Approximate Definition and 182 Threads

Approximately, what is the total mass of these materials that is contained in a "typical" Gen III or III+ PWR (e.g., EPR, AP1000...)? 1/ Zr alloy (fuel cladding and other assembly components)? 2/ Ag-In-Cd alloy (control rods)? 3/ Gd (burnable neutron absorber)? 4/ Ni-based alloys? 5/ Stainless...

Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math (Part 2) Continue reading the Original PF Insights Post.

Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math Continue reading the Original PF Insights Post.

Hi everyone, I am trying to solve a problem (related to pharmacokinetics) that requires finding t for an equation like the following: A e^{-a t} - B e ^{-b t} + C e^{-c t} = 0 where A, a, B, b, C and c are all real positive numbers (they are constants related to the absorption, uptake, efflux...

Let $X_1, ..., X_{35}$ be independent Poisson random variables having mean and variance 2. Let $Y_1, ..., Y_{15}$ be independent Normal random variables having mean 1 and variance 2. (a.) Specify the (approximate) distributions of $\bar{X}$. (b.) Find the probability $P(1.8 \leq \bar{X}...

Assume that I have absolutely no clue to what is the formula used to generate a sequence. How do I know what kind of formula that is? (Exponential / Linear / Polynomial / etc) Also assume that there is only 1 formula that generates the sequence. I have read somewhere before that: f'(x) ~...

Homework Statement For the portal frame geometry and factored loading shown in the figure below, calculate the shear force, axial load and bending moment diagrams using the Portal Frame Method. You may use the principle of superposition for gravity and lateral load effects. Note: • all...

Homework Statement Use Euler's method with h=0.1 to find approximate values of the solution of the initial-value problem y'+3y=7e^(4x), y(0)=2 at x=0, 0.1, 0.2, 0.3, ..., 1.0. Homework Equations f(x, y)=7e^(4x)-3y x0=0, y0=2 The Attempt at a Solution y(0.1)=y1=y0+f(0, 2)(0.1)=2+(0,1)f(0...

I've decided to finish off this stage of my GR problem by finding an interval over which the acceleration of the object is "roughly" constant. I don't need help with the Math per se, but I would like your opinion on the method I am proposing. The Math is sufficiently ugly that I'd like some...

Homework Statement Use Euler's method with h=0.05 to find approximate values for the solution of the initial-value problem y'=2x^2+3y^2-2, y(2)=1 at x=0.1, 0.2, 0.3. Homework Equations None. The Attempt at a Solution Here's my work: y'=2x^2+3y^2-2, y(2)=1 f(x, y)=2x^2+3y^2-2, x0=2, y0=1...

Homework Statement Find approximate expressions for T1 and T2 that are valid when h/d << 1 and h/x << 1 Homework Equations T_{1} =\dfrac{mg\left(d-x\right)}{dh}\sqrt{1+\dfrac{x^{2}}{h^{2}}} T_{2} =\dfrac{mgx}{d}\sqrt{1+\dfrac{\left(d-x\right)^{2}}{h^{2}}} h^{2}...

The thickness of an unexposed filter is 40um and a diameter of 46.2mm. I have an exposed air sampling filter with a mass concentration of the particulate (from gravimetric analysis) 20.1ug/m3. If I assume that the particulates are uniformly distributed in the surface of the filter, is it...

Homework Statement y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5 Find the exact solution of the differential equation. Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then...

This is a question inspired by the "Golf Ball" thread, which is no longer open for comments, I guess. For a black hole of constant mass, the metric external to the black hole can be written in Schwarzschild metric, which is characterized by the constant M, and the corresponding radius 2 M...

Like imagine I have to find the cube root of 8.03. So I cube 8 and use the dy=8+dy/dx*(8.03-8.00) formula. But why is this finding the value of cube root of 8.03 and why is this value approximate instead of exact?

For example at very low speed (v<<c), in Special Relativity, we can approximate relativistic motion to Classical Newtonian motion. But in General Relativity, what situation can make there an approximation to Newtonian Gravity ( just like v<<c ) ? Thanks.

How do you solve a question like this ? :you can obtain a rough estimate of the following simple experiment-let a droplet of oil spread out on a fairly large but smooth water surface .the resulting oil slick that forms On the surface of the water will be approximately one molecule thick. Given...

I am trying to make a simple formula to approximate the IRR using the IRR of each loan, their respective term and loan size. i.e. loan one is $\$1,000,$ has a term of $10$ years and an IRR of $5\%$. loan two is $\$100$ has a term of $1$ year and an IRR of $15\%$. Using a simple weighted...

Hello everyone, I want to have a simple example of an inductance calculation. The magnetic field normal to a filamentary circular current loop is not constant over the circle but if we approximate the value as that for the center, multiply by the area of the circle and divide by the current...

Take an 80 dollar pair of adjustable focus glasses, http://www.ebay.com/itm/ADLENS-HEMISPHERE-Adjustable-Reading-Glasses-Plastic-Round-Eyeglass-Frame-Gray-/310892439221?_trksid=p2054897.l4275 and use range finding hardware from a camera, add micro servos to control focus, add a computer to run...

The superconduction gap equation is: 1=VN(0)arsinh(ωD/lΔl). My book says that in the weak coupling limit VN(0)<<1 this will reduce to: lΔl = ωDexp(-1/VN(0)) But how is this obtained. We have: arsinh(ωD/lΔl) = ln(ωD2+√(ωD2 + lΔl2)), but what has the approximation of this got to do...

Homework Statement Two conductors are separated by an insulator. Model the insulator as a square barrier of height 0.01 keV and a width of 5nm. Determine the transmission coefficients for electrons of 7,000 meV. The only thing is I have to use the approximation formula for finding the...

Here is the question: I have posted a link there to this thread so the OP can view my work.

The attached pdf shows integral approximations of two sums, which are done in my book. In the first there is no result but the book simply states that one can approximate the sum by an integral. My question is: How is this done? Normally when you approximate a sum by an integral you have a sum...

Hi, I have a 3 by 3 hermitian matrix K that I need to diagonalise. More accurately, I am searching for a unitary matrix S such that S^{\dagger} K S is diagonal. The problem is that K is very complicated and the expression for S in mathematica takes up quiiiiiet a lot of space. Is it...

Assume that A,B\in\mathbb{R}^{N\times N} are some matrices which do not commute. Is there any way to approximate the matrix \sqrt{A + B} under the assumption that B is smaller than A? Could it be possible to write the square root precisely with some infinite series under some conditions...

Homework Statement Good evening. First post on this forum! The problem I wish to state would take too long to write by hand so I thought it best to do so via attachment. The question I am stuck on is part d and, in fact, part e also. Homework Equations All relevant equations are given...

I'm looking for solutions to this problem: Matrices A(m,n) and B(n,m) satisfy AB=I(m,m) where n isn't equal to m. Can I find a matrix S(m,n) such that SA=I(n,n) or SA approximates I(n,n)? By approximate I don't have preferred definition, hence any suggestion is welcome!

Consider the area between the curve y = x^2 + 2x from x = 1 to x = 5. Approximate the area of the region by using a regular partition of 4 sub intervals. a) using L4 i,e, left hand endpoints b) using R4 i,e, right hand endpoints So for the left hand endpoints would I just plug into the...

Homework Statement This is for my intro to General Relativity class, using Hartle's text Gravity: An intro to Einstein's GR. 12.1 "How many protons must combine to make one He nuclei every second to provide the luminosity of the Sun? Estimate how long the Sun could go on at this rate before...

The function for attitude vs air pressure is f(x) = 2100/x 1. Approximate the instantaneous rate of change at 100 millibars a) Use the equation to calculate the point (100,___) I found the y-value to be 21. b) We need two points to calculate a slope, so to approximate the tangent line we use...

Hello PF :smile: i was studying rotational motion it is given in my textbook that the moment of inertia of a rod of mass M and length L about an axis passing through the center of rod and perpendicular to the rod is ML2/12 This formula was prepared using calculus. So i experimented... a...

Homework Statement Use the approximate relationship to prove: Δf~\frac{df}{dx}Δx a) \frac{dx^{n}}{dx}= nxn-1 b)\frac{dcos(θ)}{dθ}=-sin(θ) Homework Equations a)N/a?? I'm not sure if I need any other equations than the one given. b) sin(ε)~ε and cos(ε)~1 when ε<<1. The Attempt at...

Homework Statement This is not a homework question, but I'm facing this from my research. I have N complex numbers defined as x_{n}=|\alpha_n| \cdot e^{j \theta_n} for n = 1,\ldots,N and my observation is the sum of those numbers r = \sum_{n=1}^{N} x_n . From the observation r, I...

Homework Statement So this isn't a homework question, just something my brother-in-law asked me. He is in the Army, and wanted to know an approximate landing force he would experience when he lands. After attempting the problem, and looking things over, I realized it may be harder than once...

Homework Statement 2 protons in a Helium nucleus are separated by about 2x10^-15 m. Calculate the approximate magnitude of the strong force holding the 2 protons together.Homework Equations Electromagnetic force equation?The Attempt at a Solution Okay now I am thinking that the strong force is...

Homework Statement Approximate uncertainty in the area of a circle of radius 5.5×10^4 cm? Homework Equations πr^2 The Attempt at a Solution

Here is the question: I have posted a link there to this topic so the OP can see my work.

Here is the question: I have posted a link there to this topic so the OP can see my work.

Determine which value best approximates the area of the region between the x-axis and the graph of ##f(x)=\frac{10}{x(x^2+1)}## over the interval [1,3]. Make your selection on the basis of a sketch of the region and not by performing any calculations. Explain your reasoning. (a) -6 (b) 6...

Here is the question: I have posted a link there to this topic so the OP can see my work.

The answer I got was: If I'am wrong please explain the correct solution and explain your reasoning thanks sarah (Sun)

Here is a problem I was having difficulty with. Took me forever just to figure out how to solve (because I stink at Calc). Here is my work: Does this look okay? What do you think of the approach?

I need to evaluate this integral \int_{x_0}^{\infty} \frac{\exp(-x)}{x}\, dx for x_0 \ll 1 Is there any cute approximate analytical expression? All I get are diverging series all over the place. The function is obviously finite...

Hi all, I have been stopped by a sextic (6th degree) polynomial in my research. I need to find the biggest positive root for this polynomial symbolically, and since its impassible in general, I came up with this idea, maybe there is a way to approximate this polynomial by a lower degree...

Homework Statement Recall that the Maclaurin series for sin(x) is \sum\frac{(-1)^{k}x^{2k+1}}{(2k + 1)!}. Use this formula to find the Maclaurin polynomial P5(x) for f(x)=xsin(x/2). Homework Equations The Attempt at a Solution I know that to approximate sin(x/2) with the Maclaurin...

Can we use Newton's method to approximate the value of definite integrals? (Thinking) EDIT: Ignore if the question doesn't make sense (which it probably doesn't).

Homework Statement consider s dipole with spacing of 2cm between the two sources. it is radiating a 100hz pure tone, and the magnitude of each source 'A' is given by 1n/M^2. calculate the pressure as a function of the angle between the reciever and the dipole for a reciever 10 m from the dipole...

Homework Statement Hey Everyone! So I have an assignment that says to approximate the integral f(x)=e^(3x), -1<x<3. Answer the following questions Run the code with N=10, N=100, and N=1000. For each approximation, when does the result agree with the exact value of the integral to 4 digits? How...

Homework Statement f(x) = sqrt(1 - x) a = 0 Approximate sqrt(0.9). Homework Equations L(x) = f'(a)(x - a) + f(a) The Attempt at a Solution I understand that linear approximation is finding the equation of a line of a point tangent to a function. But now this question is asking me...