Prove that if U, V and W are vector spaces such that U and V are isomorphic and V and W are isomorphic, then U and W are isomorphic.

Solve the given system of differential equations by systematic elimination.

consider the following equation,

max r = 4x + y + 6z

2x + y + 2z <= 10

x + 2y + z <= 9

x + 2z <= 6

x, y, z >= 0

The tableau corresponds with a step of the SIMPLEX method applied to the previous problem

what is the value of x, y, z and the objective function. Identify the entering and the leaving variables. Justify your response with the calculations performed (you can extend the previous tableau to perform the required calculations)

The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $135. The quantity demanded each month is 1000 when the unit price is $105. The suppliers will market 700 espresso makers when the unit price is $66. At a unit price of $96, they are willing to market 2200 units. Both the supply and demand equations are known to be linear.

(a) Find the demand equation.
p =  

(b) Find the supply equation.  
p =  

(c) Find the equilibrium quantity and the equilibrium price.

Using Java (Swing) language(please hard code)... Create a program that has a textfield for the user to type in a set of input. Below that textfield have the following controls to show string manipulations:

(1) A button that will change the entire textfield’s current text to uppercase.

(2) A button with its own textfield for a search value, that will tell the position the search value appears in the textfield above.

(3) A button that reports the current number of characters in the textfield above.

Problem 7 | Discrete logarithms with respect to different primitive roots

Prove that the difficulty of the discrete logarithm problem is independent of the primitive root.
Specifically, for any prime p, assuming that it is computationally feasible to extract discrete
logarithms with respect to one primitive root of p, show how one can feasibly extract discrete
logarithms with respect to any other primitive root of p.

1. Use the Fixed-Point Iteration Method to find the root of f ( x ) = x e^x/2 + 1.2 x - 5 in the interval [1,2].

Consider C . Prove that: with multiplication, we yield magma; and with multiplication C − {0} is a loop

Find All the following Laplace Transformations once using the definition of Laplace Transformation and then using the memorized Laplace Table relationships:

• L[sin⁡(ω*t)]
• L[(e^-5t)cos⁡(6t)]
• L[(e^-5t)(t²)]

use the annihilator method to show y"+3y'-4y=8x+5e^x, y(0)=1, y'(0)=2

Use MATLAB to create a script which solves for problem 5.9 in the book (5.11 in the 4th edition). Given are the equations for the moment, as a function of x, starting from the leftmost side of the beam with x=0 and ending at the other end of the beam with x=12. This piecewise function together makes up the moment equation for the beam given. 0 ≤ ? ≤ 3 ?(?) = 265? − 5.56?³ , 3 < ? ≤ 6 ?(?) = −50?² + 415? − 150, 6 < ? ≤ 10 ?(?) = −185? + 1650, 10 < ? ≤ 12 ?(?) = 100? − 1200 Use if-else statements to determine the f(x) value for each value of x (lower bound, upper bound, and the guess for the root) to use in the bisection method. Also, use a while loop to iterate until the approximate relative error is below the stopping criterion, es=0.05%. Finally, plot piecewise function and verify that the root found is at or near the point on the beam in which the moment is zero. Create appropriate labels (xaxis, y-axis, and title). Here's what should happen when the script is run:

>> Lab3Roots

>> xr =

8.918907165527344

PLEASE SHOW HOW TO TYPE THE SCRIPT! THANKS!

if order of a= order of b in a finite Abelian group , is order of ab= order of a?

find the centroid occupies y=x^2 and y=x+3 mass differs on x direction with d(x) =2(x+1) but constant on y line

compare and contrast the ANOVA with the t-test, how are similar? how are they different

Discrete Mathematics

Any degree at a university requires 4 core classes chosen from 4 groups. There are 5 English classes, 3 science classes, 6 math classes, and 4 social studies classes. Students must take exactly one of each class from each group. How many different ways are there for a student to fulfill these requirements?