Geometric Definition and 790 Threads

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...

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...

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...

Dim(V)>1.Prove that PGL(V) acts two transitively but not 3 transitively on P(V) projective space.

<y-ln(x^2+y^2),2arctan(y/x)> region : (x-2)^2+(y-3)^2=1 counter clockwise taking int int dQ/dx - dP/dy dA leads to -int int dA here my text is showing the next step as a solution of -pi not sure ..polar cords ext..

Homework Statement I am solving some convolutions, and i have come to these solutions. a)\sum2k, summing from -\infty to -1 b)\sum2k, summing from -\infty to n , where n <=-1Homework Equations the geometric series summation formula, from 0 to N \sumak = 1-aN+1 / 1-a , summing from 0 to N The...

If the fourth, seventh and sixteenth terms of an AP are in geometric progression, the first six terms of the AP have a sum of 12, find the common difference of the AP and the common ratio of the GP. I've been assuming that the fourth, seventh and sixteenth terms of the AP are the fourth...

Homework Statement (note; all column vectors will be represented as transposed row vectors, and matrices will be look like that on a Ti-83 or similar) L: R^3 -> R^2 is given by, L([x1, x2, x3]) = [2x1 + x2 - x3 x1 + 3x2 +2x3]* *Matrix Relevant...

Homework Statement (p,a) , (q,b) and (r,c) are the coordinates of three points on the parabola y^2=3x. If the x-coordinate for these three points form a geometric progression whereas the corresponding y-coordinate form an arithmetic progression, find the common ratio of the geometric...

Homework Statement Generate Geometric RV with Porbabilty of succcess 0.1 using only rand() Homework Equations rand() geometric rv P=(1-p)^(k-1) * p where p=0.1, k is number of trial in which we get 1st success The Attempt at a Solution rand(n)

For a euclidean space, the interval between 2 events (one at the origin) is defined by the equation: L^2=x^2 + y^2 The graph of this equation is a circle for which all points on the circle are separated by the distance L from the origin. For space-time, the interval between 2 events is...

Homework Statement Number of rabbits reared by Alice at the beginning of certain year is given as b. End of that particular year, the number of rabbits were given as 10+(3/2) b . Write down the number of rabbits at the end of second and third year. Find the total number of rabbits at the end...

Homework Statement Let r_{1}, r_{2}, ... , r_{n} be strictly positive numbers. Show that the inequality (1+R_{G})^{n} \leq V is true. Where R_{G} = (r_{1}r_{2}...r_{n})^{1/n} and V= \Pi_{k=1}^{n} (1+r_{k}) Homework Equations The Attempt at a Solution I've...

Homework Statement let r_{1}, r_{2}, ... , r_{n} be strictly positive numbers. Suppose an investment of one dollar at the beginning of the year k grows to 1+r_{k} at the end of year k (so that r_{k} is the "return on investment" in year k). Then the value of an investment of one dollar at...

Homework Statement \sum_{n=1}^\infty \frac{(-3)^{n-1}}{4^n} The Attempt at a Solution \sum_{n=1}^\infty \frac{(-3)^n-1}{4^n} \frac{1}{4}\sum_{n=1}^\infty \frac(-{3}{4})^{n-1} Can some one please explain how they got from the first step to the 2nd. How do you pull...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution Okay I think I handled the lnx portion of the function okay(see other figure attached), but I'm having from troubles with the, \frac{1}{x^{2}} \int x^{-2} = \frac{-1}{x} + C How do I...

I'm confused between some formulae so I'm going to give some examples and you can let me know if what I'm writing is correct. Find the Taylor series for... EXAMPLE 1: f(x) = \frac{1}{1- (x)} around x = 2 Then, \frac{1}{1-(x)} = \frac{1}{3-(x+2)} = \frac{1}{3} \left( \frac{1}{1...