Factors Definition and 428 Threads

Is there a name for product of the unique prime factors of a number? For example, for the number 12, it would be 3x2=6. Thanks.

Homework Statement Express x^4 + y^4 + z^4 - 2y^2z^2 - 2z^2x^2 - 2x^2y^2 as the product of four factors. 2. The attempt at a solution (x-y-z)(-x+y-z)(-x-y+z)(x+y+z)

Homework Statement Express as the product of four factors Is this correct? a^6 - b^6 = (a - b)(a^5 + a^4b + a^3b^2 + a^2b^3 + ab^4 + b^3)

What factors may cause the experimental value of acceleration due to gravity to be different from tha accepted value in a free fall experiment? Will it be something like air resistance , human error , instruments error or wrong calibration ??

Homework Statement A BJT has VA of 50 V and MOSFET has lambda(modulation length) = .02 V^-1, and has VGS-VTN=.5 What are the "amplification factors" of the 2 transistors. Homework Equations well, not sure, all i really want to know is what do they mean by amplification factors...

Please list the relevant factors needed. Or those of you who already got in maybe you should show off your credentials? I'm coming from an engineering (electrical) so it appears the work has been cut out: GPA : 2.5 Cumulative GPA in 3rd year college engineering (it was 4.0 in first year)...

Homework Statement My group in physics conducted a lab which is described below: The lab was to investigate a factor affecting the accel. of an object. We were supposed to change only one factor to see how acceleration would be affected. My group had decided to use a simple static pulley...

Hi guys, this is my first post but have read the forums for a long time - a quick search didnt bring up anything that could help me. So i was wondering if someone could please explain something to me. I have a differential equation (excuse the pictures, I don't know how to use the equation...

Homework Statement Consider the polynomial p(x)=x^6-1. (Apply over any field F). (a) Find two elements a,b \in F so that p(a)=p(b)=0. Then use your answer to find two linear factors of p(x). (b) Show that the other factor of p(x) is x^4+x^2+1 (c) Verify the identity...

For the first question, I am only supposed to find the general solution of the differential equation. 1) dy/dt = -2ty + 4e^(-t^2) dy/dt + 2ty = 4e^(-t^2) Integrating factor = e^(Integral of 2t) = e^(t^2) Multiply both sides by IF: e^(t^2) * (dy/dt +2ty) = 4e^(t^2-t) e^(t^2)*dy/dt...

Heat transfer is something I've been interested in since studying thermodynamics last semester, although during the course we never really covered anything much to do with what affected heat transfer. I can pretty easily understand that obviously having a higher surface area to exchange across...

Homework Statement Your niece is working on a unique science fair project - a clock built around a small mass vibrating on a little spring. Her prototype version is working ok, but it's running too slow. Given your experience in this course, you suggest to her that a stiffer spring should...

I'm looking for some advice: I am trying to determine the allowable stress in a lifting attachment we have had manufactured. The lifting attachment is a mild steel block that bolts to the component to be lifted with a lug to enable a shackle to be fitted; two of these blocks are then fitted to...

What are the casual factors of corrosion failure?

The Scherrer equation is used to determine crystallite sizes from XRD spectra. they contain K, a shape factor, that varies from 0.89 for spherical to 0.94 for cubic particles. Usually, this is set to 0.9 for particles of unknown size. Does anyone know where we could find a table with the exact...

Homework Statement Simply these rational functions: [\sqrt{(X^2)+12}-4]/(X-2) (2-\sqrt{(X^2)-5})/(X+3) (X-1)/(\sqrt{X+3}-2) Homework Equations The only example in the book used the technique of multiplying the numerator and denominator by the function p(x) if p(x) is the function...

I need some explanation regarding a solution found in our textbook. The example starts with this DE: (1) y(x3 - y)dx - x(x3 + y)dy = 0. By regrouping, exact DEs will be found and the equation can be rewritten to: (2) x3 d(\frac{x}{y}) - \frac{d(xy)}{y} = 0. The integrating factor is found...

I've just completed a simulated experiment concerning the reaction between iodine ions and persulphate ions: 2I-(aq)+S2O82-(aq)-->I2(aq)+2SO42-(aq) (1) The iodine produced from this reaction, in turn reacts with thiosulphate ions: I2(aq)+2S2O32-(aq)-->2I-(aq)+S4O62-(aq) (2)...

Is there a function f(x) that will give the average number of prime factors for x_1 0<x_1<x, in a way similar to the way that Li(x)/x gives the approximate odds that a number from 0 to x is prime?

Homework Statement http://img42.imageshack.us/img42/1231/lobgave.jpg Homework Equations The Attempt at a Solution i think that solution shuld look something like this: (x-a)2*(x-k) but I am pretty lost, so i need some help...:cry:

Homework Statement http://img33.imageshack.us/img33/1231/lobgave.th.jpg Homework Equations The Attempt at a Solution It's the solution, but i have a feeling that there is a more correct way of doing it. At least i need a way to write it so it is mathematical...

Homework Statement Calculate the mass of nitrogen dissolved at room temperature in an 80.0L home aquarium. Assume a total pressure of 1.0 atm and a mole fraction for nitrogen of .78. Homework Equations Mole fraction= moles solute/moles solution Sgas=KH x Pgas KH = 6.1 x 10-4...

Homework Statement Resolve z^5-1 into real linear and quadratic factors. Hence prove that cos\frac{2\pi}{5}+cos\frac{4\pi}{5}=-\frac{1}{2} Homework Equations z=cis\theta z\bar{z}=cis\theta.cis(-\theta)=cos^2\theta+sin^2\theta=1 z+\bar{z}=cis\theta+cis(-\theta)=2cos\theta...

What will be the numbers of positive factors of product of n distinct prime numbers? i was able to get 2^n. pls how do i prove this?

Ok, so I got this question that is about factors affecting the thermal equilibrium of an object when heated when factors are altered. Basically, the setup is that the object is heated (Maybe a glass of water heated) and we are supposed to find out what factors affect the eqm temp of the...

What are the factors that affect viscosity of incompressible Newtonian fluid? Here is what I think: Temperature: When we increase the temperature of a fluid (controlled volume) the frequency ofintermoleculer collisions increases. Does this mean viscosity decreases? And if so, does...

Hi guys.. I am currently working on a research where I have totally no idea in. What are the factors i need to take into consideration if I were to design a pressure vessel?

Homework Statement Find the mg of Fe in vitamin pill. Vitamin pill was dissolved in 25mL HCl which was then diluted to 250mL with water in flask. 25mL of that solution was then diluted to 100mL in another flask. 10mL of the second was diluted to 100mL in another flask. Absorbance of the last...

Homework Statement I have a question to find Scalar factors of parabolic cylindrical coords and element dV with provided tranformation equations. I know the values for both of them and that the product of the scalar factors is the dV, but how do i derive those scalar factors? I don't even know...

Homework Statement Let G and G' be finite groups whose orders have no common factor. Prove that the homomorphism \varphi G \rightarrow G' is the trivial one \varphi (x) =1 for all x. The Attempt at a Solution My thoughts are that we need to use lagrange's thm. somehow. or maybe...

Homework Statement "A scientist prepares 100 mL of an iron (III) nitrate solution by weighing out 4.8372 grams of the solid iron (III) nitrate and dissolving it in deionized water using a 100 mL volumetric flask. She then pipettes 5 mL of that solution into a 20 mL volumetric flask and...

Hello I have to calculate symmetry factors for the following feynman diagrams for my qft class, and would be hugely grateful if anyone could point out any mistakes (I'm sure there are lots!) that I've made. http://picasaweb.google.com/jessicagreerstanley/Physics#5259179071440262450"...

If one considers an ideal gas, what does the mean time between collissions of the molecules depend upon? molecular size? number per unit volume? temperature of the gas? I'm thinking so far, it must def depend on number density. It would usually depend on molecular size (but I thought an ideal...

Homework Statement Prove that every polynomial with real coefficients factors into linear and quadratic real factors. Homework Equations So show that f(x) = x^{n} + a_{}n-1x^{n-1}+...+ax +a_{}0 factors into some (x-r_{}1)(x^{2}+4)... The Attempt at a Solution I understand how and...

Is it true that the characteristic polynomial of an n by n matrix over GF(q) splits into linear factors over GF(q^n)? I see that it must do if the polynomial is irreducible but what if it isn't?

And if I'm heating a liquid that contains things that evaporate at different temperatures, will I have an increasing amount of trouble separating these things as I increase the amount of heat applied?

what factors affect materials behaviour? what factors affect materials behaviour? help me please...

I am having issues finding the integration factor for the following two problems. I believe the second one can be solved by inspection. 1. (y^3+2ye^x)dx + (e^x+3y^2)dy = 0 2. (x-x^2-y^2)dx + (y+x^2+y^2)dy = 0

Homework Statement A generator is constructed by rotating a coil of N turns in a magnetic field B at a frequency f. The internal resistance of the coil is R and the cross sectional area of the coil is A. Which of the following statements are true? (Give ALL correct answers, i.e., B, AC...

Homework Statement Determine the response factors for both Na and K with the Li internal standard Concentration Ratio Na : K : Li (in ppm) 5.0 : 5.0: 500 ------------------- Signal Ratio Na : K : Li (relative units) 4.9 : 6.4: 36.2 Homework Equations Ax/x = F(As/s)...

Dear friends, i was working on a hadronic decays. It appears that one has to calculate form factors. These form factors involve some very complex numerical integration. I would like to know if there are some packages available for calculating these form factors.

So I'm studying infinite limits in my calculus text (seemed close enough to good old arithematic to put in general math, though), and the following rule is mentioned: Given two functions f(x) and g(x) defined for all real numbers, when given the quotient f(x)/g(x) where f(c) is not 0 and g(c)...

I don't know if this is getting posted in the right area, so please let me know otherwise. We have some hardware that takes a 50MHz clock signal, multiplies it by up to 32, and then divides it by up to 32, with the option to divide the final output by 4 again. The output must be between 8...

Using this: http://scienceworld.wolfram.com/astronomy/TropicalYear.html I derived this unix C code, which duplicates expected outputs. Note the constant T which is a correction factor for the epoch based in 2000, or so I assume because 2451545 is Jan 1 2000. And I have about epochs in...

I am trying to determine the critical crack length of a part using finite element analysis. The software I am using (ABAQUS) has the ability to perform fracture analysis. I model the part, create a crack, and ABAQUS will output the stress intensity factors (modes I, II, and III) and contour...

What are the limiting factors in this case... Hello, I have quite recently shifted to this area in Thailand. This is a very small town, there are no big cities for more than 150km distance, & no special industrial towns nearby. Before coming here I had thought this will be a very good...

[SOLVED] Integrating factors or separating the variables Homework Statement The following equation can be solved by intergrating factors or by separating the variables. \frac{dy}{dx} - \frac{y}{4x} = 0 with the initial condition of y(2)=3 Homework Equations The Attempt at a...

I have a piece of coursework due in soon (as a matter of fact, about 2 hours from now), and I need to know what the lmiting factors were. Here's the method: (a copypasta from my handed-in plan) For this experiment, I measured out a length of a resistive metal wire, and connected it to the...

i got a ti-83 calculator, is there any way to put in a number and get the factors listed for me? like put in the number 200 and get it to return 1x200,2x100 and so on... if not is there any program out there to enter into the calculator to make that happen thanks

Ok this should be pretty simple math for you guys (Sophomore in HS) Given that x-2 is a factor of P(x)=2x^3-3x^2-17x+30, find all other linear factors. I started out doing synthetic division, and got 2x^2-x-19 with remainder -8. Shouldn't the remainder be zero since x-2 is a factor...