There is a famous puzzle called the Towers of Hanoi that consists of three pegs

and n circular disks, all of different sizes. The disks start on the leftmost peg, with the largest disk

on the bottom, the second largest on top of it, and so on, up to the smallest disk on top. The goal

is to move the disks so that they are stacked in this same order on the rightmost peg. However,

you are allowed to move only one disk at a time, and you are never able to place a larger disk on

top of a smaller disk. Let t_n denote the fewest moves (a move being taking a disk from one peg

and placing it onto another) in which you can accomplish the goal. Determine an explicit formula

for t_n.

Find the volume of the solid bounded by the surface z =5 +(x-4) ^2+2y and the planes x = 3, y = 3 and coordinate planes.

a. First find the volume by actual calculation.

b. Estimate the volume by dividing the region into nine equal squares and evaluating the functional value at the mid-point of the respective squares and multiplying with the area and summing it. Find the error from step a.

c. Then estimate the volume by dividing each sub-square above into 4 sub-squares and follow the process/steps in (b) above. Find the error from step a.

d. Keep repeating step b to a reasonable number to minimize the errors from step a.

Find the real Fourier series of the piece-wise continuous periodic function

f(x) = x+sin(x) -pi<=x<pi

use Runge Kutta 4th order method

y'=y-1.3333*exp(0.6x)

a) h=2.5 and compare the value to the exact value

b) h=1.25 and compare the value to the exact value

Thks!

Epsilon Airlines services predominately the eastern and southeastern United States. The vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon’s management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

Minimum Number of

DayEmployees Needed

Monday55

Tuesday80

Wednesday50

Thursday75

Friday45

Saturday60

Sunday50

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. Find the optimal solution and determine the total number of call-center employees under the optimal solution. Use Excel Solver.

Let Xi = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday…)

MinX1+X2+X3+X4+X5+X6+X7

s.t.

X1+X4+X5+X6+X7

X1+X2+X5+X6+X7

X1+X2+X3+X6+X7

X1+X2+X3+X4+X7

X1+X2+X3+X4+X5

X2+X3+X4+X5+X6

X3+X4+X5+X6+X7

X1, X2, X3, X4, X5, X6, X7 ≥ 0

Total Number of Employees Unde

given the expiremental data below, determine the equation that models the data. first plot the data on both a log-log graph and a semi-log graph. next, use these plots to determine the type of equation that best fits the data. finally determine the equation. x-values= 10,20,50,120,180,200 y values=4600,3200,1130,98,98,12,6

^{Define the following :}

^{- Homogenous ODE}

^{- Homogenous function}

^{- Linear ODE}

I am down to one last attempt. Please make sure both are correct.

1) Solve the given system of differential equations by systematic elimination.

(x(t),y(t))=?

2) Solve the given system of differential equations by systematic elimination.

(x(t),y(t))=?

Please make sure you solve both correctly.

1) Solve the given system of differential equations by systematic elimination.

((x(t),y(t))= ?

2)

Solve the given initial-value problem.

= y − 1

= −7x + 2y

x(0) = 0, y(0) = 0

x(t) = ?

y(t)= ?

PLEASE ANSWER ALL 3 WILL THUMBS UP

1) A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 8 m/s. Find the equation of motion.

x(t)=? m

2) Find the charge on the capacitor and the current in an LC-series circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin(γt) V, q(0) = 0 C, and i(0) = 0 A

q(t)= ?

i(t)= ?

3) Find the steady state current i_p(t) in an LRC-series circuit when L = 1/2 h, R= 20 ohms, C= 0.001 f and E(t) = 400sin(60t)+500cos(40t) V

i_p(t)= ?

For the following Cauchy-Euler equation, find two solutions of the homogeneous equation and then use variation of parameters to find xp. Before solving for xp you need to divide the equation by t2 to have the correct forcing function f(t).

t2x'' − 2tx' + 2x = 8t

xp =__________________

How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have more outcomes? Why? Provide an example in your explanation.

(please provide detailed answer with no less than 100 characters)