Interval Definition and 677 Threads

Homework Statement I am bit confused about the expression for finding the space time intervel. Some books say it is, (spacetime intervel)^{2}=(time intervel)^{2} - (space intervel)^{2} while some books say it is, (spacetime intervel)^{2}=(space...

Good morning, We are trying to understand Special Relativity through internet, and we would like to ask a couple of questions about the subject. We plan to post more questions as more doubts arise. Both doubts concern the Minkowski space-time diagram. First doubt: in the temporal dimension...

I don't know which forum to put this in... So here goes. Homework Statement Basically, I have gathered 30 data points that vary from about 1.3 - 4.7 in value (it doesn't matter what it is) with a mean of 2.98. Since I haven't done any statistics courses yet, I used the built in Excel...

if 4-x^2 < f(x) < 4 + x^2 for x in [-1,1] then what's lim as x goes to zero of f(x) ... this setup looks like epsilon form .. not sure how to interpret this guy...

How would you find CI for some function of a parameter? the case I'm particularly interested in is an approximate CI for p^2 where p is the proportion in the binomial model. http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval

Homework Statement -log5(cos(x)) = -1/2 How many answers are there in the interval [0,2pi) The Attempt at a Solution 5^-1/2 = cos(x) 1/sq rt 5 = cos(x) sq rt 5/5 = cos(x) 0.447 = cos(x) x = 63.43 Basically, I have no clue how to find the number of answers in the interval ; ( I...

Hi, if I have the confidence interval for the point estimate of an option price A which was found through simulation, can I also find a confidence interval for delta (dA/dS), where S is underlying asset price, without further simulation? thanks, sl

Homework Statement ∞ Σ √n X (x-1)^(n) n=1 Homework Equations Ratio Test let the series Σ An be a series with positive terms and lim as n ---> infinity is an+1 / an = finite number a. the series converges if r < 1 b. the series diverges if r > 1 or r is...

Homework Statement http://www.geocities.com/asdfasdf23135/stat15.JPG I am OK with part a, but I am having some troubles with part b. Homework Equations Width of a Confidence Interval The Attempt at a Solution Attempt for part b: http://www.geocities.com/asdfasdf23135/stat16.JPG...

The question is to determine the solution to the following 1st order linear DE, along with the largest interval the solution is valid on: cosx \frac{dy}{dx} + (sinx)y=1 Rewriting it shows it to be linear: \frac{dy}{dx} + (tanx)y = secx The intergrating factor is: e^{\int{tanx...

Thank you for taking the time to read this lengthy post. A car starts moving rectilinearly, first with acceleration a=5m/s2(the initial velocity is 0) then uniformly, and finally, decelerating at the same rate a, comes to stop.The total time of motion equals 25 seconds. The average velocity...

Homework Statement determine the interval algebraically for -2(x-1)(2x+5)(x-7)>0 The Attempt at a Solution the zeroes are 1. -2.5, 7 what do i do with the -2 in front?

Homework Statement The question asks me to find the general solution to (x^2-1)y' + 2y = (x+1)^2, and to determine the largest interval over which this general solution is defined. It's the latter which is tripping me up. Homework Equations I've already found the general solution as...

The following distinguishes TWO cases for large samples confidence interval for difference in means: http://www.geocities.com/asdfasdf23135/stat11.JPG where Sp^2 is the pooled estimate of the common variance, n1 is the sample size from the first population, n2 is the sample size from the...

Homework Statement Let I C R be an interval which is open and closed at the same time. Prove that I=R or I is the empty set. Homework Equations The Attempt at a Solution I'm looking more for a outline structure for the solution. I have made assumptions that I is not equal to R...

Homework Statement Suppose a function is continuous at a point, c. Does this mean there exists an interval around c which is also continuous? If so prove Homework Equations The Attempt at a Solution

Find the interval of convergence of the given series and its behavior at the endpoints: \sum^{+\infty}_{n=1} \frac{(x+1)^n}{\sqrt{n}} = (x+1) + \frac{(x+1)^2}{\sqrt(2)}+... The attempt at a solution Using the ratio test: \left|\frac{S_{n+1}}{S_{n}}\right| =...

Homework Statement An object falls from the top of a 103.6m high building. The vertical distance between two consecutive windows A and B is 4.0m. The first window/storey is also 4m from the top of the building. The object reaches window B 0.1s after it has reached window A. Which...

Cinsider please the invariance of the space-time interval in an one space dimension approach (x-0)2-c2(t-0)2=(x'-0)2-c2(t'-0)2 My question is: does it hold for arbitrary events (x,t) in I and (x',t') in I? Does it hold only in the case when the events are genertated in I and I' by the same...

The spacetime interval s between two events is s^2 = c^2*t^2 - x^2 where t is the time between the 2 events and x is the distance between the 2 events in a given frame of reference. What is the general condition on s such that two events cannot be simultaneous in any frame? I don't...

Homework Statement Problem 1 of 2: Why is it that the continuity of a function in a region R and the continuity of the first partial derivative on R enables us to say that not only does a solution exist on some interval I0, but it is the only solution satisfying y(x0) = y0? Problem 2 of...

Is there any general formula for interval bisection, rather than consider two similar triangles each time? Thanks

At any interval of space, is the net density of that interval never equal to zero?

Identify an interval [-a,a] so that |arctan(x)-x+x^3/3| < or = 10^-15 for all x E [-a,a]. Your result needs to be supported by a convincing proof I'm not sure how to go about this... can someone help me out? all i could probably do is... since.. 10^-15 is close to zero, i can find out...

Homework Statement A balls roll along a straight path with the following velocity and time intervals 3.0 s at +15.0 m/s 7.0 s at +20 m/s 6.0 s at -30 m/s 4.0 s at 3.5 m/s What is the displacement in the last 5.0-15.0 time interval: I've been looking at this question for a good 30...

Homework Statement Let I=[a,b] and let f:I->R be a function (not necessarily continuous) with the property that for every x in I, f is bounded in a neighborhood of x. Prove that f is bounded on IThe Attempt at a Solution I have no idea

Homework Statement Find an interval of length 1 that contains a root of the equation xe^{x}=1 Homework Equations The Attempt at a Solution I'm not quite sure how to find these intervals... Homework Statement Find an interval of length 1 that contains a root of the equation...

Craig Hogen, in his paper Indeterminacy of Holographic Quantum Geometry, Phys. Rev D 78, 087501 (2008), has claimed noise seen in output of the GEO600 interferometric gravitational-wave detector is evidence for a fundamental minimum interval time. What is the time-line for the survival of this...

Homework Statement Prove that the interval [0,1] is not a zero set. 2. The attempt at a solution Assume for contradiction that the interval [0,1] = Z is a zero set. This mean that given epsilon greater than 0, there is a countable coverage of Z by open intervals (ai, bi) (___I don't...

Can you just say that x(4-x) <4 for x \in (0,2) ? You don't need to prove this? Or to prove this, just find critical point which is x = 2 ?

I know that the diameter for an interval [a,b] is defined as b-a but what is 1. Diam of (-1,1]U(2,3) 2.Diam of (1,1/2)U(1/4,1/8)U(1/16,1/32)U... Thanks

Homework Statement Solve the following inequality and express the solution set in interval notation. http://www.webassign.net/www24/symImages/4/6/aaf987edafbf00c172f8cfaf01966c.gif The Attempt at a Solution I got most of the answer right, except the lower interval. the answer is...

Let's say we know this: \sqrt{n}\left(\widehat{\theta} - \theta\right) \sim \mathcal{N}\left(0, \frac{1}{F(\theta)}\right) How do we get from this information to this expression of confidence interval for \theta? \left( \widehat{\theta} \pm...

Hello, I got the following problem; Find the min and max of the following function, on the following interval; f(x) = x^3 - 6x^2 + 9x + 15, [0, 5] Ok, to my knowledge, what I need to do is I: Find the first derivative and equal it to zero, so; f'(x) = 3x^2 - 12x + 9 0 = 3x^2 -...

A mountain climber stands at the top of a 59.4 m cliff that over hangs a pool of water. He throws 2 stones vertically downwards 1.77s apart and they cause a single splash. first stone initial velocity= -2.06m/s acceleration of gravity 9.8m/s^2 How long after release of first stone will the...

Hello in SR, the interval between two events is defined to be: s^2=x^2 + y^2 + z^2 - t^2 so my question is, why does the time get a minus sign? what differs it from the other 3 dimensions, what's the physical meaning of this difference and what is the physical meaning of this interval s^2...

Homework Statement Given the IVP problem \rm{(1+x^2)^{-1} \frac{dx}{dt} = \frac{\alpha \cdot 2 \pi}{4} \cdot cos(t)} \iff \rm{(1+x^2)^{-1} dx = \frac{\alpha \cdot 2 \pi}{4} \cdot cos(t)} dt Find the maximal solution with the initial conditio condition x(0) = 0. Then alpha is...

Homework Statement Find the interval of convergence of the infinite series: ∞ [SIZE="4"]∑ (x-1)n / 2n n = 1 Homework Equations Using the ration test. It converges if the absolute value of the limit of f(n+1)/f(n) as n -> ∞ < 1. Well, I hope that's how you...

I really ain't sure whether my problem is mathematical or related to Physics but i most probably think it has a mathematical solution. I am have a situation where I have subsurface seismic velocity windows at certain Depth points. In the window I have been given the two-way time in seconds...

I am trying to calculate the chi squared function for life data and a confidence level of 95%. I have 10 data points, a specified confidence level (95%), and 1 degree of freedom. I also have the alpha and beta parameters. Based on this information how can i calculate the chi squared statistic? I...

1. The problem: The function f is continuous for -3\leqc\leq5 and differentiable for -3<x<5. If f(-3)=6 and f(5)=-2, which of the following could be false? (a) there exists c, where -3\leqc\leq5, such that f(c)\geqf(x) for all on the closed interval -3\leqx\leq5. (b) There exists c, where...

What's the probability that a confidence interval (with alpha=10%), will have at least 85 of 100 predicted means within the calculated interval range (xbar +/- 1.645(sigma/sqrt(n)))? I understand that on average 90% of my means will be located in this range (and I know how to find this...

Homework Statement Finding the Radius of interval convergence of \sum n=1(theres a infinity on the sigma), "x^n/2^n" I really don't have a clue on which way I should go. Just a hint would be great:) Homework Equations The Attempt at a Solution

Homework Statement 1. Write an interval formula for the solution f'(x)=2f(x)+e^x f(1)=0 Explicitly find the maximal interval I about 0 on which we can solve the following differential equations 2. f'(x) = xf(x) f(0)=1 3. f'(x)=[f(x)]^2 f(0)=-1 Homework Equations For...

Homework Statement Let F(x) = \int^{x}_____________{0} x*e^(t^2) dt for x\in[0,1]. Find F''(x) for x\in(0,1). My only problem is the x, because the interval of the definite integral goes from 0 to x, and x is in the integral, even though the integral is with respect to dt. So I'd just like...

Lets say you have 5 trials, and 5 output let's say {5, 43, 60, 30 , 4}...so how would u get the chi sqaure from here & the confidence interval. i haven't work on prob &statc in years, thanks a lot for help folks

Lets say you have 5 trials, and 5 output let's say {5, 43, 60, 30 , 4}...so how would u get the chi sqaure from here & the confidence interval. i haven't work on prob &statc in years, thanks a lot for help folks

A container of oil is supposed to contain 1000 ml of oil. We want to be sure that the standard deviation of the oil container is less than 20 ml. We randomly select 10 cans of oil with a mean of 997 ml and a standard deviation of 32 ml. Using these sample construct a 95% confidence interval...

I need help with this question. Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let C.I = the width of the confidence interval for the average value y...

I am hopelessly confused on a homework assignment. The problem says " (a) Find the series radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?" Attached is a sample of problems from the book. Any help would be appreciated!