A rubber ball is dropped from a height of 30 feet, and on each bounce it rebounds up 22% of its previous height. How far has the ball traveled vertically at the moment when it hits the ground for the 23rd time? Round your answer to two decimal places.

"Brief Discuss Homogeneous Differential Equations." This is the presentation topic of my Subject Differential Equation.
Explain in a simple way

The determinant of a matrix is the product of its eigenvalues. Can you prove this when A is diagonalizable? How about if A is 2 x 2, and may or may not be diagonalizable? (Hint: What's the constant term in the characteristic polynomial>

I need the answers simple and in order please!!! go with the letter a,b,c etc.

Ahmadi, Inc. manufactures laptop and desktop computers. In the upcoming production period, Ahmadi needs to decide how many of each type of computers should be produced to maximize profit. Each computer goes through two production processes. Process I, involves assembling the circuit boards and process II is the installation of the circuit boards into the casing. Each laptop requires 24 minutes of process I time and 16 minutes of process II time. Each desktop requires 8 minutes of process I time and 32 minutes of process II time. In the upcoming production period, 240 minutes are available in process I and 320 minutes in process II. Each laptop costs $1,800 to produce and sells for $2,250. Each desktop costs $600 to produce and sells for $1,000.

      Let your decision variables be:

                  X1 = Number of laptops to produce

                  X2 = Number of desktops to produce

1. Formulate an LP problem to maximize profit. Write your problem formulation.
2. Graph the constraints and show the region of feasible solutions.
3. Determine the extreme points of the feasible region and find the profit at each extreme point.
4. Draw the isoprofit line and indicate the optimum point.
5. Are there any slacks at optimum?
6. If the selling price per desktop decreases to $700 per unit would there be any change in the optimum solution? If yes, what would be the new optimum solution, and would there be any slack?
7. Assume the company does not want to produce more than 9 laptops in this production period. Add this constraint to the original problem and show the region of feasible solutions.
8. Solve the problem as stated in part g and find the optimal solution. Let the profit per Laptop to be $450 and per Desktop to be $100.
1. Let the selling price of Desktops to be $750 and solve the problem as stated in part g.

Estimate the lowest eigenvalue pair of matrix A using the Inverse Power Method

A = 2  8 10
8 4 5
10 5 7

starting with initial guess x0 = [1 1 1]T and εaλ ≤ 1%

Given the differential equation

y''+y'+2y=0,  y(0)=−1,  y'(0)=2y′′+y′+2y=0,  y(0)=-1,  y′(0)=2

Apply the Laplace Transform and solve for Y(s)=L{y}Y(s)=L{y}. You do not need to actually find the solution to the differential equation.

6) Consider the differential equation y^JJ + by^J + 16y = 0 For which value(s) of b does the solution

I. decay rapidly to 0 as t → ∞

II. oscillate regardless of t value

III. decay while oscillating

a. For b = 10 and y(0) = 0, y^J(0) = 6, solve the initial value problem.

Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a) Solve it analytically. (b) Solve it using Euler’s method using step size h = 0.1 and find an approximation to true solution at x = 0.3. (c) What is the error in the Euler’s method at x = 0.3

Manny was arrested as the main suspect in a murder investigation. Manny was brought into an interrogation room, but was not read his Miranda rights. A police officer asked Manny, “Where were you on the night of May 2?” Manny proceeded to confess to the murder, detailing the time and location of the murder and the use of a knife as a murder weapon.

The officer immediately left the room, and he then realized that he accidentally forgot to read Manny his Miranda rights. He reported his mistake to the chief, who decided to place Manny in a holding cell.

Two hours later, Manny was brought back into the interrogation room where he was questioned by a different officer. Prior to questioning, this officer properly read Manny his Miranda rights.

Manny stated that he understood his rights and repeated his confession about the time and location of the murder but did not mention the knife.

Police then went to the location and found the victim and the weapon (a knife) used in the murder next to the body. The knife was later found to have Manny's blood and fingerprints.

At his trial, Manny admitted that both of his statements were voluntarily made, but argued that they should each be suppressed, along with the murder weapon (knife) since all were the "fruit" of a Miranda violation.

Which, if any, pieces of evidence should be suppressed?

Creatine and protein are common supplements in most bodybuilding products.  Bodyworks, a nutrition health store, makes a powder supplement that combines creatine and protein from two ingredients (X1 and X2). Ingredient X1 provides 20 grams of protein and 5 grams of creatine per pound.  Ingredient X2 provides 15 grams of protein and 3 grams of creatine per pound.  Ingredients X1 and X2 cost Bodyworks $5 and $7 per pound, respectively.  Bodyworks wants its supplement to contain at least 30 grams of protein and 10 grams of creatine per pound and be produced at the least cost.

Determine what combination will maximize profits.

Use Excel Solve to determine the solution:

Amazon regularly couriers rectangular packages overseas. The girth of a rectangular package is defined to be the perimeter of a cross section perpendicular to the length.You prefer to use Speedy Couriers for your international deliveries, but they will only carry rectangular packages where the sum of length and girth is at most 150 cm. Find the dimensions of the package with the largest volume that they will carry. Assume that the critical point gives a maximum

Solve the differential equation by variation of parameters, subject to the initial conditions

y(0) = 1, y'(0) = 0.

2y'' + y' − y = x + 7

Consider the initial value problem X′=AX, X(0)=[−4,-2], with A=[−6,0,1,−6] and X=[x(t)y(t)] (a) Find the eigenvalue λ, an eigenvector V1, and a generalized eigenvector V2 for the coefficient matrix of this linear system. λ= , V1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ , V2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ $ (b) Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. X(t)=c1 ⎡⎣⎢⎢ ⎤⎦⎥⎥ + c2 ⎡⎣⎢⎢ ⎤⎦⎥⎥ (c) Solve the original initial value problem. x(t)= y(t)=