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?

Show that the two definitions of continuity in section 2.1 are equivalent. Consider separately

the cases where z0 is an accumulation point of G and where z0 is an isolated point of G.

2.1 :

Definition1. Suppose f : G → C. If z0 ∈ G and either z0 is an isolated point of G or lim f(z) = f(z0) (z→z0)
then f is continuous at z0. More generally, f is continuous on E ⊆ G if f is continuous at every z ∈ E.

Definition 2.

Suppose f : G → C and z0 ∈ G. Then f is continuous at z0 if, for every positive real

number ε there is a positive real number δ so that
|f(z)−f(z0)|<ε for all z∈G satisfying |z−z0|<δ.

Thanks.

a) Find the approximations T₁₀, M₁₀, and S₁₀ for

from pi to 0 , 38sin(x)dx

T10	=
M10	=
S10	=

(Round your answers to six decimal places.)

Find the corresponding errors E_T, E_M, and E_S. (Round your answers to six decimal places.)

ET	=
EM	=
ES	=

(b) Compare the actual errors in part (a) with the error estimates given by the Theorem about Error Bounds for Trapezoidal and Midpoint Rules and the Theorem about Error Bound for Simpson's Rule. (Round your answers to six decimal places.)

|ET|	≤
|EM|	≤
|ES|	≤

(c) How large do we have to choose n so that the approximations T_n, M_n, and S_n to the integral in part (a) are accurate to within 0.00001?

n	=		for Tn
n	=		for Mn
n	=		for Sn

The monthly cost of owning a car depends on the number of kilometers it is driver. Taylor found that in May it cost her $500 to drive 800 km and it June it cost her $650 to drive 1400 km.

1. Express the monthly Cost C as a function of the distance driven d, assuming that a linear function is a suitable model.
2. Use this function to predict the cost of driving 2000 km per month.
3. Find the derivative of the function with appropriate units. What does the derivative of the function represent?
4. Does it cost more to drive the car in December than it does in August? Explain.

Consider the the differential equation

2xy''+ 5y'+xy= 0

1) determine the indicial equation and its roots

2) For each root of the indicial equation, determine the recurrence relation

3) Do the indicial roots differ by an integer? If yes, find the general solution on (0,∞). If not, find the series solution corresponding to the larger root on (0,∞)

Suppose that A equals 10. What are the values for (d1+) and (d1-) in the following constraint? A + (d1-) - (d1+) = 7

Group of answer choices

(d1-) =0, (d1+) =3

(d1-) =3, (d1+) =0

(d1-) =7, (d1+) =0

(d1-) =0, (d1+) =7

(d1-) =10, (d1+) =3

2.

The optimal solution is to select only two of the alternatives. Suppose you wished to add a constraint that stipulated that alternative 2 could only be selected if alternative 1 is also selected (i.e., if alternative 1 is not selected, you may not select alternative 2; however, you may select #1 and not select #2). How would this constraint be written?

Group of answer choices

A - B = 0

A - B <= 0

A -B >= 0

A + B = 2

none of the above

A goal programming problem had two goals (assume equal weights of 1). Goal number 1 was to achieve a cost of $2,400 and goal number 2 was to have no idle time for workers in the factory. The optimal solution to this problem resulted in a cost of $2,400 and no idle time. What was the value for the objective function for this goal programming problem?

Group of answer choices

2300

100

-100

0

none of the above

3.

In a basic transportation problem with 3 factories and 5 warehouses, there would be ___ decision variables.

Group of answer choices

3

5

8

15

None of the above

4.

In a basic transportation problem with 3 factories and 5 warehouses, there would be ___ constraints.

Group of answer choices

3

5

8

15

None of the above