Exponential Definition and 1000 Threads

Homework Statement I'm working out a differential equation problem that I am supposed to solve with the formula \mathcal{L}\{t^\alpha\} = \frac{\Gamma{(\alpha + 1)}}{s^{\alpha+1}}. The problem is \mathcal{L}\{t^{\frac{1}{2}}\} (finding the Laplace transform of the given function)...

exam problem : solve exponential withh ... log? This one is killin me! 36^x-6*6^x=-9 please show and explain steps

Differentiate the following: u = 2 (x-t2 / 3)et/3 Here is my attempt I have to find du/dx and du/dt du/dx = 2 (x-t2 / 3)et/3 du/dt = -4t/9 (x-t2 / 3)et/3

Homework Statement e^{ \begin{bmatrix} \lambda_{1} & 0 \\ 1& \lambda_{2} \end{bmatrix}t } =\begin{bmatrix} e^{\lambda_{1}t} & 0 \\ \frac{e^{\lambda_{2}t} - e^{\lambda_{1}t}}{ \lambda_{2} - \lambda_{1}} & e^{\lambda_{2}t} \end{bmatrix} with \lambda_{1}\neq \lambda_{2} Homework...

Homework Statement I'm writing a lab report and I'm having trouble understanding how to set up these experimental equations. I understand Linear (y=mx+b) but my professor wants us to use separate equations to illustrate power and exponential forms. Power : y=bx^m Exponential: y=be^(mx)...

Homework Statement Use the function y=2e^-0.5x^2 to answer the following questions a) state the domain b) Determine the intercepts, if any c) Discuss the symmetry of the graph d) Find any asymptotes e)determine the intervals of increase and decrease f)what is the maxima and/or minima...

5(0.10)^x = 4(0.12)^x... x = ? getting aggravated Homework Statement 5(0.10)^x = 4(0.12)^x this problem is driving me nuts. i graphed it and got x~1.2239011 but I can't find it on paper. i have been using the property ln(a^x) = x*ln(a) The Attempt at a Solution i tried doing...

For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value from searching in internet I found that E{X|X>a}=a+E{x} but I can not prove it Help please

Homework Statement For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value Homework Equations The Attempt at a Solution

Fix some constant 0<\alpha \leq 1, and denote the floor function by x\mapsto [x]. The conjecture is that there exists a constant \beta > 1 such that \beta^{-n} \sum_{k=0}^{[\alpha\cdot n]} \binom{n}{k} \underset{n\to\infty}{\nrightarrow} 0 Consider this conjecture as a challenge. I don't...

Homework Statement A manufacturing process produces 92% good chips (G) and 8% bad chips (B). The lifetime, in seconds, of chips is exponentially distributed E(\lambda). For good chips, \lambda1=1/20000 For bad chips,\lambda2=1/1000 Every chip is tested for 50 seconds prior to leaving the...

Let's say you have a random sample of 5 values that are drawn from an exponential distribution with a mean of 8. How do I find the distribution of Ybar, which is the sample mean of the 5 random variables? [Note: Ybar = 1/5(Y₁+Y₂+Y₃+Y₄+Y₅)] I know that for an exponential distribution with...

Please help i have these two questions and i am Stuck! Question 1 The linear equation you have found (y=.771x+1.609) is in the form of y= mx +c. it should be however more appropreiatly be considered as being in the form, lny = mx + lnA. by using appropriat logarithmic and exponential laws...

Hi all, I am now doing revision for one of the statistics module. I am having some difficulty to proove the following: Given n iid Exponential distribution with rate parameter \mu, using convolution to show that the sum of them is Erlang distribution with density f(x) = \mu...

Modeling with exponential and logarithmic functions help? Homework Statement Use Newton's Lay of Cooling, T = C + (T0 - C)e-kt, to solve this exercise. At 9:00 A.M., a coroner arrived at the home of a person who had died during the night. The temperature of the room was 70 degrees F, and at...

I'm reading that if you have a complex exponential exp(iω0n) where n is in the set of integers, then unlike for the case of a continuous independent variable, the set of complex exponentials that is harmonically-related to this one is finite. I.e. there is only a finite number of distinct...

I'm rather confused on how to operate exponents on fractions. For example (4/3)^-1 or (4/3)^1 Please explain?

I got a question here, and I am stuck at understanding the step of the solution. Any help will be appreciated. http://img841.imageshack.us/img841/6589/40155869.jpg I would like to know how to get from the second to the third step, where the summation comes in. It looks like multiplication of...

I am trying to understand the physics of an exponential horn. I got most of my references online and according to the Horn Physics by Martin King, the volume velocity at the mouth is greater than the applied volume velocity at the throat (the horn is driven by a speaker/buzzer). This is what i...

Homework Statement Let v(λ) = ∫0∞ λe-λy f(y)dy a) Prove that limλ→ ∞ v(λ) = f(0). b) Determine and prove limλ→ ∞ λ(v(λ)- f(0)). α β γ δ ε ζ η θ ι κ λ μ ν ξ ο ° π ρ ς σ τ υ φ χ ψ ω Ω ~ ≈ ≠ ≡ ± ≤ ≥ Δ ∇ Σ ∂ ∫ ∏ → ∞ Homework Equations Assume there exists some constant M where maxx∈ℝ...

Hi everyone, There's something that's kind of been bugging me about applying exponential decay formulas to real world phenomena. For example let's say the discharging of a parallel plate capacitor. Let's consider the negative plate. As it discharges excess electrons leave the plate. The...

Homework Statement im wondering if e^i(x+y) + e^-i(x+y) can be simplified to 2cosxcosy Homework Equations 2cosx= e^ix + e^-ix so i separated e^i(x+y) + e^-i(x+y) into; e^ix(e^iy) + e^-ix(e^-iy) can that become 2cosxcosy?

Homework Statement Determine the limit and then prove your claim. limx\rightarrow\infty (1+\frac{1}{x^2} }) xHomework Equations I know that the formal definition that I need to use to prove the limit is: {limx\rightarrow\infty (1+\frac{1}{x^2})x=1}={\forall \epsilon>0, \exists N > 0, \ni x>N...

We know how to solve problems like e^ax+e^bx=k, when a=2b. But how to solve equations of this type when a is not equal to 2b?

Hi, I'm in a signal processing class, and I'm having some trouble with complex numbers. As an example, I've attached a pretty simple question about an exponential Fourier series. I don't find these questions particularly hard, it just takes me ridiculously long to do them. I mean, after I...

Homework Statement Find the exact value of P(|Y- μ| < 1.4σ) for an exponential random variable with parameter β. Homework Equations The only equation that I can think of is the exponential distribution equation: ∫(1/β)e^(-y/β) The Attempt at a Solution I have been unable to...

Hi, I have a conceptual question. Looking at exponential smoothing methods I came across relationship between the autocorrelation function and lambda. It says that if the time series doesn't apper to be autocorrelated then lambda is expected to have a low value :confused: .Any help will be...

Homework Statement Consider a Poisson process for which events occur at a rate of 2 per hour. (a) Give the probability that the time until the first event occurs exceeds 2 hours. Use an exponential distribution to find the probability.Homework Equations The Attempt at a Solution \lambda = 1/2...

1.\frac{dx}{dt}= \stackrel{9 -12}{2 -1} x(0)=\stackrel{-13}{-5} So I seem to be having issues with this problem There are 2 eigenvalues that I obtained from setting Det[A-rI]=0 That gave me r^{2}-8r+15=0 solving for r and finding the roots i got (r-3)*(r-5)=0 so the...

Homework Statement I need to use the relation exp(i*Pi/4) = (1+i)/sqrt2 but I'd like to know where it came from. I am clueless about how to arrive at this.

- exp(f) = Laplacian(f) where f is a real valued function of two variables in an open domain.

The problem is (\sqrt[4]{6x})^3 And i have to convert it to exponential form, and I forgot how to do this, so i need some help. Thank you.

Hello, Suppose you observe some foam. The foam is formed by a set of bubbles, and each bubble blows up after a random time. The density function of the time each bubble will take to blow up is probably exponential, with rate lambda. The total amount of foam (Q) must also decay exponentially...

Homework Statement At how many points in the xy-plane do the graphs of y=x^{12} and y=2^{x} intersect? Homework Equations none The Attempt at a Solution I have no idea what to do. I thought of trying to narrow it down to some intervals where the graphs may cross, but, since they're...

Homework Statement Solve y''(t) - k^2 y(t) = e^{-a|t|} where a and k are both positive and real. Homework Equations The solution was obtained trough a Fourier transform. The Attempt at a Solution I got the solution y(t) = \frac{ke^{-at} - ae^{-kt}}{k(a^2 - k^2)} but when i...

D_n=\frac{1}{\pi}\int_0^\pi\sin{(t)}\cdot e^{-i2nt}dt=\frac{2}{\pi(1-4n^2)} I have no idea on how they get from one side of the equation symbol to the other, can i get some tips and tricks ? I have try ed writing sint as an exp function, but i don't feel it gets me anywhere close.

Homework Statement I am searching for a proof of convergence of matrix exponential series. Where I can find it? Thanks! Homework Equations The Attempt at a Solution

Homework Statement Find the number of ways to place 8 toys amongst 4 children where 1 child gets at least two toys. Homework Equations (x^2/2! + x^3/3! + x^4/4! +...) = ex-1-x (1 + x + x^2/2! + x^3/3! +...)3 = e3x The Attempt at a Solution [(x^2/2! + x^3/3! + x^4/4! +...) =...

Homework Statement let X1, X2,... Xn form a random sample of size n from the exponential distribution whose pdf if f(x|B) = Be-Bx for x>0 and B>0. Find an unbiased estimator of B. Homework Equations The Attempt at a Solution nothing yet. i don't really know where to get started. a...

Homework Statement find the Fourier transform of complex exponential multiplied to a unit step. given: v(t)=exp(-i*wo*t)*u(t) Homework Equations ∫(v(t)*exp(-i*w*t) dt) from -∞ to +∞ The Attempt at a Solution ∫([v(t)]*exp(-i*w*t) dt) from -∞ to +∞...

how to write 1/x in exponential form ?

this is just something has been bugging me for the last few days. it seems like it has a very basic solution. Muons decay randomly, but have a mean lifetime of about 2 us. If I plot the # of muons that decay vs. time (say the axis spans from 0 to 20 us), why is the plot exponential decay...

Homework Statement If I have a matrix M, say 30 5 20 16 How do I calculate M^{1870} mod 101 using Euler's Theorem. Homework Equations I have so far worked out M ^{2} mod 101 to be 91 28 11 53 and thought I could use this as 2x935=1870 The Attempt at a Solution I...

Homework Statement Annoying problem, I recently got a graphing calculator (t1-89) and according to instructions i can calculate the i (interest) on it but each problem before i attempt on a graphing calculator i attempt to solve myself manually without a graphing calculator as a safeguard to...

Homework Statement The question is located here http://i51.tinypic.com/nex2q1.jpg Homework Equations The value I have been given for a) is 5 The value I have been given for b) is 5PI/6 The Attempt at a Solution Note that e^(a + bi) = e^a e^(bi) = e^a (cos b + i sin b). (e^a is...

Homework Statement Water is pumped into a tank. Volume V, is kept constant by continuos flow. The amount of salt S, depends on the amount of water that ahs been pumped in, call it X. ds/dx = -S/V Find the amount of water needed to eliminate 50% of the salt. Take v AS 10,000 gallons...

exponential equation (simple??) x = Ae ^ kt initally (at t = 0) x = 0.2 and when t = 2 then x = 1.5 a) Find A and k b) Find x when t = 1.5 c) How long will it take x to decay to x = 0.01 Really struggling, any help would be greatly appreciated.

Homework Statement \lim_{x \to \infty} \left(e^x-x \right )^{1/x} Homework Equations The Attempt at a Solution Should I be equating this to f(x), taking the log of both sides, using L'Hopital's rule on the resulting indeterminate quotient? If I do that, then I end up with a perpetual...

I need to prove that ez1 x ez2 = e(z1 + z2) using the power series ez = (SUM FROM n=0 to infinity) zn/n! (For some reason the Sigma operator isn't working) In the proof I have been given, it reads (SUM from 0 to infinity) z1n/n! x (SUM from 0 to infinity)z2m/m! = (SUM n,m)...

Homework Statement Problem: find t in the following equationHomework Equations 64000e^{-1600t}+4000e^{-400t}=50000e^{-1000t} The Attempt at a Solution I know the answer: t=6.17\cdot\;10^{-4}s. But I'm struggling with how to get there. This is my attempt: Factorizing down to...