Ratio Definition and 1000 Threads

Hello, Second term of a geometric series is 48 and the fourth term is 3... Show that one possible value for the common ratio, r, of the series is -1/4 and state the other value. ar=48, ar^3= 3... so ar^3/ar=3/48 which simplifies to r^2 = 1/16, therefore r = 1/4 Can anyone explain where...

Homework Statement So what I was taught was that if the lim of the ratio test is the series is always absolutely convergent. If it is >1 the series is always divergent. But if it is =1 then we don't know. So would that mean that all conditionally convergent series would have a limit = 1? I...

Hi, Can anyone help explaining the points of action of drag and thrust forces on an aeroplane in flight and also the realtionship between Lift-Drag ration and wing configuration?! Any help would be great!

I am trying to prove e^z converges on all C. Here is my attempt. e^z=series(z^n/n!) use the ratio test on the coefficents 1/n! gives lim(1/(n+1))=0, which from rudin means radius of convergence R=1/0 -> R=infinity.

Homework Statement The problem is that using a human powered bike-like machine we have to climb up a 16 meter long rope. The total weight of the machine + human is 1300N and the theoretical force delivered by the human is 250 Newtons. The crank is 17cm long (that's the length of the arm, the...

Hi, there is a proof of the ratio test that I have seen a couple of times here: http://tutorial.math.lamar.edu/Classes/CalcII/RatioTest.aspxI don't know how to use latex, so abs(x) will mean absolute value I am ok with this: abs( aN+1) < r abs(aN) I don't understand where the r2 come from in...

$$\sum\limits_{n = 0}^{\infty}\frac{2\pi^{n+1}M}{(n+1)!}z^n$$ So we get $\lim\limits_{n\to\infty}\left|\frac{\pi z^n}{n+2}\right|$. This converges but I don't see how. z is in C.

Homework Statement Sodium is, to a good approximation, a monovalent free-electron metal which has the body-centred cubic structure. (a) Calculate the ratio of the Fermi wavevector to the radius of the largest sphere that can be inscribed in the first Brillouin zone. Remember that the...

Say we shoot the surface of the moon with various sized steel balls of size a cm and larger, say up to a km in size. Say the balls hit the surface of the moon moving at 20,000 mph. Is there a simple formula for the mass of the ejecta as a function of the mass of the projectile? Will the formula...

The ratio of integrals ∫〖a(x) b(x)dx〗/ ∫c(x) b(x)dx can be maximized by choosing b(x) equal to the delta function at the point where a(x)/c(x) is a maximum. Can anyone provide the solution for choosing b(x) when b(x) cannot equal the delta function, b(x) is greater than zero with a...

A few years ago for every fresh PhD graduate in MIS, there were three open faculty positions. Then the ratio of graduates to positions dwindled to 1: 2, then to 1:1.5, later to 4:1. Finally MIS departments all over started shutting down or being merged into Management, Operations or other...

Homework Statement Air at sealevel is composed of 80% nitrogen and 20% oxygen, but at the top of Mount Everest the composition of air is different. Give an expression for the ratio (f_O) of oxygen in the air as a function of height z above sealevel, assuming the temperature T is constant and...

Hi All; The following attachment shows a diagram of the ratio R[2m] = g^2[2m]/g[2m-2]*g[2m+2] where g[2m] is the number of goldbach partitions for the even number 2m. What is the reason for the "forbidden zones". I understand this is somehow to do with the factors of the even number...

Homework Statement Two identical satellites orbit the Earth in stable orbits. One satellite orbits with a speed v at a distance r from the center of the earth. The second satellite travels at a speed that is less than v . At what distance from the center of the Earth does the second...

This isn't a homework question in its entirety, I'm just wondering what the difference is between a Mode ratio and a mode shape? I'm taking a mechanical vibrations course and trying to figure out what the problem is asking for when it wants a mode shape...

Hey guys, I've been given a worksheet with a couple of questions concerning radioactivity, half-life etc. It is high school level and for me, it seems like the first year doing physics as our current teacher is the first one who really knows something about the subject. :) So please be patient...

Given a power series, what is the condition on its coefficients that means the ratio test can be applied?

Homework Statement Investigate the convergence of the following series. (2n)!/(n!n!) The Attempt at a Solution Number one, I don't see how they get that if an = (2n)!, then an+1 = ((2n+2))!, it should be (2n+1)! Number two, I don't see how they go to the second step, why is the second step...

Is the converse of the ratio test true?

Homework Statement The drawing shows two positive charges q1 and q2 fixed to a circle. At the center of the circle they produce a net electric field that makes an angle 28.6° with the vertical axis, measured counterclockwise. Determine the ratio q2/q1. [the drawing shows a circle with two...

Homework Statement Two body move apart by force. Frictional forces are considering. How to calculate the ratio of weight? m1<m2 Ft1=k*g*m1 Ft2=k*g*m2 Homework Equations v1(t1)=\frac{F_{t1}-F}{m_{1}}*t_{1} x1(t1)=\frac{F_{t1}-F}{m_{1}}*\frac{t^{2}_{1}}{2}...

Pentagon diagonal - parallel ratio proof Homework Statement Suppose P is a convex pentagon such that each diagonal is parallel to one side. Prove that the ratio of the length of a diagonal to that of its corresponding side is the same for all five diagonals, and compute this ratio...

The ratio of Pu238 and O2 in Plutonium dioxide? Hello, guys. I was wondering if I can find a ratio of Pu238 and O2 in PuO2. In my problem set, these are all I have. - 238/94 Pu -----86yrs----> 4/2 He + 234/92 U + 5.59 Mev - 238PuO2 : 6000 gram in a sphere (10 cm diameter) -...

Homework Statement According to genetic linkage theory, observed frequencies of four phenotypes resulting from crossing tomato plants are in the ratio 9/16 + a : 3/16 - a : 3/16 - a : 1/16 + a. In 1931, J.W. MacArthur reported the following frequencies: Observed...

Homework Statement A round bar of 10 mm diameter is made of aluminum alloy 7075-T6 (see figure). When the bar is stretched by axial forces P, its diameter decreases by 0.016 mm. Find the magnitude of the load P. (Obtain the material properties from Appendix H.) From Appendix H: Modulus of...

Homework Statement if(i have attached the equation's pic) then prove a=b=c or (a+b+c)(x+y+z)=ax+by+cz Homework Equations if a/b=c/d=e/f each ratio = (a+c+e)/(b+d+f) The Attempt at a Solution I was able to prove (a+b+c)(x+y+z)=ax+by+cz like this: each ratio=...

Homework Statement 16. A car completes a horizontal circle of radius r in time T. The same car then completes a larger horizontal circle of radius 2r in half the time. What is the ratio of the centripetal acceleration ac for the car in the second circle to that in the first circle a c2 a c1...

Can anyone help me to find out the definition of "carrier swing"&"deviation ratio"? The definitions which i found on surfing the net is too vague.Can someone help me with this?

I'm new to this site so excuse me if I'm posting in the wrong area. We are having a discussion about motor, idler pully (yes wheel) ratios and we can't agree on this problem. What we have is basically an old record player, The motor shaft is turning a single idler, and this idler is...

Homework Statement Undamped oscillator's period T_0 = 12s. Damped oscillator's angular frequency \omega_1 = \omega_0 * 97\% where \omega_0 is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes? Homework Equations Equation of damped...

Homework Statement Unknown amounts of methane and ethane are mixed at STP. The resulting mixture has a density of 1.18 g/L. Find the ratio of ethane to ethane. The Attempt at a Solution Since it's a ratio, we can convert it to 1 mol methane : X mol ethane 1 L methane at STP = \frac{RT}{P} =...

Homework Statement The Attempt at a Solution I got that the limit goes to infinity using the Ratio Test and that would mean B. But I'm not 100% percent sure. Just looking for some to verify my answer if I'm correct or not.

Homework Statement Ʃ((x-3)^(n)) / (n*2^(n)) Homework Equations lim as n→ ∞ (An+1 / An) The Attempt at a Solution When dividing two fractions, invert the second and multiple to get what you see below. (x-3)^(n+1)/((n+1)*2^(n+1)) * (n*2^(n))/((x-3)^(n)) Do some cross...

First of all, let me apologize if this question is in the wrong place. It's fundamentally a statistics question but it relates to computer science. I'm also not sure if this falls under the "homework" category, since it's for a class, but I need assistance on a general idea, not a problem set...

Hello. I'm trying to understand why, in terms of Maxwell's Equations, the ratio of the number of turns in a transformer converts an input voltage to an output voltage. EE explanations only seem to go as deep as this article: http://en.wikipedia.org/wiki/Transformer#Basic_principles They state...

Homework Statement I had a general inquiry about a relation in my physical chemistry textbook. It stated that when determining the partial pressure of an ideal gas component in a mixture/solution, instead of using the standard Dalton's law: Pi = xiPtot, one can simply use the relation Pi =...

Homework Statement The original problem is determining the dispersion relation of an ordinary wave in plasma damped by collisions. That part was easy enough but the next part is to find the damping rate (-Im(ω)) of the wave, assuming k is real and \nu << \omega where \nu is the collision...

Which method of determining turns ratio is more accurate and why? 1. From the voltage readings in no-load condition 2. From the current reading in loaded condition We used an auto transformer (VARIAC) to supply voltage to a single phase transformer. Supplied voltage was 220 V. Then we...

I have few questions as i am bit confused Q1. I want to know what are the influence of the air/fuel ratio on engine output and Brake specific fuel consumption (BSFC). Q2. why bsfc increases at low engine output? Q3. why bsfc improves as engine output increases? Q4. what are the...

Homework Statement The same diffraction grating is used with two different wavelengths of light, λA and λB. The fourth-order principal maximum of light A exactly overlaps the third-order principal maximum of light B. Find the ratio λA/λB. Homework Equations sin theta = m lambda /...

Homework Statement Determine whether Ʃ(1→∞) n^2/e^n converges or diverges. Homework Equations L = lim (n→∞) abs [a_n+1/a_n] The Attempt at a Solution The prof was out of town so left us a "self-study" task. We're looking at the Ratio Test and I want to see if my methodology is...

Hi, I'm new to this forum but I've read over probably a dozen threads so I figured that someone should probably be able to help me; please forgive me if this is the wrong area to post this question as well. Dilemma: So the problem right now is that I'm trying to use a gear reduction system...

hello everybody. can we define a poisson ratio for fluids, eg for water?? if no, why? n if yes, how?? thnx.

Let F_n and F_n+1 be successive Fibonnaci numbers. Then |(F_n+1)/(F_n) - Phi | < 1/(2(F_n)^2) Where Phi is the Golden ratio.

If a 6 speed gear box has a 1st gear ratio of 7:1 and a sixth gear ratio of 1:1 how would you calculate the 2nd,3rd,4th and 5th gear ratio's? If you use the equation for geometric progression which was my first thought - it doesn't work! Any ideas?

Homework Statement Hello! I've come upon this question and haven't been able to find it anywhere. The goal is to find Mp/Me with basis on the Bohr's atomic model and hydrogen emisson spectrum lines.Homework Equations l=rp=nh_ ; h_=h/2pi ; E=-K.e^2/2r ; r=(n^2.h_^2)/Me.e^2.k ...

Homework Statement Two objects moving in opposite directions with the same speed undergo a totally inelastic collision, and half the initial kinetic energy is lost. Find the ratio of their masses, m1/m2. Homework Equations m1v1+m2v2=(m1+m2)vf The objects are moving in opposite directions...

Homework Statement Consider a stationary normal shock wave in pure diatomic nitrogen. The velocity and temperature upstream are known. Calculate the temperature ratio across the shock, assuming local thermodynamic equilibrium. Neglect any chemical reactions and electronic energy...

In stenger's book he claims that the ratio between gravity and the electro magnetic is not 1039 Let me know if you think he's right Note that N1 (ratio of EM force to gravity) is not a universal number; it depends on the charges and masses of the bodies you use in the calculation. For an...

Homework Statement In each of the following the properties of a compound are given. In each case find A:B:C 1. 3/8 of A with B and C 1:2 2. A, B, C are mixed according to the ratios A:B=1:7 and B:C=13:9 Homework Equations The Attempt at a Solution I just can't seem to...