Geometric Definition and 813 Threads

Homework Statement Hi, I'm trying to solve the problem in the attachment. I was asked to evaluate the left hand side equation of the equal sign. I was unsure how to go about evaluating it so I consulted my solutions manual to look up the first step. The right hand side equation of the...

Homework Statement Q. Find the range of values of x for which the sum to infinity exists for each of these series: (i) 1 + \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + ... (ii) \frac{1}{3} + \frac{2x}{9} + \frac{4x^2}{27} + \frac{8x^3}{81} + ... Homework Equations S\infty =...

Homework Statement Q. Find, in terms of x, the sum to infinity of the series... 1 + (\frac{2x}{x + 1}) + (\frac{2x}{x + 1})^2 + ... Homework Equations S\infty = \frac{a}{1 - r} The Attempt at a Solution S\infty = \frac{a}{1 - r} a = 1 r = U2/ U1 = (\frac{2x}{x + 1})/ 1...

Homework Statement Q.: A geometric series has first term a and common ratio r. Its sum to infinity is 12. The sum to infinity of the squares of the terms of this geometric series is 48. Find the values of a and r. Ans.: From textbook: a = 6, r = 1/ 2 Homework Equations...

Hi there. I have this exercise in my practice for differential equations, and it asks me to find the curve that satisfice for every point (on the xy plane) the distance from (x,y) to the points of intersection for the tangent line and the x axis, and the normal with the x-axis remains constant...

Homework Statement 3,6,12...1536 determine the number of terms in the progression Homework Equations The Attempt at a Solution a=3 r=2 n= ar^n-1 1536= (3) (2)^n-1

Homework Statement A 35mm slide(picture size is actually 24 by 36 mm)is to be projected on a screen1.80m by 2.70 m placed 7.50m from the projector. What focal length lens should be used if the image is to cover the screen?Homework Equations the only equation i can think of is the lens equation...

Hi all, I would like to ask for the geometric interpretation of the riemann-stieltjies integral. Suppose we have an integral, (integrate f dg) over the interval [a,b], where g is monotonically increasing. Can i interpret it as the area between f and the g function? Moreover, i am a...

Homework Statement Point A is on a circle whose center is O, AB is a tangent to the circle, AB = 6, D is inside of the circle, OD = 2, DB intersects the circle at C, and BC = DC = 3. Find the radius of the circle. Homework Equations Power of a point theorem (several cases found online...

So, suppose for visualization there are only two dimensions: ct and x. Now if the metric where Euclidean, we could visualize this space is a simple plane. What would be the shape of the "plane" when the metric is +1, -1 (Minkowski)? Is it somehow hyperbolic?

I have a quick question. First let me give a definition. Let a_1, a_2, ..., a_k be independent vectors in R^n. We define the k-dimensional parallelopiped \mathbb{P}(a_1, ..., a_k) to be the set of all x in R^n such that x = c_1a_1 + \cdots + c_k a_k for scalars c_i such that 0 <= c_i...

i know how the basic geometric sequence system works, but what if i want to subtract a fixed amount every For example if i start with $5000 (a1) and is multiplied by 1.05 (5% / r) every day for 20 days (n) I would have $13,267. But what would I have if $20 dollars was subtracted from the...

James came to a place where there was a bridge, supported by parabolic arcs. In the middle waving a transparent gelatinous substance in the form of spherical shell of exotic matter. He had come to " delighted well", a horizontal formation, which is much talk and little experienced. Slowly James...

Homework Statement This isn't the whole question, I understand the prior parts but somehow stuck on the "easy" part :( Need to solve a geometric progession problem.. find the sum of: h(1 + 3^h + 3^2h + ... + 3^(n-1)h) Where nh = 1 The sum should equal to (2h)/((3^h) -1) which is...

Homework Statement The normal vector of each of the following planes is determined from the coefficients of the x-, y-, z- terms. pi1: a1x+b1y + c1z + d1=0 pi2: a2x+b2y+c2z+d2=0 pi3: a3x+b3y+c3z+d3=0 Define the extended vector for each plan as follows: e1= [a1, b1, c1, d1] e2= [a2, b2, c2...

Homework Statement You must enter 3 numbers between 31 and 496 so there will be an increasing geometric series with 5 components. The Attempt at a Solution It tells me I'm off. That q=2. But how? http://img716.imageshack.us/img716/8895/300xk.jpg

I am looking at a geometric series problem that has already been worked out, so not assigned, but I do not see where they get a number: Summation from n=1 to inf: 1/(n^2+4n+3) In doing the partial sums, he has (1/2)* summation... 1/(i+1) - 1/(i+3) I understand the breakup, but where does...

Homework Statement Assume that the drug administered intravenously so the concentration of drug in the bloodstream jumps almost immediately to its highest level. The concentration of the drug decays exponentially. A doctor prescribes a 240 milligram (mg), pain-reducing drug to a patient who...

Homework Statement http://img833.imageshack.us/img833/681/a1a2.jpg Calculate which number you have to add to a1, a2 and a3 in order to get 3 subsequent numbers in a geometric series The Attempt at a Solution Getting a2 and a3 was easy. Plugging in the values I need for n, I get...

Homework Statement [/b] There are two problems I need help with, which are posted below. Any help is appreciated. 1)Let X have a Poisson distribution with parameter λ. If we know that P(X = 1|X ≤ 1) = 0.8, then what is the expectation and variance of X? 2)A random variable X is a sum of...

A ball is dropped from a height of 3 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. (a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter your answer as an improper fraction.) Can...

I was reading Tom Apostol's expostion of Euler's Summation Formula ( http://www.jstor.org/pss/2589145) and it occurred to me that it would be convenient to visualize \int_a^b x f'(x) geometrically. In that article, it arises from integration by parts: \int_a^b f(x) dx = |_a^b x f(x)...

I'm stuck on these three maths questions. 1) In a geometric progression, the sum to infinity is four times the first term. (i) Show that the common ratio is 3 (ii) Given that the third term is 9, find the first term. (iii) Find the sum of the first twenty terms. 2) Solve the...

I'm confused about the sum of the geometric series: \sum ar^{n-1} = \frac{a}{1-r} when |r|<1 but if you have a series like: \sum (1/4)^{n-1} the sum is: \frac{1/4}{1-(1/4)} should't it be \frac{1}{1-(1/4)} because there is no a value?

What is the meaning of (e1^e2)\cdote3? (outer product multiplied by inner product)

"If u and v are any two vectors of the same length, use the dot product to show that u + v is perpendicular to u − v. What fact from geometry is does this represent." This is basically the last question in an assignment on vectors (first year university, linear algebra). The questions all focus...

Question: John took a bank loan of $200000 to buy a flat. The bank charges an anual interest rate of 3% on the outstanding loan at the end of each year. John pays $1000 at the beginning of each month until he finishes paying for his loan. Let Un denote the amount owed by john at the end of the...

Homework Statement Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. \sumn=1infinity (-3)n-1/4nHomework Equations A geometric series, \sumn=1infinity arn-1=a + ar + ar2 + ... is convergent if |r|< 1 and its sum is \sumn=1infinity arn-1 =...

I'm having trouble with a word problem: The people of Gossipopolis cannot keep a secret. Upon being told a secret, a person from Gossipopolis will spend the next hour telling three people. In turn, those friends will spend the next hour each telling 3 more people. This process continues and...

Making a change of basis in the matrix representation of a linear operator will not change the eigenvalues of that linear operator, but could making such a change of basis affect the geometric multiplicities of those eigenvalues? I'm thinking that the answer is "no", it cannot.. Since if...

Homework Statement \lambda=0 is an eigenvalue of A= |1 1 1 1 1| |1 1 1 1 1| |1 1 1 1 1| |1 1 1 1 1| |1 1 1 1 1| Homework Equations Find the geometric multiplicity of \lambda=0 as an eigenvalue of A The Attempt at a Solution I row reduced it then got the last four rows of all 0s...

It is a 5x5 matrix with 1s in all of its entries. Find the geometric multiplicity of \lambda=0 as an eigenvalue of the matrix.

Homework Statement It is a 5x5 matrix with 1s in all of its entries. Homework Equations Find the geometric multiplicity of \lambda=0 as an eigenvalue of the matrix. The Attempt at a Solution WHat i did was use the characteristic equation of A-\lambdaI and then row reduce it...

A school phone tree has 1 person responsible for contacting 3 people. If there are 1500 students in the school, how many levels will there be on the phone tree (assuming 1 person is at the top of the tree)? My Solution: This question forms a geometric series: A(first term)=1 R(common...

A finite geometric sequence has t1 = 0.1024 and t2 = 0.256. How many terms does this sequence have if its middle term has a value of 156.25? My Solution Common Ratio: T2/T1=(.256)/(.1024)=2.5 What term # is the middle term? tn=ar^n-1 a=0.1024 r=2.5 tn=156.25...

Homework Statement Find the equivalent resistance across Rab Homework Equations Series: Req=R1+R2...Rn Parallel Req=(R1 * R2 *...Rn) / (R1 + R2 +...Rn) The Attempt at a Solution its the geometry that is throwing me off in this problem. Starting on the left side, I want to put...

Hi, I have a problem I need to solve for a piece of software I'm writing, and I think I've got it but it would be great if somebody could take a quick look at this proof and see if I've overlooked anything. Thanks in advance. Here is the problem: We're working in R_3 here. Given a line...

Is anyone familiar with this method of determining square roots? http://www.cs.cas.cz/portal/AlgoMath/Geometry/PlaneGeometry/GeometricConstructions/SquareSquareRootConstruction.htm I have an equation that I'm working on that expands on this a bit and I'd love some feedback.

well it is easy to construct sqrt(2) with a triangle with two sides of length 1. but what about sqrt(2 + sqrt(2)) or the iteration sqrt(2 + sqrt(2 + sqrt(2))). the question is how to construct a line with length sqrt(sqrt(2)) i guess(beginning with lines of length 1), but i am not sure.

Homework Statement A) In a certain geometric sequence every term is the sum of the two preceding terms, viz. the Fibonacci sequence, what can be said about the common ratio of the sequence? So how do I go from 1,1,2,3,5,8,13,21,34... to (1+/-sqrt(5))/2? Then find numbers A and B such (for...

Hi! Do you know if there are softwares where you can put in numbers and it tries to find a geometric structure that fits them? Like 1,2 and 5 becomes a triangle. Thank you!

just a check of my work please. I have to write an expression for the nth term of this geometric sequence. a1=100 a2=106 a3=112.36 I've worked out the ratio to be r=1.06 I am using the formula un=ar(n-1) so the expression i have come up with is un=100(1.06)(n-1) Is this correct? I have...

Homework Statement An experiment consistion of tossing three fair coins is performed repeatedly and "success" is when all three show a head. What is the probability that the success is on the third performance of the experiment? Homework Equations Geometric distribution equation p(x) =...

hello, what does exactly mean geometrically that time and space switch roles at the event horizon of a nonrotating black hole?. I understand that the - for time becomes a + and the + for space becomes -, but how to interpret it geometrically? also I want to know if after the event horizon...

Homework Statement OK, so I understand how to calculate this stuff. But I want to know the geometric significance of a line integral over a vector field, a double integral over a vector field, and of course curl. Homework Equations \int_C \vec{F} \cdot d\vec{r} \int \int_C \vec{F}...

Note: I didn't use the template because I feel it did not fit the question well enough. This is concerning a system of linear equations in two variables where its constants in " ax+by=c " form show a geometric sequence, i.e. " nx + any = a2n ". Another way of putting this is " y=(-1/a)x + a...

I want to preface this by saying that these questions are not to find an exact answer, just to build intuition. If you find them ill-posed or incorrect, it would be most helpful if you could show me a "better way" of looking at it. So, I'm trying to gather a geometric viewpoint of...

Homework Statement The sum of ((n+1)*3^n)/(2^2n) Homework Equations absolute value of r must be less than 1 for the series to be convergent. The Attempt at a Solution i tried multiplying it out and splitting it up like: 3^n*n/(2^(2n))+3^n/(2^(2n)) but then i am stuck when I...

Let f(x) = \frac{4-4x}{4x^{2} -8x -5}; given the partial decomposition, \frac{4-4x}{4x^{2} -8x -5} = \frac{1}{5-2x} - \frac{1}{1+2x}, find the Taylor series of f(x) about 1. Express your answer in sigma notation and simplify as much as possible. Dtermine the open interval of...

Hi, Everybody: I am trying to understand torsion and relative cycles in a more geometric way; I think I understand some of the machinery behind relative cycles (i.e., the LES, and the induced maps.), and I understand that by ,e .g., Poincare duality, in order to have torsion in...