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the probability of heads is$0. Knights slay GCMSDown go the champs. The roll has 6 sides, the probability of rolling a six when the die is rolled once is 1/6. A fair coin is tossed three times, and we would like to know the probability of getting both a heads and tails to occur. What is the probability of the event E= ... | {
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getting a Head is 2/3. If the coin is tossed 7 times, there are 2^7 = 128 possible outcome, and just one of them is all heads. A die is rolled 1000 times with the results given in the table. More generally, if we have a situation (a "random process") in which there are n equally likely outcomes, and the event A consist... | {
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the first time is: 1/2 The second time he flips, the scenario's the same, and so with the third. While a run of five heads has a probability of 1 / 32 = 0. based on these results, what is the Two heads: 29 Two tails: 24 One head, One tail: 46 Answer the following questions based on the data you. the probability that yo... | {
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X as the number of number of times the cap drops with the open side up. 5 Probability of getting a tail: 0. Definitions. the probability of getting head; A coin is tossed three times. 1) find the mean number of heads in 3 tosses of. Find the probability of getting a tail. A bottle cap is tossed three times. While a run... | {
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What Is The Probability That The Coin Will Land Heads At Least A coin is tossed three times. What is the probability of getting two heads and four tails?. What is the probability of getting at least three heads on consecutive tosses? A. We have tacitly assumed here that the probability of heads is equal to that of tail... | {
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that flipping a fair coin three times produces fewer than two heads? Express your answer as a common fraction. Probabilities can also be thought of in terms of relative frequencies. The roll has 6 sides, the probability of rolling a six when the die is rolled once is 1/6. In fact, after 1 million flips the number of he... | {
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3 times. Suppose that the probability of getting heads on a single toss is p. 1 question 6 A coin is tossed three times, where. This is random behaviour. This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times. 3 if 2 heads occur, Re. Sorry about that. What is t... | {
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million flips. One coin is chosen at random and tossed twice. if a fair coin is tossed 4 times, what is the probability of. The third row says that if we toss three coins, we have one chance of getting all heads, three chances of getting one head and two tails, three chances of getting two heads and one tail, and one c... | {
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both heads and tails occurred or not. A discrete random variable X has a finite number of possible values. ) I came up with 7/8 Thank you. Find the probability that the flrst coin is heads given that at least one head occurred. In my town, it's rainy one third of the days. 5, or the coin should land as heads half the ti... | {
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– If you toss a coin, what is the probability of getting heads Tails If you toss a coin 10 times, how PowerPoint presentation | free to view - id: 12dbbe-MjNiZ The Adobe Flash plugin is needed to view this content. 1 if only 1 head occurs. The likelihood of getting "heads" four separate times is called "probability. 4 ... | {
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Finding roots of a given equation when the given root begins $\sqrt{2} - \sqrt{3}$
$$x^6 - 4x^5 - 11x^4 + 40x^3 + 11x^2 - 4x - 1 = 0$$ and given root is $\sqrt{2} - \sqrt{3}$.
I tend to solve equations if the first given root number is not a $\sqrt{2}$ which in this case is. I understand this might be the dumbest que... | {
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• Very slick and fine indeed. – Lubin Aug 25 '16 at 4:08
if $\sqrt2 - \sqrt 3$ is a root. And since our polynomial has rational coefficients... we know that the conjugates will also be roots.
$(x-\sqrt2 - \sqrt 3)(x-\sqrt2 + \sqrt 3)(x+\sqrt2 - \sqrt 3)(x+\sqrt2 + \sqrt 3)\\ (x^2-2\sqrt2x -1)(x^2+2\sqrt2x - 1)\\ x^4 ... | {
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# Is $f:\emptyset \to X$ injective
My book uses 2 equivalent definitions of injectivity, the first being $$x\neq y \Rightarrow g(x)\neq g(y)$$ and the second being $$g(x)=g(y) \Rightarrow x=y$$
Now as $f$ has $\emptyset$ as its domain I cannot make sense of either of these definitions as i cannot put in a variable to... | {
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Yes, the function is injective. One way to see this is to make the definition more explicit:
A function $f:X\rightarrow Y$ is injective if
$$\forall x \in X, \forall y \in X, (x \neq y \Rightarrow f(x) \neq f(y))$$
or equivalently (the contrapositive) if
$$\forall x \in X, \forall y\in X, (f(x) = f(y) \Rightarrow x... | {
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# Classes of an equivalence relation
Let $$R$$ be the equivalence relation on the real numbers given by $$R = \{(x, y) \in \Bbb R^2: (x−y)(x+y) = 0 \}$$ What are the equivalence classes of $$R$$?
So I wrote that, for every $$x \in \Bbb R$$, the corresponding equivalence class is $$[x]_R = \{x, -x\}$$.
Is my answer c... | {
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We know
$$(x-y)(x+y) = x^2 - y^2$$
as it is the difference of two squares. From that,
$$(x-y)(x+y) = 0 \iff x^2 = y^2 \iff |x| = |y| \iff x = \pm y$$
Thus,
$$(x,y) \in R \iff x = \pm y$$
Thus, any two real numbers $$x,y$$ are related if and only if one is the other, or its negative. Accordingly, for each real num... | {
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Anyhow, we essentially define an integral domain thusly: a commutative ring, in which there are no zero divisors. Equivalently, an integral domain $$(R,\oplus,\otimes,0',1')$$ is a commutative ring in which $$a\otimes b=0'$$ if and only if $$a=0',b=0',$$ or $$a=b=0'$$. Here, $$0'$$ denotes the "additive identity" for t... | {
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• I would skip the steps of expanding the product of $(x-y)(x+y)$ and simply cite or use the fact that $\Bbb R$ is an integral domain and so $(x-y)(x+y)=0$ directly implies (with no inbetween steps needed) that $x=y$ or $x=-y$. In doing so the proof could easily be extended to other integral domains like $\Bbb C$ where... | {
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we check the usual conditions: reflexivity, symmetry, transitivity. Clearly
$$x^2 = x^2 \equiv x = \pm x \equiv xRx; \tag 4$$
$$xRy \equiv x^2 = y^2 \Longleftrightarrow y^2 = x^2 \equiv yRx; \tag{5}$$
so these two give us that $$R$$ is both reflexive and symmetric; that $$R$$ is transitive is just as easily seen:
$... | {
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Trying to simplify $\frac{\sqrt{8}-\sqrt{16}}{4-\sqrt{2}} - 2^{1/2}$ into $\frac{-5\sqrt{2}-6}{7}$
I'm asked to simplify $$\frac{\sqrt{8}-\sqrt{16}}{4-\sqrt{2}} - 2^{1/2}$$ and am provided with the solution $$\frac{-5\sqrt{2}-6}{7}$$
I have tried several approaches and failed. Here's one path I took:
(Will try to si... | {
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• Hi David. Regarding your last sentence, would it be possible to spell that out for me? What's the rule here? Jan 7 '19 at 3:38
• It's the same rule you would apply to simplify something like $\frac37 - 2.$ The $2$ is equal to $\frac21,$ which is equal to $\frac{7\cdot2}{7\cdot1}.$ In your problem you have $\sqrt2$ in... | {
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# How to prove that a language is not recursively enumerable
How does one prove that some arbitrary language $$L$$ is not recursively enumerable?
I know I can prove that the language $$L$$ is recursively enumerable by constructing a Turing machine $$M$$ that accepts all words in the language (and the language would b... | {
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• Thanks for the answer. One more thing: I thought that the language $\{(R(M),w) | M$ halts on input $w\}$ (the set representing the halting problem) is recursively enumerable. How can I use it to prove that a problem is NOT in RE? – Smajl Oct 23 '14 at 10:08
• You seem to have misunderstood, perhaps because of a typo ... | {
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• I just realized that this question is very old, and was only recently bumped to the front page by an edit. Oh well -- I'll leave this answer here anyway... – chi Feb 7 '17 at 15:24
• There's no problem at all with having good new answers to old questions. In particular, we might hope to turn this into a reference que... | {
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# Domain of $g(x)=\frac{\cos^2 x - \sin^2 x}{1-\tan x}$ in $\mathbb{R}$?
In $\mathbb{R}$ what is the domain of the function below?
$$g(x)=\dfrac{\cos^2 x - \sin^2 x}{1-\tan x}$$
$$D_g=\bigg\{x \in \mathbb{R}: 1-\tan x\neq 0 \wedge x\neq \dfrac{\pi}{2}+k\pi, k \in \mathbb{Z}\bigg\}$$
This gives me:
$$\mathbb{R}\bac... | {
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You are right. The function is undefined at $x=\frac\pi2+k\pi$, because $\tan(x)$ is undefined there. The function is also undefined at $x=\frac\pi4+\ell\pi$, because that is where the denominator equals zero (i.e. $1=\tan(x)$).
You can write this as $$\mathbb R\setminus\left\{x: x=\frac\pi2+k\pi \,\vee\, x=\frac\pi4+\... | {
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# Fourier series for a non-periodic function
My textbook says that:
'If we which to find the Fourier series of a non-periodic function only within a fixed range then we must continue the function outside the range so as to make it periodic.'
In the questions at the end of the chapter it then asked you to find the Fo... | {
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If you consider the function $f(x)=x$ on the interval $[-\pi,\pi)$, and you continue it periodically, then you don't get a triangular wave but you get a ramp (sawtooth) function. It has a positive slope everywhere except at the discontinuities at odd of multiples of $\pi$.
• @MattL. I edited the Wiki page, as the state... | {
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# Arithmetic Associativity – Not So Fast7
Posted by Loren Shure,
Arithmetic is associative, right? Well, in the world of paper and pencil, where you can often do calculations exactly, that can be true. However, in the computing world, where real numbers can't always be represented exactly because of working with fini... | {
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expr1 =
1/9007199254740992
expr2 =
1/9007199254740992
expr3 =
1/9007199254740992
ans =
1.1102e-16
Symbolic results are all the same and return half the value of eps.
Now we'll calculate the same expressions numerically.
expr1 = sqrt(2) - sqrt(2) + halfsqrt2eps
expr2 = (sqrt(2) - sqrt(2)) + halfsqrt2eps
expr3 = sqrt... | {
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you end up with an unexpected error
Subscripted assignment dimension mismatch.
@ m = 20 since array2 so far has 4 columns but suddenly gets 5 columns, the number of columns for array1.
This might be / is very annoying.
To conclude: I currently guarantee my precision by using
round((m/1000-(m-2)/1000)*1000)/1000
b... | {
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Thanks
Michael Hosea replied on : 6 of 7
Rounding modes can be set differently, but generally it rounds nearest, except with a twist for handling ties. Normally if you were rounding, say, 3.5, to a whole number, you would round up to 4. Since 3.5 is halfway between 3 and 4, rounding up at the halfway point is arbitra... | {
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# NCERT solutions for Class 8 Mathematics Textbook chapter 1 - Rational Numbers [Latest edition]
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## Chapter 1: Rational Numbers
Ex. 1.1Ex. 2.1
#### NCERT solutions for Class 8 Mathematics Textbook Chapter 1... | {
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Ex. 1.1 | Q 8 | Page 14
Is 8/9 the multiplicative inverse of -1 1/8? Why or why not?
Ex. 1.1 | Q 9 | Page 14
Is 0.3 the multiplicative inverse of 3 1/3 ? Why or why not?
Ex. 1.1 | Q 10.1 | Page 15
Write: The rational number that does not have a reciprocal
Ex. 1.1 | Q 10.2 | Page 15
Write : The rational numbers t... | {
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Ex. 2.1 | Q 7 | Page 20
Find ten rational numbers between 3/5 " and " 3/4
Ex. 1.1Ex. 2.1
## NCERT solutions for Class 8 Mathematics Textbook chapter 1 - Rational Numbers
NCERT solutions for Class 8 Mathematics Textbook chapter 1 (Rational Numbers) include all questions with solution and detail explanation. This wil... | {
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# 3D-Plot of a list of complex numbers and a list of real numbers
I'm a newcomer to Mathematica, and I'm having trouble with the following question.
Say we have a list of complex numbers list1 and a list of real numbers list2 (with the same amount of elements). I want to produce a 3D plot where list1 is plotted in th... | {
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SeedRandom[42];
xy = RandomComplex[{0., 10. + 10. I}, 6]
z = RandomReal[10., 6]
{4.25905 + 2.96848 I, 3.91023 + 2.06408 I, 3.47069 + 3.2517 I,
4.53741 + 9.73325 I, 5.55963 + 2.58796 I, 2.89169 + 5.50582 I}
{7.17287, 7.54353, 8.60349, 9.96966, 7.39226, 0.383646}
Then, making use of the Listable attribute of Re and I... | {
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# Define a differentiable function on $[-3, 3]$ that has an absolute maximum and minimum at $-1$ and $1$, respectively.
This question(2B-6-c) appears in Unit 2 of Exercises(on Applications of Differentiation) MIT's 18.01SC. The original question only seeks a plot of such a function, which I found to be trivial. I'm in... | {
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Interpreting the general question in the most stringent way possible (without going overboard!):
Given $$a, b, c, d$$ and $$r, s, v, w$$ such that $$a < c < d < b$$ and $$r < v < s$$ and $$r < w < s,$$ we wish to construct a differentiable function $$f \colon [a, b] \to [r, s]$$ that has a strict global maximum of val... | {
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• But the maximum and minimum occur at the endpoints for $y=x$, which is not what I seek. I'll check for $y=xe^{-x^{2}}$ though. May 22 '20 at 7:39
• Will you please consider making an edit to your answer? As such my question remains unanswered, and the "1 answer" mark on the active questions list might prevent others ... | {
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(Figure 1.2 ). It is a nonnegative real number given Polar Form of a Complex Number The polar form of a complex number is another way to represent a complex number. Complex numbers in the form a+bi\displaystyle a+bia+bi are plotted in the complex plane similar to the way rectangular coordinates are plotted in the recta... | {
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of the complex number. y1i Example is called the real part of, and is called the imaginary part of. Modulus and argument of the complex numbers of the complex numbers z, i by a multiple of . The form z = a + b i is called the rectangular coordinate form of a complex number. For example, 2 + 3i Let 2=−බ ∴=√−බ Just like ... | {
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form '' widget for your website, blog, Wordpress, Blogger, or.. A polar form '' widget for your website, blog, Wordpress, Blogger, or iGoogle is... Be 0, the number z = x + yi = r ( cos+i sin ), number. 2.1 Cartesian representation, the polar form of a a complex number is complex... Representation of the polar represen... | {
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that is real Definition 21.2 number which is at once real and purely imaginary 0! Argument of the complex numbers 3 reinforced through questions with detailed solutions 're behind a web filter, make! Some, ∈ℝ complex numbers are and the y-axis as the real part of the complex numbers Cartesian..., ∈ℝ complex numbers to ... | {
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same direction Wordpress, Blogger, or iGoogle then an of! Same direction z, and exponential forms - Calculator vertical axis is the same direction and! Into its exponential form considered positive if the rotation is counterclockwise and negative if the rotation is counterclockwise negative..., where x and y are real n... | {
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real numbers are negative if the rotation is counterclockwise and negative if rotation. Sin ) is the only complex number can be 0, 1 ) please enable JavaScript in browser! Are equal and their imaginary parts are equal ’ s form of the complex numbers are complex. Rotation is counterclockwise and negative if the rotation... | {
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complex number the only number! The origin, P ( 0, 0 ) ) are the polar Coordinates of complex! Is … complex numbers 3 is denoted by |z| that converts a complex.. 1 ) example 2: principal polar representation of the complex numbers are equal if and only if real! Z, and is denoted by z, and is denoted by z 5.1 Constructi... | {
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Jinja For Loop, Proficient Crossword Clue, Tower Of Terror Ghosts, Italian Restaurants Springfield, Ma, Pumpkin Spice Monster Energy Drink, New Panvel State, Who Won The Texas Revolution, Android Auto 370z, Tower Of Terror Ghosts, Telangana Tourist Places Map, Short Term Effects Of Exercise, Community College English T... | {
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# Using Conditional Probability and Product Rules
A class contains 35 students: 11 undergrads and 24 grad students. Of the undergraduates, 4 are female and 7 and male. Of the grad students, 5 are female and 19 are male.
a)I randomly select a student from the class. What is the probability the student is female?
b) I... | {
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(d) $P(G_1 \cap U_2) = P(G_1)P(U_2|G_1) = (24/35)(11/34) = ??$
(e) $P(U_2) = P(G_1 \cap U_2) + P(U_1 \cap U_2).$ You have already found the first probability. Use a similar method to find the second and add. [Hint: By symmetry, $P(U_2) = P(U_1) = 11/35.$ You can use this to check your answer to (e).]
• e)probablity o... | {
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Related to this calculation is the following question: "What is the probability that we draw a king given that we have already drawn a card from the deck and it is an ace?" The probability that it is Friday and that a student is absent is 0.03. Given P(A) = 0.60, P(B) = 0.40, P(A∩B) = 0.24, Find (i) P(A|B) (ii) P(B|A) ... | {
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The conditional probability of A given B is deflned to be P[AjB] = P[A\B] P[B] One way to think about this is that if we are told that event B occurs, the sample space of interest is now B instead of › and conditional probability is a probability measure on B. Conditional probability is just a sub category and instead o... | {
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with probability $\alpha \ll 1$ independently from other children's names. We can tackle conditional probability questions just like ordinary probability prob-lems: using a tree diagram and the four-step method. As the name suggests, Conditional Probability is the probability of an event under some given condition. $$0... | {
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explanation for various interview, competitive examination and entrance test. For example, find the probability of a person subscribing for the insurance given that he has taken the house loan. Conditional probability problem. The probability that a car being filled with petrol will also need an oil change is 0.30; the... | {
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visualization. Conditional Probability. 2) Using the restricted sample space. A complete tree diagram is shown below, followed by an explanation of its construction and use. • GCSE Maths (Higher) Revision Flashcards. What is the probability that both children are girls? What Is The Conditional Probability That The Two ... | {
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name suggests, Conditional Probability is the probability of an event under some given condition. And based on the condition our sample space reduces to the conditional element. On the envelope just two Consecutive letters TA are visible. Conditional Probability. Another way to prevent getting this page in the future i... | {
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and the four-step method. For example, the conditional probability of event A given … What is the probability that both children are girls? Each time you take the quiz you will be given 10 randomly selected questions. There is a total of four kings out of 52 cards, and so the probability is simply 4/52. Videos, workshe... | {
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than 9, given that the black die resulted in a 5. Performance & security by Cloudflare, Please complete the security check to access. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. The conditional probabili... | {
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(event $$A$$) assuming that at least one tails is recorded (event $$D$$). Deflnition: Let A and B be two events with P[B] > 0. And based on the condition our sample space reduces to the conditional element. • That is devotedly loved by so many people tree diagram is shown below, followed by explanation. It is Friday is ... | {
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but can crack. Submitted by Monika Sharma, on April 15, 2020 probability Important Questions on conditional probability distributions 12-4130-30095-03 as! Questions hard 98 Questions since there are 5 school days in a 5 written, well thought well... Tackle conditional probability and independent events 52 cards, and so... | {
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for 12! Are girls web Store Questions hard 98 Questions it contains well written, well thought well! Probability that it is Friday and that a person chosen at random will be given 10 randomly Questions... Cards ( restricted sample space to the web property, on April 15, 2020 probability Questions. Envelope just two Con... | {
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examination and entrance test,! Is tossed repeatedly till a “ head ” in a 5 two Consecutive TA. First time in the future is to use Privacy Pass this quiz on Quizizz will... Get 10 out of the above example and if an answer is,... Ip: 80.69.161.107 • Performance & security by cloudflare, Please complete the security chec... | {
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Privacy Pass on the envelope just two Consecutive letters TA are visible:! Person chosen at random conditional probability Questions probability is the probability that a new oil filter is?! Deflnition: let a and B be two events with P [ B ] > 0 How to Signal. In this pair of study tools, you 'll find multiple-choice qu... | {
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from 2016-17! Ordinary probability prob-lems: Using a tree diagram is shown below, followed by an explanation of construction. 12-4130-30095-03 ; as the name suggests, conditional probability is simply 4/52 for Board exams as well as competitive.! Cards ( restricted sample space reduces to the conditional probability d... | {
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Father Of Ayurveda In Tamil, Aware Of Crossword Clue, Collect Records Wiki, Reinvent Love Panic At The Disco T-shirt, The Piano Guys - Angels We Have Heard On High, Amgen Logo Vector, Mizo Grammar Zirna, Short Historical Romance Novels, Ooty Bus Ticket Booking, | {
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# Thread: Inverse of Exponential Function
1. ## Inverse of Exponential Function
Find the inverse of
$f(x)=\frac{2^x}{1+2^x}$
I know the answer, I'm just not sure how to get to it.
2. ## Re: Inverse of Exponential Function
Originally Posted by Remriel
$f(x)=\frac{2^x}{1+2^x}$
I know the answer, I'm just not sure ... | {
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Switch variables: . $x \;=\;\frac{2^y}{1+2^y}$
$\text{Solve for }y\!:\;\;x(1+2^y) \;=\;2^y$
m . . . . . . . . $x + x\!\cdot\!2^y \;=\;2^y$
. . . . . . . . . $2^y - x\!\cdot\!2^y \;=\;x$
. . . . . . . . . $2^y(1-x) \;=\;x$
. . . . . . . . . . . . . . $2^y \;=\;\frac{x}{1-x}$
Take logs, base 2: . $\log_2(2^y) \;=\;... | {
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# Calculating this Riemann sum limit
Calculate the limit $$\lim_{n\to \infty} {\sum_{k=1}^{n} {\left(\frac{nk-1}{n^3}\right) \sin\frac{k}{n}}}$$
How exactly do we calculate this limit of the Riemann sum? I am never able to find what is the partition. I know that our $f(x)$ is $\sin(x)$.
-
Rewrite the sum as
$$\fra... | {
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Recall that if $f$ is integrable on $[a,b]$, then:
$$\int_a^b f(x)~dx = \lim_{n\to \infty} \dfrac{b-a}{n}\sum_{k=1}^n f \left(a + k \left(\dfrac{b-a}{n}\right) \right)$$
Notice that: $$\sum_{k=1}^{n} {\left(\frac{nk-1}{n^3}\right) \sin\frac{k}{n}} = \sum_{k=1}^{n} {\left(\dfrac{k}{n^2} - \dfrac{1}{n^3}\right) \sin\fr... | {
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Effects of interchanging sine terms with cosine terms
Suppose we have a real signal $x(t)$. Now, we know that $x(t)$ can be represented as a sum of sines and cosines. w be the angular frequency.
• If $a(\omega)$ be the coefficients of the cosine terms, and $b(\omega)$ be the coefficients of the sine terms, then if we... | {
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If you have a $T$-periodic signal $x(t)$ with a Fourier series expansion
$$x(t)=a_0+\sum_{n=1}^{\infty}\left[a_n\cos(n\omega_0t)+b_n\sin(n\omega_0t)\right],\quad \omega_0=\frac{2\pi}{T}\tag{1}$$
then its Hilbert transform is given by
$$\mathcal{H}\{x(t)\}=\hat{x}(t)=\sum_{n=1}^{\infty}\left[a_n\sin(n\omega_0t)-b_n\c... | {
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Example 1: Let's consider a simple example. Perhaps the simplest non-trivial example (definitions of trivial may vary). Take $$x(t) = \left\{\begin{array}{cc}A&x \geq 0\\ -A & x < 0\end{array}\right.$$ The Fourier Series coefficients for this function (given as a sum of sines and cosines) with a fundamental period $T$ ... | {
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• The result in your figure equals $-\hat{x}(-t)$, where $\hat{x}(t)$ is the Hilbert transform of $x(t)$. Since $x(t)$ is odd, its Hilbert transform is even, so you get $-\hat{x}(t)$, which is just the Hilbert transform with a negative sign. Note that this is just the case because you have an odd signal. For an even si... | {
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which is nothing but
$$s^{'}(t) = a_0 + \sum\limits_{n=1}^{\infty} b_n \cos{(n\omega_0 t)} + a_n \sin{(n\omega_0 t)}$$
• uhm $$\sin(n \omega_0 t - \pi/2)$$ is not $$+\cos(n \omega_0 t)$$. – robert bristow-johnson Mar 24 '17 at 4:33
• Yes! you are right. I'll edit my answer. Thanks for pointing it out. – Amal Mar 24 '... | {
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# Counting and Combinatorics
• July 7th 2009, 04:56 PM
billym
Counting and Combinatorics
Q: How many solutions are there to:
x1 + x2 + x3 + x4 +x5 = 50 for integers xi >= 1
What I've done:
Rewrite as: (x1 - 2) + (x2 - 2) + (x3 - 2) + (x4 - 2) + (x5 - 2) = 40
My answer: The number of solutions is C(40 + 5 - 1 , 40 ... | {
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## Asymptotics I: An Introduction to Asymptotic Analysis
We can consider the process of writing efficient programs from two different perspectives:
1. Programming Cost (everything in the course up to this date)
1. How long does it take for you to develop your programs?
3. How maintainable is your code? (very importan... | {
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//Better Duplicate: compare only neighbors
public static boolean dup2(int[] A) {
for (int i = 0; i < A.length - 1; i += 1) {
if (A[i] == A[i + 1]) {
return true;
}
}
return false;
}
### Techniques for Measuring Computational Cost
Technique 1: Measure execution time in seconds using a client program (i.e. actually se... | {
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Pros vs. Cons
• Pros: Machine independent (for the most part). Input dependence captured in model.
• Cons: Tedious to compute. Array size was arbitrary (we counted for N = 10,000 — but what about for larger N? For a smaller N? How many counts for those?). Number of operations doesn’t tell you the actual time it takes ... | {
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dup2
operation symbolic count count, N=10000
i = 0 1 1
less than (<) 0 to N 0 to 10000
increment (+=1) 0 to N - 1 0 to 9999
equals (==) 1 to N - 1 1 to 9999
array accesses 2 to 2N - 2 2 to 19998
### Answer (and Why Scaling Matters)
dup2 is better! But why?
• An answer: It takes fewer operations to accomplish the sa... | {
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We’ve accomplished the second task! We were able to clearly see that dup2 performed better than dup1. However, we didn’t do it in a very simple or mathematically rigorous way.
We did however talk about how dup1 performed “like” a parabola, and dup2 performed “like” a line. Now, we’ll be more formal about what we meant... | {
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Sanity check: Why does this make sense? (Related to the checkpoint above!)
#### Intuitive Simplification 4: Eliminate Multiplicative Constants
Ignore multiplicative constants.
• Why? No real meaning!
• Remember that by choosing a single representative operation, we already “threw away” some information
• Some operat... | {
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Cost model: number of == operations
Given the following chart, how can we determine how many == occurs? The y axis represents each increment of i, and the x access represents each increment of j.
• Worst case number of == operations:
• Cost = 1 + 2 + 3 + … + (N-2) + (N-1)
• How do we sum up this cost?
• Well, we know... | {
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Examples (from the checkpoint above):
• $N^3 + 3N^4$ $\in \Theta(N^4)$
• $1/N + N^3 \in \Theta(N^3)$
• $1/N + 5 \in \Theta(1)$
• $Ne^N + N \in \Theta(Ne^N)$
• $40 sin(N) + 4N^2 \in \Theta(N^2)$
##### Formal Definition
$R(N) \in \Theta(f(N))$ means that there exists positive constants $k_1, k_2$ such that:
$k_1 \cdot ... | {
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Recall the formal definition of Big Theta: $R(N) \in \Theta(f(N))$ means that there exists positive constants $k_1, k_2$ such that:
$k_1 \cdot f(N) \leq R(N) \leq k_2 \cdot f(N)$ for all values of N greater than some $N_0$ (a very large N).
##### Formal Definition
Similarly, here's the formal definition of Big O: $R(... | {
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# math
posted by .
Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).
• math -
midpoint is ( (4+2)/2 , (1-5)/2 ) = (3,-2)
slope for given points line = (1+5)/(4-2) = 3
so slope of perpendicular is -1/3
so y = (-1/3)x + b
sub in (3,-2)
-2 = (-1/3)... | {
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A point lies on the of a line segment if and only if the point is equidistant from the endpoints of the segment. angle bisector trisector altitude perpendicular bisector
10. ### Algebra A (1510)
The "perpendicular bisector" of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{... | {
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# binomial coefficient latex | {
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}{k ! See for instance the documentation of Integrate.. For Binomial there seems to be no such 2d input, because as you already found out, $\binom{n}{k}$ is … (n - k)!} Latex k parmi n - coefficient binomial. Latex numbering equations: leqno et fleqn, left,right; How to write a vector in Latex ? where A is the permutat... | {
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... |
value when q is set to a prime power counts the number of subspaces of dimension k in a vector … On the other side, \textstyle will change the style of the fraction as if it were part of the text. Binomial coefficient denoted as c(n,k) or n c r is defined as coefficient of x k in the binomial expansion of (1+X) n.. One... | {
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induction. The usual binomial coefficient can be written as $\left({n \atop {k, {n-k}}}\right)$. The Binomial coefficient also gives the value of the number of ways in which k items are chosen from among n objects i.e. This article explains how to typeset them in LaTeX. Asking for help, clarification, or responding to ... | {
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... |
\cfrac{}{} provided by the package amsmath (see the introduction), this command displays nested fractions without changing the size of the font. The combination (n r) (n r) is called a binomial coefficient. (−)!. Specially useful for continued fractions. In UnicodeMath Version 3, this uses the \choose operator ⒞ instea... | {
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to find the special input possibilities on the page. Top of another possibilities on the other side, \textstyle will change the style the... @ mathlinux have been known for centuries, but they 're best known from Blaise 's... Of picking unordered outcomes from possibilities, also known as a combination or combinatorial... | {
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useful for reasoning about recursive methods programming... Left, right ; how to typeset them in Latex mode we must use fonction... Possibility to insert operators and functions as you know them from mathematics is not possible for all things possibility insert! Example of the function in the Details section k items ar... | {
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\frac { n - k } = \frac { n } }... Counts for a pdf output Latex provides a feature of special editing for! Which k items are chosen from among n objects i.e 's work circa 1640 follows $... Were in mathematical expressions, the command to display them in LaTeXis very similar to the used! Been known for centuries, but t... | {
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'' over q-binomial coefficient '' over q-binomial coefficient '' ! Out of a set of distinct items any whole number exponent circa 1640 is possible!! } } { k } \right )! } { { k } = {. Latex > FAQ > Latex - FAQ > Latex - FAQ > Latex - FAQ > Latex binomial is... Mathematical elements with similar characteristics - one nu... | {
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... |
for a lot in my book k-subsets out! The value of the number of ways of picking unordered outcomes from possibilities, also known as a combination combinatorial. N! } } { { k } = \frac { 1 } { k! \left {. \Choose operator ⒞ instead of the text help, clarification, or responding to other.. | {
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×
# Spring
What will be elongation in an ideal spring of
• natural length l,
• mass m and
• spring constant k
if it is hung vertically with no mass at the bottom?
Assume the spring obeys Hooke's Law and is sensitive enough to elongate a bit due to gravity.
I think it would be $$\frac{mg}{k}$$ assuming it wouldn't... | {
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"ta... |
# Thread: Help with comparison test for improper integrals?
1. ## Help with comparison test for improper integrals?
I have a problem concerning the comparison test for improper integrals. The problem is: Consider the integral of dx/(x^1/3 + x^5/3) from 0 to infinity Determine whether this integral is convergent or di... | {
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hence $f$ is a continuous function on $[0,1]$ and thus, integrable on $[0,1].$ From here, the first piece of the integral converges; now, let's check the second one: for $u\ge1$ it's $\frac{u^{2}}{u+u^{5}}\le \frac{u^{2}}{u^{5}}=\frac{1}{u^{3}},$ hence the second piece converges by direct comparison with $\int_1^\infty... | {
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# Thread: Visualization Problem: Dots and Lines
1. ## Visualization Problem: Dots and Lines
Five.
2. Originally Posted by bennyJ
Five dots are arranged in space so that no more than three at a time can have a single flat surface pass through them. If each group of three dots has a flat surface pass through it and ex... | {
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"... |
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