Formulas Definition and 522 Threads

There are certain formulas for which only inductive proofs are known. But since we need to know the formula first to prove it using mathematical induction, how do they get the formula in the first place? Here is an example: - Euler's formula in graph theory states that v-e+f=2 for all planar...

Hello, I'm new here and this is the first thing I ever write on this forum, hence the question if this is the wrong place to post anything remains unanswered on my part. I came across this forum doing something on the internet, I can't remember what. I'm certain though that it was related...

Homework Statement While doing a physics assignment today, I came up with an expression in my answer that appears to be equivalent to sin(θ), however, i couldn't find a way to manipulate the expression to prove that it was. Could anyone point me in the right direction as to a way that I could...

I have a problem with physics when it comes to relating new ideas with new formulas. Like right now I'm learning about Solids and Fluids, and the problem i have now is remember what formulas to use when, what each of the parts of the formula mean, etc. Is there a site or a list of questions that...

Hello there! I'm currently working on an essay regarding astrophysics. The level of this essay is of high school standards but I do like math and physics so advanced calculations doesn't frighten me. :redface: Anyway so the essay's is about the astrophysics behind our search for...

Homework Statement House one is going for 250.000 in the suburb and has a new power plant being built and also has a decrease in crime. House two is also 250.000 in city has an increase crime rate but has a new school being built. What house will be the best value in a 10 year span if you buy...

Homework Statement House one is going for say 350.000 and House two is going for 250.000, both have the same bed and bath. Yet i want to add variables for instance house one has a decline in crime rate variable also a newly build mall. House two has new schools and crime is on the rise. So my...

not sure if I am in the right place or not but nevertheless need some help I am trying to figure the correct steel to use for sign support. I am trying to determine if a 5 x 5 inch with .25 wall is as strong or stronger than a 6 x inch tube with a 3/16 wall. Can't find any formulas to help...

I am an EET student. The professor I have is not very thorough in his examples and if you can't keep up with him or have x-ray vision to see through him to the board while he is working the problems then you just don't get the information needed. That said, I am currently trying to do a take...

Homework Statement The test has two parts. In Part A, you predict the results and give qualitative reasoning and in Part B, you actually calculate the values and verify if your predictions and the calculations are in agreement, and then give correct physics reasoning. Consider three events...

Homework Statement Use power-reducing formulas to rewrite 152sin^2 x cos^2 x Homework Equations sin^2θ= 1-cos2θ/ 2 and cos^2θ= 1+cos2θ/2 The Attempt at a Solution 152(1-cos2x/2)(1+cos2x/2), 152/4 (1^2 - cos^2 2x), 30(1-(1+cos4x/2), and I got 30-30+30cos4x/2 as the answer but the...

This isn't homework. A friend asked about this so I decided to work out the formulas, but wanted to know if this was already done by someone here (otherwise I'll do the math). p = power (constant) a = acceleration v = velocity x = position t = time f = force Assume an object is...

Homework Statement You know the U substitution proofs for inverse trig functions that go like this: \int\frac{1}{a^{2}+x^{2}}dx \int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx let u = x/a du= dx/a ... \frac{1}{a}tan^{-1}(x/a)+cI have searched google and can't find any of these proofs for...

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Is anyone familiar with the Roark's text that can clarify some terms for me? I am trying to clarify what Roark is referring to in the above mentioned text in the section on short beams (in the 5th edition 7.10 and in the 7th edition 8.10). Throughout the text, he uses the terms "span" and...

Homework Statement Are there any sample problems worked out for trig functions of higher powers which are integrated by reduction formula? Like cos^8 or cos^10 or even just cos^6 or maybe?

if f=mc squared what is m=?

One thing I enjoy as a new physics student is using formulas. I have been playing with the fundamental formulas in terms of units rather than their names. That is instead of a=v/t m/s/s=(m/s)/s or v=at m/s=(m/s/s) x s m/s=m/s Simple maths yea, but when I am getting to the bigger...

Homework Statement Suppose that the position vector for a particle is given as a function of time by (t) = x(t) + y(t), with x(t) = at + b and y(t) = ct2 + d,where a = 1.70 m/s, b = 1.20 m, c = 0.122 m/s2, and d = 1.18 m. (a) Calculate the average velocity during the time interval from t =...

Very Stuck on Deriving Projectile Motion Formulas Hey, I need some help :( . I've got an exam next Thursday, and I really suck at this stuff right now. So I need to get better! We are studying kinematics (1d and 2d). In this problem I need help with, we are given the attached diagram...

Dear Forum, I am familiar with the formulas between inertial frames of reference that move at a constant speed between each other. The observed object move at a constant speed or at a constant acceleration. It can be shown that while the positions and velocities are different in the two...

How to prove "Satisfiability of boolean formulas is NP-complete" I can not figure out how to prove this. I have been trying to find something that explains it step by step, possibly even with an example. I can not find anything. Can somebody perhaps explain how you prove it or show me where I...

Are you expected to know all of the trig formulas for the math gre subject test? I don't mean the easy ones, i mean ones such as the sum-to-product or product-to-sum. thanks!

Hello, Simple but perhaps odd question. e^{i(kx+\omega t)} and e^{i(-kx-\omega t)} The first formula describes a wave (with wavevector k and angular frequency omega) traveling to the left. And the second formula? I thought that it physically describes exactly the same situation...

The formulas in question are: Beta = Ic/Ib Ie = Ib ( 1 + beta ) Ie = Ib + Ic

Hi All, I'm trying to write a program that will prove that a certain mathematical formula that is entered by a student is the same as the goal formula that I want. For example, if the goal formula is: 2 * X + Y then any of this student's answer can be considered correct: -> X + X + Y...

1.Homework Statement . Can someone give me more accurate mathematical models on thermal expansion? for example, linear expansion. 2.Relevant equations L=L0(1+α∆T) this equation is not accurate. for example. When an object 100m long at 0oC (example: aluminum, α=2.4x10-5) is heated to...

Hello. I am attempting to design a generator that works with the (admittitedly) inefficent design or rotating a conductive material inside a magnetic field to produce current flow. I could use help finding the formulas I need to calculate the amount of spin and size of coils i will need to...

Homework Statement Can anybody help me think of Energy formulas/equations in the form below? Any form of Energy. (Please also state what does each variable stands for.) Homework Equations E = \frac{1}{2}ab2 = \frac{1}{2}ac Where c = ab The Attempt at a Solution So far, this...

Hello, I am trying to work out the resistor values for an 'O' attenuator. I am using the attached formula to work out resistor 3's value. My values to insert into this formula are: Input impedance (Z1) = 50 Ohm Load impedance (Z2) = 600 Ohm a =1.995 However when I substitute these figures I am...

Hi. 1. Can anyone definitively tell me what the dimension formula for the classical Lie algebras? For example, I know for SO(2n) or D_n, the dimension formula is SO(N)--> (N*(N-1))/2 E.g. SO(8) is 8*7/2 = 28. Ok, so what about SU(N+1) i.e. A_n, SO(2n+1) i.e. B_N and Sp(n) i.e...

Homework Statement Let M = \begin {bmatrix} 8 & -1 \\ 2 & 11 \\ \end{bmatrix} Find formulas for the entries of M^n, where n is a positive integer. Homework Equations N/A The Attempt at a Solution I honestly have no clue where to start. We recently covered diagonalization, but I...

Homework Statement I am currently working on a computer science program which calculates the landing of a craft on a given planet. The user will enter in various known variables. I need some direction on what formulas to use for my program. I am strong in computer science however I...

Hi, I see that Boltzmann constant comes in different forms like: k=8.62*10-5 eV/K and also k=1.38*10-23J/K. Which one should I use in , say formula for intrinsic carrier concentration ni = sqrt(Nc*Nv)*e-Eg(T)/2kT ?

34. Turner's syndrome is a rare chromosomal disorder in which girls have only one X chromosome. It affects about 1 in 2000 girls in the United States. About 1 in 10 girls with Turner's syndrome also suffer from an abnormal narrowing of the aorta. a. In a group of 4000 girls, what is the...

Do I made a mistake in writting this formulas. I don't see them. Tnx for your answer. V1=(Kps*(1-ra**2)*(1-cos(6.2831853*y(1))))/(6.2831853**2* (1+ra**2+2*ra* cos(6.2831853*y(1)/2))**2) V2=(Kps*ra*(1-ra**2)*(1-cos(6.2831853*y(1)))*...

Hey there, I'm very confused between the difference of these power formulas. P= VI P= (I^2)(R) P=(V^2)/(R) Why is it that I often get different answers with all of them? Don't they all equal power? What are the situations I can use each one in?

Hey, I'm wondering if anyone knows of a trig identity for arct(a/b) where a and b are rationals.

Homework Statement http://u.spig.in/forum/105320795.jpg Homework Equations general Electrostats formulas The Attempt at a SolutionI tried to solve the problem using Energy conservation ie., Change in PE = Work done. But that seem to yield wrong answer (1) while the correct answer is 2. I...

Homework Statement We have Work=Kinetic Energy which is : ##A=E_k=Fd=\frac{1}{2}mv^2## Find formulas of : Force, distance, mass, velocity squared and velocityHomework Equations ##A=E_k=Fd=\frac{1}{2}mv^2##The Attempt at a Solution ##F=\frac{\frac{1}{2}mv^2}{d}## ##d=\frac{\frac{1}{2}mv^2}{F}##...

Integrate sin2(x)cos4(x)dx using reduction formulas? My book says integral sin2(x)cos4(x)dx= integral cos4(x)-integral cos6x dx Now the reduction formula for n=6 for integral cos6(x)dx= (1/6)cos5(x)sinx+(5/6) integral cos4(x)dx Here is the part I don't get: It then says ...

Let A ,B and C represent vectors. we have 1) d/dt (A . B) = A. dB/dt + dA/dt .B 2) d/dt [ A . (BxC) ] = A . (Bx dC/dt) + A . ( dB/dt x C) + dA/dt . (B xC) now the problem in these formulas is that we know that Dot product between two vectors and Scalar triple product of vectors is...

I don't understand why 4 ∏ is in so many physics formulas. For instance, Heisenberg's uncertainty uses h / 4∏. Or Coulomb's law for the electric force Or the formula for the Magnetic permeability of free space: Many formulas use 4 ∏ or 8 ∏. I just don't...

Homework Statement I'm not sure where to begin with this problem A car is traveling West at 35mph. 45 feet in front of this car is an intersection , and another car is about to turn in front of the westbound car. Could the car safely complete the left hand turn , or would the westbound car...

Say for the recursive formula 2, 5, 9, 19 , 37...Instead of writing it as an = an-1 + * 2 an-2 can you write it as: an = 2an + (-1)nJust double checking. I encountered this earlier helping someone and I haven't done recursive formulas in a while..

Homework Statement Show that the two formulas are equivalent integral [sec x dx] = ln|sec x + tan x| + C integral [sec x dx] = -ln|sec x - tan x| + C Homework Equations Pythagorean ID's? Log rule of addition The Attempt at a Solution Well, I realized the formulas can only be equivalent if...

Homework Statement Find a collection of well-formed formulas Ʃ such that Ʃ has no independent equivalent subset. Homework Equations N/A The Attempt at a Solution So far I have been able to show that Ʃ must be infinite. However, after this, I get stuck. Could anyone give me a hint...

problem: have a table (but not the one I need) with three 3 variables (one of these changing) and known answer for these. I need to change one variable but I do not know the formula. Is there any way to figure this out: known table: v1: 1,833 v2: 15,89 v3: 53/9 this gives me a table...

Gravity Formulas urgent I have to find the gravity acting upon an object, given an ANGLE. What would be the simplest formulae to use, I forgot my wrk sheet at school. I just need the simplest formulae, i found some but these are hard for me, we didn't use these (I'm in grade 11)...

TI-84 HELP! The formulas under the CONICS app keeps converting into trig... It saying a circle is x=rcos(T) + H instead of (x-h)^2 + (y-k)^2 = r^2 How do I get the 'normal' formulas back? PLEASE HELP!