Formula Definition and 1000 Threads

here is a link with the formula: https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms.pdf i'm talking about the formula that says the integral of f'(x)/f(x)dx = ln(f(x))+C it's kind of hard to put this into Google. where does this formula...

Hello, This algorithm overall is probably more complicated than is correct for the pre-university forum but this question is about a relatively simple aspect of the calculations so I hope that this will be the proper place to ask. I am writing a little program to do some computational geometry...

Homework Statement If ##v## is an integer greater than or equal to ##2##, then ##P_v## is the graph having vertex set ##\{1,2,3, \dots, v \}## and edge set ##\{\{1,2 \}, \{2,3 \}, \{3,4 \}, \dots, \{v-1,v \} \}##. Prove that this graph has ##v-1## edges. Homework EquationsThe Attempt at a...

Let \triangle ABC be a right triangle with right angle at C. Suppose this right triangle has legs BC=a, AC=b, hypotenuse AB=C, and circumradius R. Two copies of this triangle can be joined to form an isosceles triangle in two ways. With a as a common side, you can form an isosceles triangle...

https://en.wikipedia.org/wiki/Euler's_formula (1) eix = cos(x) + isin(x) (2) eixidx = (-sin(x) + icos(x))dx (3) eix = (-sin(x) + icos(x)) / i (4) eix = cos(x) + isin(x) Just lost in circles. Just for fun.. post a solution for x.

Hi, Sorry for this weird question. My computer crashed and also the notes in it. I had a book wherein I'd written all the formulae. There is one formula in notes of Power System. X = cube root of R. I remember there was a website that even had its derivation, but I don't have the bookmarks...

In refraction of spherical surfaces, We derived the formula to be: ## u_2 L^{'} = u_1 L + (u_2 - u_1) R## Where ##L^{'}## is the reciprocal of the distance of the image. ##L## is the reciprocal of the distance of the object. ##u_2## is the refractive index of the medium that the light ray is...

Homework Statement Homework EquationsThe Attempt at a Solution I only need help on part c. I tried to add up t1 and t2 and differentiate it. However what variables should I differentiate with respect to? If I differentiate with respect to f I got f=root(2) * h, if i differentiate with respect...

Homework Statement 2. Homework Equations 3. The Attempt at a Solution [/B] I tried to solve this question with the general formula n=sin i / sin r. 1.5 = sin 30/sin r, r = 19.4 = 19 which is option A. But option A is incorrect. Please guide me where am I wrong..

Let's say we have a tank with 1000 psi pushing in all directions, if we remove one square inch from an end, now the tank has 1000 psi more at one end than the other. Does this mean that there is a 1000 lb push in the opposite direction of the removed square inch?

Hi, We are not learning this in class, but I am giving a presentation on special relativity and as part of my presentation I would like to show that time is not absolute and that if a ship moves away from the Earth for a time t at a speed v then if like 8 years pass on board the ship a greater...

Homework Statement The Attempt at a Solution I don't understand what an affine function \mathbb{R}^{2}\rightarrow \mathbb{R} expresses... I don't know if it's a coordinate function. And i also don't understand (i'm sorry) why for any parallelogram, u(P) + u(R) = u(Q) + u(S)

Hello. Here is the formula that computes the sample skewness: Sk = [ (n / [(n-1)(n-2)] ] x [ ∑ (Xi - X)3 / s3 ] , where n is the number of elements in the sample, Xi is the specific i-th value of the sample, where i starts from 0 and ends at i=n, X is the arithmetic mean, s - standard...

Homework Statement Calculate Σ (i=1, n) √i I want to write general formula, then use it for any n (like we have for Σ (i=1, n) i Homework Equations Σ (i=1, n) i = n (n+1) / 2 Σ (i=1, n) i^2 = n (n+1)(2n +1) / 6The Attempt at a Solution Comparing formulas provided above: I assume the answer...

After watching this video: The mystery of 0.577 4k1jegU4Wb4 My problem is at position 7 mins 26 secs where he states the following: 1 - Ln = 1 1+ 1/2 - Ln2 = 0.81 1 + 1/2 + 1/3 - Ln3 = 0.73 And so on until we arrive at Eulers Mascheroni Constant Being that he is using 'Ln' have learned this...

c² = (n/m) ∂²U/∂n² where U = vacuum energy density as a function of the quasiparticle density n = quasiparticle number density m = bare mass of quasiparticle Is there a book, article where this formula is explained? Thank you.

Sir, In 1927 the English Pound was USD 4.86. What would be the reverse for $1.00, with the Pound value expressed in £ s d. Would there be a formula for this conversion? Thank you for any help you may provide. Regards, P.N.

Homework Statement Homework Equations I=1/12*bh^2+Md^2 The Attempt at a Solution for the highlighted 600mm^2 (and the 300mm^2 below) in the middle of the page, when finding the moment of inertia, what the solution used is an area, yet for related formula required the use as for mass in the...

Homework Statement Hello! Please, help me to understand the mathematical logic behind one of the financial instruments called the "money market yield". Here is the equation: money market yield = [ 360 x r BD ] / [360 - (t x rBD)] where rBD is the band discount rate, and for simplicity we...

In school we have numerous exercises that ask you to find the time when a body passes a certain point for the nth time in simple harmonic oscillation. But it is a bit mentally taxing to solve with the actual formula of x=Asin(ωt + φ), just because you have to sort out all the infinite solutions...

Homework Statement Hello, so I’ve been trying to find some possible way to calculate this: The initial Velocity and angle needed to launch a projectile and reach the coordinates (x,y). The maximum height the ball can reach before it starts to head down to the target value should be y+5m The...

Considering the linear thermal dilation formula ΔL=Li*a*ΔT (length change equals initial length times thermal dilation coefficient times temperature change), I was wondering why does it not work backwards? am I using it wrong or is there something missing? For instance if we assume a=5*10^-5 ...

Homework Statement Draw the Lewis structure and structural formula for: a) HCN b) SO3 2- Homework Equations none The Attempt at a Solution Did I do these correctly? Thanks!

I've written a short text adapted from a previous post by Count Iblis. I'll append it below. It shows that irreversible PV-work is always smaller than reversible, which fits very nicely with W = Pext ΔV. I'd be interested if there's a way to show that W is exactly equal to Pext ΔV for all...

Is the significance of an excess calculated by Asimov formula given in units of sigma? Z_0 = \sqrt{2((s+b) ln(1+ s/b)-s)} where s are the signal events and b are the background events. If no, how can I calculate it in units of sigma? Thank you in advance!

Homework Statement I'm writing a program to plot the trajectory of a baseball. the formula is given to me by the book, but I'm not sure what it means. Homework Equations The Attempt at a Solution I am given that v_d = 35 m/s and delta = 5 m/s what is v? as in what does it represent? is it...

Homework Statement I found out that Bauxite has 2 formula, which one is 2Al(OH)3, and the other one is Al2Si2O5(OH)4⋅2H2O. What's the difference of these formula? Homework EquationsThe Attempt at a Solution

I'm studing classical physics and I'm stuck with the simple pressure formula defined as: P=\frac{dF_{\perp }}{dS} Now, i know some calculus and the concept of infinitesimal in physics; however what i don't understand is : 1) according with the fact that in Calculus dF_{\perp } represent an...

Hypothetical question: Let's say there's a granite cube with a volume of 60 cubic centimeters. A cannon ball is shot at it, reducing it to rubble, and the kinetic energy of the ball was 10,000 joules. We use the same ball with the same kinetic energy output on a stronger unknown substance with...

1. Homework Statement I'm doing lab, and to start we have to find ΔX of a projectile launched an angle. The first step for us is to find time, and to make it easier our teacher recommended us to first set the angle to zero, and find time like that. I don't have enough X information to find...

So I have two formulas for calculating voltage drop. The first is: Vdrop = Vin * R1 / ( R1 + R2...). This let's me calculate the voltage drop on the first resistor in a series of 2 resistors. You can also extend this to more resistors in series just by summing all the resistors. However, I do...

I found this formula when I was studying neutron diffusion equation in Weston M. Stacey's book Thanks in advance cosβ=cosθx cosθ+sinθx sinθ cos(ψy−ψ) Edited by moderator for clarity: ##\cos(\beta) = \cos(\theta_x)\cos(\theta) + \sin(\theta_x)\sin(\theta)\cos(\psi y - \psi)##

I am seeing this formula in a textbook, unexplained. Can someone tell me the origin, the book just says it is an identity. $$Re(Ee^{jwt})=\frac{1}{2}(Ee^{jwt}+E^*e^{-jwt})$$ The book doesn't explain what ##E^*## is, it just lists the formula. Re = real, as in take the real part. E is the...

I am trying to understand the geometric intuition of the above equation. ##\rho(\tau)## represents the rank of the linear transformation ##\tau## and likewise for ##\rho(\tau\sigma)##. ##Im(\sigma)## means the image of the linear transformation ##\sigma## and lastly, ##K(\tau)## is the kernel of...

Hello PF, I was reading through “A First Course in General Relativity” by Schutz and I got to the part where he derives the divergence formula for a vector:$$V^α { } _{;α} = \frac {1} {\sqrt{-g}} ( \sqrt{-g} V^α )_{,α}$$I’m having trouble with a couple of the steps he made. So we start with the...

Hello all. Been a long time since I took a thermal course. I'm looking for a formula to work with the thermal stabilization of something. Specifically, I want to minimize the time required for thermal stabilization to occur and how to mathematically calculate what that set temperatures should...

When studying equations, formulas, laws - am I supposed to understand each bit of information ? For example, let's take Fick's law: So I can memorize the law and I can tell with words what is "t", what is "x", what is "D", and so on, but I don't truly understand why is one divided with the...

I think that dU = Cv dT can only be used when the volume of the gas is constant. Similarly, Cp = dQ/dT can only be used when the pressure is constant. Such as We have Cv=dQ/dT and ΔU=Q+W dU=Q+pdV Therefore, dU/dT = dQ/dT only when dV is zero Why am I wrong? Thank you so much for your help. The...

Homework Statement The initial speed of a ball up an inclined plane is 3 m/s upwards. The ball reaches its highest point after 1.2 seconds. a) find the acceleration. b) how far has the ball gotten during this time? c) how far has the ball rolled after 0.4 s and after 2.4 seconds? Homework...

Homework Statement Say I have four categories which make up a "whole" that I'll call a unique "deal". Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or...

Hello everyone, I am trying to work out how much force is generated when a tyre fails at a certain pressure. The tyre will be inside an OSHA section 1910.177 compliant tyre cage. What calculation would be used to solve the following?: The tyre size is 35 x 11.5-17 with a rated inflation of...

I was trying to Extrapolate Eulers formula , after deriing the basic form I wanted to prove: ∂F/∂y - d(∂F/∂yx)/dx +d[SUP]2[/SUP](∂F/∂yxx)/dx2 = 0 Here is my attempt but I get different answers: J(y) = ∫abF(x,yx,y,yxx)dx δ(ε) = J(y+εη(x)) y = yt+εη(x) ∂y/∂ε = η(x) ∂yx/∂ε = η⋅(x)...

Homework Statement How big must N be for the simple version of stirlings formula to be accurate to within 2% Homework EquationsThe Attempt at a Solution So I think the starting point is ##\frac{N lnN-N}{lnN!} =\alpha ## where ##\alpha=0.98## But i have no idea how to solve this expression...

Hi everyone, Im a little bit confused about deBroglies procedure on introducing his famous Matterwave formula. People already knew that the wavelength of the light was equal to Lambda = h/p. The term p comes from the energy-momentum formula; for the light the restmass = 0 so E =pc etc. As...

Hello, this formula was given to me in an exam to find the moment of inertia of an I beam, https://ibb.co/jY7ZKG However this formula seems to give a different answer to the standard bd^3/12 method, is the formula in the image wrong ? Thanks

I was thinking about a diagram (in the category of proof without words) for Hero's formula for area of a triangle with sides a, b, and c and given that 2s = a+b+c. A = √[(s(s-a)(s-b)(s-c)] I tried to develop one but could not. Can anybody give or give me an hint to proceed.

Scenario: An average of 5 test subjects are brought into a study in subsequent months and are administered 1 monthly test for as long as they remain part of the study. The time they remain in the study is 3 months. Could someone please explain a formula or technique to sum the number of...

Hello everyone! I'm having a bit of a problem with comprehension of the Cauchy integration formula. I might be missing some key know-how, so I'm asking for any sort of help and/or guideline on how to tackle similar problems. I thank anyone willing to take a look at my post! Homework Statement...

Hello, If I understand correctly, according to Kepler, a planet orbiting a star should cover a constant surface area of its ellipsoid or circular orbit per time unit, regardless of the distance of that planet to the star. I have tried to prove this by using a scenario in which a planet is...

Good day ! I have an issue with the sign minus inside the skew bending (unsymmetric) formula First we all know that the stress generated by the bending moment is the following: and then after we have the formula I really don't understand why we don t have the sign minus in all the formula...