Geometric Definition and 790 Threads

Homework Statement 1)A hard rubber ball is dropped from a moving truck with a height of 5 m. The ball rises of the height from which it fell after each bounce. the total vertical distance the ball has traveled at the moment it hits the ground for the eighth time, to the nearest tenth of a...

Hi everybody: does anyone know of a good book on special relativity that takes a geometric approach? I'm doing research that requires that I know special relativity, and, while working problems out for personal-practice, all I do is either: 1) make gamma-messes 2) clumsily-use invariants...

Homework Statement Chose a point at random in a square with sides 0<x<1 and 0<y<1. Let X be the x coordinate and Y be the y coordinate of the point chosen. Find the conditional probability P(y<1/2 / y>x). Homework Equations No clue. The Attempt at a Solution Apparently, according...

Hi, can someone just confirm that to get the GSD of a distribution, I simply take the natural log (or log 10?) of all the numbers then find the arithmetic standard deviation of that? Thanks :)

Homework Statement If the ph of battery acid should be 0.8, what is the pH of the acid in a battery that is one-fifth as acidic as it should be? Homework Equations The Attempt at a Solution We just learned how to comparing pH in Geometric unit, using the formula 10^(ph1-ph2). But...

Homework Statement hi guys, i'm having trouble applying Kirchhoff's laws to determine the equivalent resistance of this symmetrical array of resistors (see attachment); i think there is a quick trick, using 4 current loops, but i can't remember it... nor find relevant documentation – this is...

Homework Statement Given matrix A: a 1 1 ... 1 1 a 1 ... 1 1 1 a ... 1 .. . .. ... 1 1 1 1 ... a Show there is an eigenvalue of A whose geometric multiplicity is n-1. Express its value in terms of a. Homework Equations general eigenvalue/vector equations The Attempt at a Solution My...

Homework Statement The experiment was changing dimethyl maleate into dimethyl fumerate, with the intent of being analogous to changing maleic acid into fumeric acid. In the experiment, we added 1 M Bromine in dimethylchlorine to our dimethyl fumerate, put the mixture in a hot water bath and...

I recently found out how to calculate the potential energy of a charged insulated sphere of radius R and charge density rho. I would like to know how to calculate the potential energy for other geometric objects, such as a line of charges, a sheet of charges, or a pyramid of charges. I don't...

Hi. Tried solving, but no idea how. At the end of 1995, the population of Ubris was 46650 and by the end of 2000 it had risen to 54200. On the assumption that the population at the end of each year form a g.p. find a) The population at the end of 2006, leaving your answer in 3 s.f. b)...

Homework Statement Let X be a random variable with distribution function px(x) defined by: px(0) = a and px(x) = Px(-x) = ((1-a)/2)*p*(1-p)^(x-1), x = 1,2... where a and p are two constants between 0 and 1, and px(0) is meant to be the probability that X=0 a) What is the mean of X...

Homework Statement Hi, there are two questions that I'm quite stuck with. 1.Find the number of terms in each of these geometric sequences. a) 1,-2,4...1024 b) 54,18,6...2/27 Homework Equations ar^n-1 The Attempt at a Solution 1. a) r= -2 1x-2^n-1 ? b)...

Homework Statement Hi, I was trying to work out this question, but i kinda got stuck. Can anyone help me please? Thanks 4. Find the number of terms in each of these geometric sequences. 2,10,50...1250 Homework Equations ar^n-1 The Attempt at a Solution 1250=2x5^n-1

A matrix is diagonalizable when algebraic and geometric multiplicities are equal. My professor proved this in class today, but I did not fully understand his explanation and proof. Can someone please help?

A matrix is diagonalizable when algebraic and geometric multiplicities are equal. I know this is true, and my professor proved it, but I did not understand him fully. Can someone please explain?

Homework Statement A beam of light in air makes an incident angle with the normal at 53 with an unknown substance. Part of the light is relected and part is refracted into the substance. The reflected ray and the refracted ray make an angle of 90 degrees. a) What is the refracted angle...

1. 1. Find the exact(no approximations)sum for the finite series S sub n= (2 + 2 + 2(2+...+64 i used the parentheses to represent a radical sign 2. Show that the sum of the first 10 terms of the geometric series 1 + 1/3 + 1/9 + 1/27+... is twice the sum of the first 10 terms of...

Homework Statement A ball is dropped vertically from height h onto a flat surface, after the nth bounce it returns to high h / 3^n. Find the total distance traveled by the ball. Homework Equations Sum (infinity) = \frac{a}{1 - r} The Attempt at a Solution I don't see the...

Is there a geometric interpretation of any n*n matrix?

ok so i know how to calculate the partial sum of a geometric series. But let's say i only want to calculate the sum of every other term, how would i do this? example: .5^0+.5^1+.5^2+...+.5^n = (.5^(n+1) - 1)/(.5-1) but what equation can i use to get the sum of only these terms...

given: ln (x) = integral 1/t dt from 1 to x and x=30 Without a calculator and only a graph of y=1/x How could you show that this geometric area under this curve (with any type of unit) is equal to 3.4 area units, the ln (30) not homework, I am looking for a tangible/physical...

Not homework but this is probably the best suited place for a puzzle: A large rectangle in the plane is partitioned into smaller rectangles, each of which has either integer height or integer width (or both). Prove that the large rectangle also has this property. I've given this several...

Is there a point to geometric proofs? The ones that I have encountered are so obvious that it almost seems useless to have to use them for anything.

Some years ago I used the device of representing composite numbers by rectangular forms to demonstrate the structure of numbers to third grade students. Primes were represented by lines of various lengths. Number 10 would be a 2x5 rectangle and 20 a 2x2x5 rectangular solid. (I used various...

I'm taking a class in abstract algebra this summer, so I thought I'd get ahead by reading the book before class starts. This is from a book called "Abstract Algebra: A Geometric Approach", chapter 1: Applying the Principle of Mathematical Induction with a slight modification. If S' \subset \{n...

Homework Statement \int 1/(1-xyz)dxdydz = \sum1/n3 from n = 1 to infiniti dx 0 to 1 dy 0 to 1 dz 0 to 1 Homework Equations The Attempt at a Solution Not sure how to relate the two of them

Homework Statement In a Geometric Sequence find t10. t3 = 4 and t6= 4/27 Give a recursive definition for the sequence: 1, 4, 13, 40... Homework Equations I know that a Geometric sequence is: tn=t1(r)n-1 And that a recursive formula starts off with tn-1 I'm not sure where to go...

Homework Statement Show that the ratio of areas is proportional to the sides squared: \frac{[ACD]}_{[CDB]} is proportional to \frac{AC^2}_{CB^2} Please, see the picture: http://dl.getdropbox.com/u/175564/geo_henry.JPG . Homework Equations AC = 2 * CB \frac{AD}_{DB} is propotional to...

Geometric Distribution? Geometric Distribution: In an experiment, a die is rolled repeatedly until all six faces have finally shown.? What is the probability that it only takes six rolls for this event to occur? ANSWER = 0.0007716 What is the expected waiting time for this event to occur...

Sorry, the title should be: geometric intepretation of moments My question is: does the formula of the moments have a geometrical interpreation? It is defined as: m(p) = \int{x^{p}f(x)dx} If you can't see the formula it is here too: http://en.wikipedia.org/wiki/Moment_(mathematics) with c=0...

Hello everyone, I am studying for an upcoming exam and have become somewhat confused as to exactly what geometric and material buckling represent. Are they representative of the shape of the neutron flux distribution in the reactor? Are these quantities related to the structural deformation...

Homework Statement Let {x_n} be a sequence. and let r be a real number 0<r<1. Suppose |x_(n+1) - x_n|<=r|x_n -x_(n-1)| for all n>1. Prove that {x_n} is Cauchy and hence convergent. Homework Equations if |r|<1 then the sequence \sum r^k from k=0 to n converges to 1/(1-r) The...

Homework Statement Suppose RX(t) = E[(1 − tX)−1] is called the geometric generating function of X. Suppose the random variable Y has a uniform distribution on (0, 1); ie fY (y) = 1 for 0 < y < 1. Determine the geometric generating function of Y . Homework Equations The Attempt at...

Hello, I have recently started to study some Geometric Algebra. I was wondering how should I interpret complex-vectors in \mathcal{C}^n in the framework of Geometric Algebra. I understand already that a complex-scalar should be interpreted as an entity of the kind: z = x + y (\textbf{e}_1...

what is the nth partial sum of 1-x+x^2-x^3+.. i don't understand why i can't do this? i have \sum_{k=1}^{n} ar^k=\frac{a(r^{n+1}-r)}{r-1} ok but then when i sub in i get messed up i get \frac{(-x)^{n+1}+x}{-(1+x)} is there any way of simplifying this? also when i set n=1 i get that...

Is it possible to find the partial sum equation for (2^m - 1)/3^m, from m=0 to m=n-1? I know that I'm supposed to rearrange the expression into the format ar^m, so the exponent m must only be on the value r, and not on the constant a. So far the farthest I've gotten is to rearrange it into...

Homework Statement In each case give a geometric description of the cosets of H in G. a) G=R*, H=R+ b) G=C*, H=R Homework Equations The Attempt at a Solution I have no idea about geometric description...

Using the formula for the sum of geometric series, show that the values of p(n) sum to 1 p(n)=(1 - \alpha)^n \alpha My attempt: \alpha \sum^\infty_{{\bf n=0}} (1- \alpha)^n I am not sure where to go from here. Any help to show this is true!

Homework Statement If A = [ -4e^4t sin(9t) -4e^5t cos (9t) ] [ 4e^4t cos (9t) -4te^5t sin (9t) ] then A^-1 = [ ___ ___ ] [ ___ ___ ] Homework Equations how do you deal with the exponents? The Attempt at a Solution Put into RREF, and then see what the inverse is?

Homework Statement actually got two questions but both are related so put them in the same place the question asks Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. Inf 1.) E 6(0.9)^(n-1) n=1 Inf (-3)^(n-1)...

Recently I discovered geometric algebra which looks very exciting. I was wondering if there is any connection between geometric algebra and differential forms? I see that different research groups recommend the use of differential forms (http://www.ee.byu.edu/forms/forms-home.html" ), and...

Homework Statement Calculate the angle of incidence for an angle of refraction of 10° for a) Diamond (2.42) to air θ2=Angle of refraction=10° n2=Index of refraction on refractive medium=1 n1=index of refraction on incident medium=2.42 θ1=? Homework Equations n1sinθ1=n2sinθ2...

Homework Statement Assume that each of your calls to a popular radio station has a probability of 0.02 of connecting, that is, of not obtaining a busy signal. Assume that your calls are independent. What is the probability that it requires more than five calls for you to connect...

Homework Statement http://img16.imageshack.us/img16/2327/nummer1.jpg Homework Equations Sn=(u1(rn-1))/(r-1) The Attempt at a Solution I think i need to use the equation for geometric series(above). Or do i use the arithmetic furmula since ln(a/b)=ln(a)-ln(b). I think i am a bit...

I'm trying to study geometric algebra using Artin's book and am having some difficulty with what degenerate symmetric bilinear forms would be like. Does someone know of an example and brief explanation. Also, the opposite being "nondegenerate nonsymmetric bilinear form" would help me out. If I...

I'm trying to build up enough understanding to work through some GR on my own, but I'm horribly confused by some of the math concepts. So terribly so, that I'm not even sure how to ask my questions. Please bear with me. Lets work in a 2D plane. Assume I have a vector u which I can write out...

Homework Statement Define the following terms: a) Midpoint M of segment AB. b) Perpendicular bisector of a segment AB (you may use the term "midpoint" since ypu have just defined it). c) Ray BDbisects angle ABC (given that point D is between A and C) d) Points A, B, and C are collinear...

Homework Statement I'm doing a report for a physics lab experiment where we are calculating the radius of the Earth by measuring the time it takes to see the sunset from the base of a cliff looking out into the pacific ocean till when it sets in relation to an observer at the top of the...

Homework Statement Draw and name all of the structural isomers of hydrocarbons with the formula C6H12 (cyclohexane). 2. Relevant information This is "only" a grade 11 Chemistry Assignment, therefore I only really need the basics when it comes to isomers- not some of the more complex...

We were discussing in an https://www.physicsforums.com/showthread.php?t=284322" that pinholes work like lenses, in that they form inverted real images. The other day, a friend told me, that pinholes even do bend the light rays like a lens do. I can - as being nearsighted - actually use a pinhole...