intervals Definition and 288 Threads

Just a quick question on spacetime intervals in spacetime. Why is the spacetime interval between two events given by Δs^2 = -c^2(Δt^2) + Δx^2 + Δy^2 + Δz^2, rather than c^2(Δt^2) + Δx^2 + Δy^2 + Δz^2 (as if it were the distance between two points in four spatial dimensions)? Or more succinctly...

Am i right in saying i can use this formulae: - W/EI((x^3/12) - (xL^2/16)) + w/EI((Lx^3/12) - (x^4/24) - (xL^3/24)) please help. See attached question. Question aii. Thanks

Homework Statement I need to show that [0,1] and [0,2] have the same cardinality by giving a formula for a function that is bijective. Aren't there a number of functions that can fit this description? Can I then use any one? I'm a little confused, my teacher didn't really elaborate much upon...

Homework Statement function is (X) / (X^2 - 1)The derivative(as far as I know) is (-X^2-1) / (X^2-1)^2The Attempt at a Solution So I set it equal to zero, and I get -X^2 -1 = 0, which means X^2 = -1 This does not exist, so what would I say for the intervals? When I graph it, the function is...

First consider the following definitions from Baby Rudin: Interval: A set of real numbers of the form [a,b] where for all x \in [a,b] we have a \le x \le b. K-Cell: A set of k-dimensional vectors of the form x = (x_1, ...,x_k) where for each x_j we have a_j \le x_j \le b_j for each j from...

How do you see if the following inequality holds true for (-2,0)? (-x/4)*(x+2)>1 For that matter how do you test inequalities for a given interval in general? Certainly there must be a way other than to check all values of (-x/4)*(x+2) in (-2,0) and see if they are greater than 1?

Hi everybody! I have been asked to show that the Borel-algebra can be generated from the set of half-open intervals of the form [a , b) where a<b. I know that the set of open intervals of the form (a,b) where a<b generates the Borel-algebra and thought I would go about showing that the to...

Hello, I'm having a bit of trouble calculating the area under the curve of x^2 on the interval x=-3 to x=1. The question says that there I have to use n subintervals and left endpoints. Relevant Equations Δx=b-a/n xi=a+(Δx)(i-1) -its i-1 because we're using a left endpoint, otherwise...

I do not understand positive and negative intervals and increasing/decreasing intervals. I included 2 examples from my textbook which I did not understand and I was wondering if someone can explain it to me. Example 1: f(x) = 2 - x x intercept is (2, 0) and y-intercept is (0,2)...

Hello, I'm having trouble understanding the concept of confidence intervals... I have written a program using MatLab which takes set of data points and using nonlinear least squares it produces a curve to fit these data points, and in the process calculates three parameters that determine...

The question is as follows: Prove that if I1, I2 are intervals and J = I1\capI2 then J is an interval. To be honest I don't even know where to start. There's a "hint" that suggests that I first write out the definitions of I1, I2, J as intervals and of the intersection between I1 and I2, but...

Hello again. Still trying my hand at a physics simulation, as I've been re-learning a lot of forgotten physics and math in my journey! Been stuck on this problem for a few days now though, and thought I'd consult the experts! I'm probably missing something obvious, and the solution is...

Homework Statement If the domain of a continuous function is an interval, show that the image is an interval. Homework Equations Theorem from book: f is a cont. function with compact domain D, then f is bounded and there exists points y and z such that f(y) = sup{ f(x) | x ∈ D} and...

For a time-like interval between 2 events, it is impossible to find an inertial reference frame in which the events occur at the same time. This can be seen from the space-time interval s^{2}=c^{2}t^{2}-l^{2} where s must be real number for a time-like interval. However, how does it follow...

Homework Statement F(x)=6/x-(1/1-x) Find the intervals on which the function is increasing/decreasing? Homework Equations F(x)=6/x-(1/1-x) F'(x)= -6/x^2 -1/(1-x)^2 The Attempt at a Solution Critical points are x=0 and x=1 Function has a discontinuitiy at 0...

A theorem of real analysis states that any open set in \Re^{n} can be written as the countable union of nonoverlapping intervals, where "interval" means a parallelopiped in \Re^{n}, and nonoverlapping means the interiors of the intervals are disjoint. Well, what about something as simple as an...

Hi! I think I have to ask this since I'm having health problems- from Kreyszig, for xy'=-y how do you verify the solution y=h(x)=clnx by differentiating y'=h'(x)=-clnx^2? I don't see how you get the x^2 term also for ODEs the solution is on an open interval a<x<b but how does it include...

Hi If two events are separated by a time-like interval, then all inertial reference frames will agree on the order of the two events. For example, if event A occurred before event B in one inertial reference frame, then event A occurred before event B in all inertial reference frames. The...

Homework Statement f(x) = x+1 for -1,x<0 x-1 for 0<x<1 0 for x=0 expand it in an appropriate cosine or sine series Homework Equations f(x) = a0/2 + \sum [ancos (n\pix/p) + bn sin (n\pix/p) a0 = 1/p \intf(x).dx an = 1/p \int f(x)cos...

Homework Statement Hello. Can someon help me understand the difference between these two problems? #1: f(x)+3 #2: f(x+3) The reason I want to know if becuase my question tells me to use the domain of f(x) as [4, 8] and the range as [2, 6] Then it wants to know the domain and range...

Homework Statement During a space flight an astronaut communicates with Earth by sending radio signals at regular intervals. If he travels out and back at a speed of 0.9c. What is the ratio of the frequencies of receipt by a receipt by a terrestrial observer on the outward and return...

Hello, I know one proof of this well known theorem that assumes on the metric of R being the standard metric. Does this result generalize to arbitrary metrics on R? thank you

I have two files, one the function m-file: function dy = yprimewithdrag(t,y) % Provides derivatives dy(1) - dy(4) required to solve problem of % projectile in flight. % Variable definitions: % y(1) = vx (horizontal velocity component) % y(2) = vy (vertical velocity component) % y(3) = x...

There the well known theorem that every open set (I'm talking about R here with standard topology) is the union of disjoint open intervals. Now, looking at the geometry, it seems that between any two adjacent open intervals which are in the union constituting our open set there is a closed...

Homework Statement I reduced another problem to the following problem: If I is an interval and A is a subset of I, then A is either an interval, a set of discreet points, a union of the two. Homework Equations The Attempt at a Solution Is this trivial?

Hey all, 2 quick questions: 1. When dealing with the difference between 2 population means (independent samples) or differences of paired data (dependent), a lot of the questions are similar to: "is there sufficient evidence to prove that the difference is 0" or "is there enough evidence to...

Homework Statement a) Let I be a subset of the real line. Prove I is an interval if and only if it contains each point between any two of its points. b) Let Ia be a collection of intervals on the real line such that the intersection of the collection is nonempty. Show the union of the...

Homework Statement I can find the graphs amp and period. The only problem is finding the sub points or sub intervals. Say... Y = 3 sin (4x) Amp = 3 Period = 2pi/4 = pi/2 But.. don't know how to get the key points of the sub interval. The textbook says I have to divide interval [0...

Homework Statement my professor tell me that when looking at the case ∫ √ (a^2 - x^2) , the trig substitution of course is asinϑ where -pi/2 ≤ ϑ ≤ pi/2. What I don't understand is why my professor tells me that when this term, √ (a^2 - x^2), is in the denomenator of the integrand that we must...

I am a physics student new to the world of electronics and I have a question that may turn out to be very simple. What I am trying to design requires that a single output given some input be held in memory for a specified time despite any differing input being sent through during that time...

Hi, I am new to this forum so hello to everybody. I have this problem to solve: Homework Statement Q is moving away from P at speed 4/5 c. After 3 years (in Q's frame of reference) he turns around (assuming that turning takes no time) and is moving back to P at speed 4/5 c. What are spacetime...

Homework Statement I have two series of data consisting of samples of a noisy sine wave and need to determine the amplitude and phase and the confidence intervals. I determined the amplitude and phase but don't know how to calculate the confidence intervals, help! The Attempt at a Solution By...

Homework Statement Let property 1 be : If [ai,bi] is a sequence of intervals that are closed such that for each i the interval [a(i+1), b(i+1)] is either the left half of [ai,bi] or the right half, then there exists precisely 1 number in all intervals sequence. Show if a field f...

Hi all, When working out confidence intervals based on population samples are you supposed to always use t-distributions, standard normal (z) distributions, or do you make a choice based on the sample size? Up until now I've been lucky enough to have large sample sizes (for some work I'm...

Homework Statement Show that: Let S be a subset of the real numbers such that S is bounded above and below and if some x and y are in S with x not equal to y, then all numbers between x and y are in S. then there exist unique numbers a and b in R with a<b such that S is one of the...

Homework Statement I know the sample size n, the observed sample mean x, and the observed sample standard deviation s. I need to determine a value v such that I'm 95% confident that the average is v or less.The Attempt at a Solution If I calculate the 95% confidence interval, then I know...

Hey guys, doing another rudin-related question. Here Goes: Show that if E \subseteq \Re is open, then E can be written as an at most countable union of disjoint open intervals, i.e., E=\bigcupn(an,bn). (It's possible that an=-\infty bn=+\infty for some n.) My attempt: Take the set of all...

I have recently been extremely bothered by the fact that we can construct a bijection from [0,1] onto the entire two-dimensional plane which itself contains [0,1]. Similarly, I have been bothered by the fact that we can construct a bijection from (0,1) to all real numbers. Indeed we do so...

When i did a business statistics course some time ago, I was able to calculate confidence intervals, but i didn't understand ‘why’ they were calculated in the way they were. I considered that the size of a confidence interval is based on the number of observations and ‘the range of possible...

I'm having trouble grasping this concept. This is the part in question: Why is the point x uniquely determined by the nested sequence? if i pick two rational numbers, no matter how close together they are, surrounding say the square root of two, shouldn't there always be another two...

the function is: x/(x^2 - 9) i have found the horizontal asymptote(y=0) and vertical asymptote (x=3, x=-3) the first derivative is giving me problems =(

Confidence intervals [b]1. Homework Statement [/ Use CLT to construct approximate symmetric 100(1-alpha)% confidence interval [L,R] for p then show that [L,1] is then an approximate 100(1-alpha/2)% confidence interval for p The Attempt at a Solution When [L,1] then we have a one...

Hello all, I always come across the technique of decomposing a real interval into intervals with rational end point, however, I am a bit confused with the half-open/half-closed cases. For example, [0,t) = \cup_{q < t, q \in \mathbb{Q}} [0,q) . And for the case of [0,t] , we can only...

Homework Statement (a) Find the intervals on which is increasing or decreasing. (b) Find the local maximum and minimum values of . (c) Find the intervals of concavity and the inflection points. F=x2/(x2+3 The Attempt at a Solution a) f ' =6x/(x2+3)2 6x=0 => x=0 What...

Homework Statement (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflection points. x2/(x2+3) Homework Equations The Attempt at a Solution a) I find that f'(x)=6x/(x2+3)2 I am...

Hi! I'm reading up on confidence intervals for means. This is leaving my mind boggled. I caught the part where the interval = tc*(sample standard deviation/the square root of n). What's boggling my mind though is the variable tc. I see that t refers to a T distribution. But, I can't...

A random sample of 35 trading days is taken and the volume of a particular stock is recorded to determine whether the mean volume of the stock has changed from its 2007 value of 35.14 million shares. The sample resulted in a mean trading volume of = 39.48. Assuming a population standard...

Is there a smallest time interval?

Homework Statement a) Find the intervals of unit length on which f(x) = 2x^{4}-8x^{3}+24x-17 has it's zeros. b) For each of the following starting intervals, tell which of the zeros of f(x) will be found by the bisection method associated with the proof of Bolzano's THeorem. (Label the zeros...

Homework Statement Using the Schroeder-Bernstein Theorem, prove that any two intervals of real numbers are numerically equivalent. Homework Equations Schroeder-Bernstein Theorem: Let A and B be sets, and suppose that there are injections from A into B and B into A. Then, there exists a...