x^2 y ′′ + xy′ + λy = 0 with y(1) = y(2) and y ′ (1) = y ′ (2)
Please find the eigenvalues and eigenfunctions and eigenfunction expansion of f(x) = 6.
In: Advanced Math
Suppose that the economy’s production function is Y = K1/2 (AN)1/2 , that the saving rate, s is equal to 16%, and that the rate of depreciation, ?, is equal to 10%. Suppose further that the number of workers grows at 2% per year and that the rate of technological progress is 4% per year.
Find the steady values of the variables listed in (i) through (v).
The capital stock per effective worker.
Output per effective worker.
The growth rate of output per effective worker.
The growth rate of output per worker.
The growth rate of output.
Suppose that the rate of technological progress doubles to 8% per year. Recompute your answers in part a. Explain.
Now suppose that the rate of technological progress is still equal to 4% per year, but the number of workers now grows at 6% per year. Recompute the answers to a. Are people better off in a or c? Explain.
In: Economics
1)calculate the polar moment of inertia of a wire with a 2 mm diameter
2) what is the difference between the elastic modulus (E) and the shear Modulus (G) ?
In: Mechanical Engineering
What is the Maclaurin's series for (-2x/(1+x^2)^2) and its radius of convergence.
In: Math
1.)is the function f (x) = x exp^ (-x ^ 2/2) a proper
function of the operator O= d2 / dx2-x2? if so, what is the
intrinsic value?
2.)is the function f (x) = exp^ (4ix) -exp ^(-4ix) its own function
of the operator d2 / dx2? if so, what is the intrinsic value?
3.)is the function f (x) = exp^ (2ix) -exp ^(-2ix) a proper
function of the operator d^2 / dx^2? if so, what is the intrinsic
value?
4.)is the function f (x) = exp ^ (x ^ 2/2) the eigenfunction of the
operator d ^ 2 / dx ^ 2 + x ^ 2? if so, what is the intrinsic
value?
In: Physics
Use the Newton’s method to find the root for ex+1 = 2 + x, over [−2, 2]. Can you find a way to numerically determine whether the convergence is roughly quadratic using error produced at each iteration? Include your answers as Matlab code comments
In: Advanced Math
Given a point P = (2, 1, 2) and using the homogenous representation:
Calculate the coordinates of the transformed point P* if P is rotated about the X, Y, and Z axes by angles 60°, 30°, and 60° respectively.
If the point P* obtained in part (a) is to be rotated back to its original position, find the corresponding rotation matrix. Verify your answer.
Calculate P* if P is translated by d = 2i – 3j + k and then scaled uniformly by s=3.0.
In: Mechanical Engineering
Consider the following reaction at 321 K: 2 A (aq) + 1 B (aq) → 2 C (aq) + 1 D (aq) An experiment was performed with the following intitial concentrations: [A]i = 1.33 M, [B]i = 2.05 M, [C]i = 0.25 M, [D]i = 0.29 M. The reaction was allowed to proceed until equilibrium was reached at which time it was determined that [A] = 0.51 M. What was the maximum amount of work that could have been performed as the reaction began? Maximum amount of work performed as the reaction began (in kJ)=
In: Chemistry
2. Determine the area of the region between x = −1, x = 2, f(x) = 3x2, and the x-axis.
(a) 27
(b) 2 (c) 9 (d) 48 (e) 16
In: Math
2. 1. The provider orders Oxytocin to be started at 2 MU/min at 0500. You are to increase the Oxytocin 2 MU/min every 30 minutes. There is 30 units of Oxytocin in 1000mL of LR.
In: Nursing