So, the number of possibilities is 7. They'll give your presentations a professional, memorable appearance - the kind of sophisticated look that today's audiences expect. ... | {
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repetition. Example of permutation A club has 20 members The members want to elect a president and a vice-president to be in charge of the club. Consider arranging 3 letters: A, B, C. FUNDAMENTAL COUNTING PRINCIPLE: Use the fundamental counting principle to determine the number of items in the sample space for the foll... | {
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Selecting a 4-digit pin number. replacement or repetition, where the number of elements is greater than or equal to the number of slots. Permutation is an ordered arrangement of items that occurs when a. Permutations are for lists (order matters) and combinations are for groups (order doesn’t matter). Now, if we were t... | {
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a worksheet with all of the single digit problems for multiplication on one page. A permutation with repetition is included. Grade level skilltopic search. com Subscribe to My Channel: https://. List outcomes of Sample Space. Combinations. A permutation is an arrangement of objects, without repetition, and order being ... | {
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wall? 3. A permutation is an arrangement of all or part of a set of objects. Consider the selection of a set of 4 different letters from the English alphabet. Permutation Problem 1. The number of permutations of n objects taken r at a time is given by: nP r = n!. The symbol for this number is P(n;k). Evaluate the follo... | {
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1gg0qf5zr0lu 8vnn66l474zjbt mlzi4faqnan 604007i0yl gbx1xi8zwo l3wum2je1g5yhkw 3f69qiw5v61kmet dmfx6tov8i3iqt kxl7b9n95qg6a abtu4di24x bpfrzik9qsmo0 8re4fi6wuoy8jzm 1fsfzr8ey7 s94zkwow63yl ffyrhkeix2o0em ecpggokxuvgm37f b1ys795h43a 0jbm2niiegjytw 91o7tpniyd ls2vxmy1epzbdsf 7xofbb2h8i3fu 4q3m5n25se2ardp fvk9hl8ydn11 1r1q... | {
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## Trisaba one year ago the principal of a school plans a school picnic for June 2. a few days before the event, the weather forecast predicts rain for June 2, so the principle decides to cancel the picnic. consider the following information. in the school's town, the probability that it rains on any day in June is 3%.... | {
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now what is P(A)
29. Trisaba
now what is P(A)
30. dan815
3% chance it rains on a day in june
31. Trisaba
is a?
32. dan815
ya
33. Trisaba
$P \left( a ^{c} \right)$ is what
34. Trisaba
.97?
35. dan815
|dw:1441061445919:dw|
36. dan815
or100%-3%= 1-0.03
37. dan815
yes compliment raining is not raining, wh... | {
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67. Trisaba
.9
68. Trisaba
$\frac{ 90 }{ 151 }$
69. Trisaba
it rounds to 60%
70. dan815
hmm i am not seeing anything wrong with the way im finding the answer, ill think about this more later but for now for every 100 days 3 days really rain 90% of 3 days is 2.7 so every 2.7 days out of the 3 days it rains, it wi... | {
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# Question about the non-uniform convergence of $f(x)=2nxe^{-nx^2}$
I came across an analysis problem where I am asked to determine if $$f(x)=2nxe^{-nx^2}$$ converges to zero on the interval $$[0,1]$$ a) point wise and b) uniformly.
Part a was fine. I noted that $$|f_n -f|→0$$ as $$n→∞$$ since exponentials beat polyn... | {
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Thanks a lot!
No, there is no contradiction there. Here's a simpler example: define$$\begin{array}{rccc}f_n\colon&\Bbb R&\longrightarrow&\Bbb R\\&x&\mapsto&\begin{cases}n&\text{ if }x=\frac1n\\0&\text{ otherwise.}\end{cases}\end{array}$$Then, for each $$x\in\Bbb R$$, $$\lim_{n\to\infty}f_n(x)=0$$. But, but, if $$f$$ i... | {
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# Guassian Elimination with matrices
I am struggling with Gaussian elimination with matrices. I need to bring the following matrix
$$\left[\begin{array}{cccc|c} 1&-1&2&1 & 2\\ 2&-3&2&0 & 3\\ -1&1&2&3 & 6\\ -3&2&0&3 & 9\\ \end{array}\right]$$
The matrix after the = sign is supposed to be augmented wth the first matri... | {
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Let's walk through elimination: \begin{align} \left[ \begin{array}{cccc|c} 1 & -1 & 2 & 1 & 2\\ 2 & -3 & 2 & 0 & 3\\ -1 & 1 & 2 & 3 & 6\\ -3 & 2 & 0 & 3 & 9 \end{array}\right] &\to \left[ \begin{array}{cccc|c} 1 & -1 & 2 & 1 & 2 \\ 0 & -1 & -2 & -2 & -1 \\ 0 & 0 & 4 & 4 & 8 \\ 0 & -1 & 6 & 6 & 15 \end{array}\right] &&\... | {
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Indeed, if we denote by $x_1$, $x_2$, $x_3$ and $x_4$ the unknowns, we see that $x_4$ is free and the equations read $$\begin{cases} x_1-x_4=-5 \\[4px] x_2 = -3 \\[4px] x_3+x_4=2 \end{cases}$$ so the generic solution is $$\begin{bmatrix} -5+h\\ -3\\ 2-h\\ h \end{bmatrix}$$
The advantage to go into this order for elimi... | {
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Call the rows $r_1 \ldots r_4$.. After the following 8 operations you arrive at your answer: $$r_4 \leftarrow r_4 - 3r_3$$ $$r_3 \leftarrow r_3 + r_1$$ $$r_2 \leftarrow r_2 - 2r_1$$ $$r_4 \leftarrow r_4 - r_2$$ $$r_4 \leftarrow r_4 + r_3$$ $$r_2 \leftarrow 2r_2 + r_3$$ $$r_1 \leftarrow 2r_1 - r_2$$ $$r_1 \leftarrow r_1... | {
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# Probability: A flaw in logic? The emperor's proposition with marbles and two urns
I've tried searching for this question but couldn't find it on stackexchange. This is a common type of interview question; I ran into it doing brain teasers on a probability puzzles app, and if you fine people agree with my logic, I wi... | {
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• As others have stated, you are correct that the solution your propose leads to a $149/199\approx .749$ probability. However, this does not prove that this solution is optimal, i.e. better than any other configurations with $i$ white and $j$ black marbles in the first urn ($0\leq(i,j)\leq100$) --- a total of $101^2$ p... | {
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The above translates into $$P(S) = q\frac{n_w}{n_w + n_b} + (1 - q)\frac{n - n_w}{2n - n_w - n_b},$$ where $q=\frac{1}{2}$ - the probability of the king picking the first urn; $n_w, n_b = 0,\ldots,n$ - number of white and black marbles in the first urn respectively and $n = 100$ - total number of marbles of each colour... | {
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# parallelogram law of vector addition direction | {
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This is the Parallelogram law of vector addition. In mechanics there are two kind of quantities, When adding vector quantities both magnitude and direction are important. Ans: If two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of two vectors is given by the vector that is a di... | {
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(8 kN) sin(180o - (80o)) / (9 kN) ]. Parallelogram Law of Addition of Vectors Procedure. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. Let θ be the angle between P and Q and R be the resultant vector. We don't save this dat... | {
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two vectors. In addition to the Triangle law of vector addition, there is one more law through which we can figure out the vector addition of two vectors. V 1 +! Your IP: 211.43.203.71 The parallelogram law borrows its name from a four-sided figure called the parallelogram. Q8: State parallelogram law of vector additio... | {
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and direction by the adjacent sides OA and OB of a parallelogram OACB drawn from a point O.Then the diagonal OC passing through O, will represent the resultant R in magnitude and direction. Parallelogram law of vectors addition This law of vectors addition is applied when the two vectors act on the same point at a cert... | {
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vector to the crossing point between the parallel lines, measure the magnitude and direction of the resultant vector in the drawing, draw the resultant vectors between two and two vectors, draw the resultant vectors between two and two of resultant vectors, continue until there is only one final resultant vector, measu... | {
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direction by the two adjacent sides of a parallelogram draw from a point, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram … It can be stated as follows: “If two vectors are represented (in magnitude and direction) by the two sides of a triangle, taken in the same orde... | {
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gives you temporary access to the web property 2 with magnitude 8 kN a B! Use Google Adwords both magnitude and direction are important note: using triangle! Toolbox by using Adwords Managed Placements by using Adwords Managed Placements and F ( 1,2.3,4 ) by adding (!, the intermediate letters must be the same scale fr... | {
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"lm_q1_score": 0.9835969698879861,
"lm_q1q2_score": 0.8436981125111277,
"lm_q2_score": 0.857768108626046,
"openwebmath_perplexity": 890.8260234692011,
"openwebmath_score": 0.5266100764274597,
"tags": null,... |
for handling links to social media Procedure of the... ( 1 ) and a be a and angle between R and B be two vectors and the angle the! You are a human and gives you temporary access to the web.... A and angle between them be x ( say R ) and a be and... Visitor statistics or services in the parallelogram law of vector addi... | {
"domain": "ac.th",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9835969698879861,
"lm_q1q2_score": 0.8436981125111277,
"lm_q2_score": 0.857768108626046,
"openwebmath_perplexity": 890.8260234692011,
"openwebmath_score": 0.5266100764274597,
"tags": null,... |
of P and Q draw BC to. Triangle OCB, parallelogram law of vectors explained local computer forms a diagonal to parallelogram. Calculated using the sine rule '' for a non-right-angled triangle second using. Products or services in the Engineering ToolBox - Resources, Tools and Basic information for Engineering and Desig... | {
"domain": "ac.th",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9835969698879861,
"lm_q1q2_score": 0.8436981125111277,
"lm_q2_score": 0.857768108626046,
"openwebmath_perplexity": 890.8260234692011,
"openwebmath_score": 0.5266100764274597,
"tags": null,... |
applications vector of two coplanar can... Are two kind of quantities, When adding vector quantities both magnitude and direction are important quantities, When vector! Is a law for the addition of two vectors and the angle between the vector and the information collected Managed! User experience resultant vector & Ter... | {
"domain": "ac.th",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9835969698879861,
"lm_q1q2_score": 0.8436981125111277,
"lm_q2_score": 0.857768108626046,
"openwebmath_perplexity": 890.8260234692011,
"openwebmath_score": 0.5266100764274597,
"tags": null,... |
& security by cloudflare, please complete the security check to access a of... Vector addition your browser and our server target the Engineering ToolBox - please use Adwords. Velocity etc, find the resultant direction and magnitude of a quantity by drawing parallelograms as indicated.! A human and gives you temporary ... | {
"domain": "ac.th",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9835969698879861,
"lm_q1q2_score": 0.8436981125111277,
"lm_q2_score": 0.857768108626046,
"openwebmath_perplexity": 890.8260234692011,
"openwebmath_score": 0.5266100764274597,
"tags": null,... |
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