Give the Newton-Raphson iteration scheme for computing the pth power of a number.
Specialize this to computing the fourth root of 20. You can take the initial guess to be 2.
At each iteration, state the number of correct digits.

Answer the following questions about shipping lobsters. For each problem:
★ Include the equations or formulas you used.
★ Explain, in words or with mathematical steps, how you arrived at your answers. You do not have to submit sketches, but you may find that drawing parts of the problem on scr...

Question 6: 15 points
The biggest inventory problem at the Barko facility is the storage of boom sections for their various Knuckleboom models. There are two types of boom sections: short and long. The following table outlines the demand in the next 5 months and the projected purchase price for eac...

Problem 1
Suppose a manufacturing company makes a certain item. The time to produce each item is normally distributed around a mean of 157 minutes with a standard deviation of 46 minutes.
(a) What proportion of the items will take more than 2 hours to make?
(b) What proportion of the items will...

1. After a weekend at the Mohegan Sun Casino, Gary finds that he has won $1020—in $20 and $50 chips. If he has more $50 chips than $20 chips, how many chips of each denomination could he possibly have?
2. If there are 2187 functions f : A→B and |B| = 3, what is |A|?
3. Let A ⊆ {1, 2, ...

(1) Solve by separation of variables and solution to the ODE (see attached file for formula).
(2) Solve the equation (see attached file for formula).
(3) For the given graph, re-sketch a graph for x01 and indicate the system progress from x01 as t --> infinity. Identify any critical points as st...

See the attached file.
Harvesting:
x = a1*x - a2*x^2 - h a1 > 0, a2 > 0, h>0
1. |x| = tons and |x| = tons/years
What are the dimensions of a1, a2, and h?
(see attached file for more details)
2. Use the quadratic formula to show that the phase diagrams (x vs. x)have no interce...

I am currently working on sets and how to identify/recognize variations based on symbols.
Is there any kind of "outline" or list/reference that I can utilize to better understand their core meaning?
A' =
B' =
element of...
subset of...

Problem: A number is divisible by 2 if the last digit is divisible by 2. A number is divisible by 4 if the last two digits form a number divisible by 4. A number is divisible by 8 if the last three digits for a number divisible by 8.
Objective:
Find a possible pattern. Use this pattern to des...

Use separation of variables to solve to the ODE:
N ̇=〖{k〗_+-k_- ln〖(N)}N〗;k_+,k_- and t>0;N(0)= N_0>0.
Hint: Use u = ln(N) for u-substitution.
Substitute your solution into the differential equation and show that it is in fact the solution.
Evaluate your solution for N(t)...

Please see attached Excel sheet. Also below is the link to the free book for reference. (I would start there!) The question is on Page #308.
http://www.xn--klker-kva.hu/wp-content/uploads/2013/03/Introduction-to-Business-Statistics-7th-Edition-2008.pdf
1. Item C in the description o...

Determine the order of each differential equation, and whether or not the given functions are solutions of that equation on some interval of x values.
(a) (y')^2 = 4y; Y1 = X^2, Y2 = 2X^2 , Y3 = e-x
(b) Y" +9y =0; Y1 = 4sin3X, Y2 = 6sin(3X+2)

Using Excel, prepare a frequency distribution from the data collected (see attached below).
Calculate the Standard Deviation of your data.
Is this a normal distribution?
Every day I leave my house 15 min before I need to be to work, what are the chances I will be late to work on any given ...

1. Find the solution to the two-dimensional wave equation
[see the attachment for the full equation]
2. Solve the two-dimensional wave equation for a quarter-circular membrane
[see the attachment for the full equation]
The boundary condition is such that u=0 on the entire boundary.
3. Consi...

Given the points x={xo, x1, x2,.... xn}^T and the function values f={fo, f1, f2, ....fn}^T at those points, we want to generate a 7th degree spline, i.e. a piecewise 7th degree polynomial approximation.
a) Why would we want to do this? Why not just use Newton's Interpolatory Divided Difference f...

Please solve the following problem using the step by step method:
Find the unique solution (and proof that it is unique) and the maximal interval of the initial value problem x' = x^3, x(0) = xo for any xo E R.

Please solve the following numerical analysis problem:
Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with
f(x) = [ -x1 ]
[ x1^2 + 2x2 ]
and show that the set S = { x E R^2l x2 = -x^2/4 } is invariant with res...

Show that for any constants c and d, |d| < 1, the equation x = c + d cos (x) = g(x) has a unique solution alpha. In addition, show that the iteration x_n+1 = c + d cos (x_n) will converge to alpha. Bound the rate of convergence.

An arrow of mass m is shot vertically upward with initial velocity 160 ft/sec. it experiences both the deceleration of gravity and a drag force of magnitude kv^2 due to air resistance, where v is the velocity and k is a coefficient of air resistance. Assuming a drag coefficient of k=1/800 lb m/ft, h...

The BSM equation for a derivative F on a stock paying no dividends is:
-See attachment
If you were to transform this PDE with the substitution S = Ke^x, where x is a variable and K a constant, what would be the resulting equation?

Suppose that y(x)' : f(x,y(x)) on the interval [x0, x1] with y (x0) = y0. Assume that a unique solution y exists such that it and all of its derivatives up to and including the third order are defined and continuous on [x0, x1]. Using Taylor's Theorem (and the Mean Value Theorem, if necessary) prove...

Use the Secant method (defined in the book) to show that sequence below converges to (square root Q), where Q > 0, given "good" starting values x_0 and x_1:
x_n+1 = (x_n x_n-1 + Q) / (x_n + x_n-1).
Come up with a similar recursion for calculating Q^(1/3) using the secant method.

1. Suppose that 0 < q < p and that alpha_n = alpha + O(n^-p). Show that alpha_n = alpha + O(n^-q).
2. Make a table listing h, h^2, h^3, and h^4 for h = 0.5, 0.1, 0.01, and 0.001, and discuss the varying rates of convergence of these powers of h as h approaches zero.
Please provide a brief text...

Hello. I am having some trouble with the following PDE:
Laplacian(u(x,y,z)) = u(x,y,z) * (-2*E/h^2)*(1 + (GM/(2(x^2+y^2+z^2)^(1/2))))^4
Where, G,M,E, and h are all constants.
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of th...

The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 5 years, how long will it take to triple? To quadruple?

(1) Show u belongs to C^1(U), and calculate ux, uy.
(2) Calculate uxx, uyy, uxy and show that uxx and uyy are continuous in the whole disk, but u does not belong to C^2. Calculate f := - delta u.
Please see the attached image for complete question.