You are advising a co-worker on saving for retirement. The co-worker gives you two possible scenarios:

Scenario 1: Suppose you invest $170 a month for 6 years into an account earning 10% compounded monthly. After 6 years, you leave the money, without making additional deposits, in the account for another 22 years. How much will you have in the end?

Scenario 2: Suppose instead you didn't invest anything for the first 6 years, then deposited $170 a month for 22 years into an account earning 10% compounded monthly. How much will you have in the end?

Include the following in a report.

• What is the future value of each scenario?
• What is the total amount invested for each scenario?
• What is the total interest earned for each investment?
• How many more monthly deposits would you need to make for the first scenario to have the same future value as the second scenario?
• How many more monthly deposits would you need to make for the second scenario to have the same total interest as the first scenario?

Prove a (Dedekind) set is infinite iff there exists an injective function f : N→ A.

please help prove this clearly and i will rate the best answer thank you

Use Laplace transforms to solve the system.

x' - 5x - 4y = 0 x(0) = 1

y' + x - y = 0 y(0) = -1

Hello,

Kindly give a 500 words answer for the following title,

and please, use your own words without copy-paste from the internet

"Explain, fully, the principles of discretization"

Thanks in advance

Prove that if (6; a) = (6; b) = 1, then 24 | (a^2 - b^2).

In terms of menu navigation define Breadth and Depth

Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4

a)Construct the diagraph for this relation

b)show that R is an equivalence relation

Part B: Now consider the relation R on A defined by aRb iff a divides b (Divides relation)

c) Show that R is partial ordering

d) Contruct the hasse diagram for this relation

Can you explain in detail what Gaussian Elimination with pivoting is? and how is it different from Gaussian Elimination without pivoting?

I need the matlab codes for following question

(1) (a). Solve the following second-order differential equations by a pair of first-order equations, xyʹʹ − yʹ − 8x³y³ = 0; with initial conditions y = 0.5 and yʹ = −0.5 at x = 1.

(b). Solve the problem in part (a) above using MATLAB built-in functions ode23 and ode45, within the range of 1 to 4, and compare with the exact solution of y = 1/(1 + x²)

[Hint: ode23 à 0.0456, ode45 à 0.0588]

(c). How can we improve the accuracy for the solutions obtained in parts (a) and (b) above?

How can you have a basis through the spanning set theorem? I thought the spanning set has to be linear independent? Doesn't the spanning set theorem say that the vectors in the set are linear dependent as you can them as a linear combination of each other? Am I overthinking this or am I getting this wrong?

**UPDATED

I think I have the answer to my question, we use the theorem to basically turn the set into a linearly independent set by getting rid of the vectors we can write a combination of, correct?

Let x, y, z be a primitive Pythagorean triple with y even. Prove that x+y ≡ x−y ≡ ±1 mod 8.

a) The 10 members of the committee have to choose one president and two vice presidents (these have to be three different people). In how many ways can they choose these officers? (Note: here is no distinction between the two vice presidents; there is not a “first” VP and a “second” VP).

b) Three couples go to a movie theater. They sit in consecutive seats such that each couple is seating together, that is each person is seating next to his/her partner. If there are 6 seats available, in how many ways can they sit?

c) A university wants to assign a three digit number to each classroom of a new building. They can use the digits {1,2,3,4,5} but they cannot use any digit more than once. How many classroom numbers can they assign if the numbers have to be less than 250?

d) The University wants to select 4 students for a feedback survey. They want all four students from either Prof. X’s section or Prof. Y’s section. Prof. X has 40 students in his class and Prof. Y has 30 students in his class. How many selections are possible?

**MATLAB

8)The structure for students' quiz data for a class is organized as below

write a script to print the students' data by ascending order of ID number. The index vector method must be used and the MATLAB functions for sorting CANNOT be used.

9)In a physics measurement, the density of the water is measured at different depth. Here are the depth vector and density vector.

depth=[100,200,300,400,500]

density=[6.1,6.9,8.0,8.8,10.2]

USE polyfit to fit the data with 1,2, and 3 degree curves and use subplot to over plot your fitting curves on your original data.

Solve the wave equation, a2  ∂2u ∂x2 = ∂2u ∂t2 0 < x < L, t > 0 (see (1) in Section 12.4) subject to the given conditions. u(0, t) = 0, u(π, t) = 0, t > 0 u(x, 0) = 0.01 sin(9πx), ∂u ∂t t = 0 = 0, 0 < x < π u(x, t) = + ∞ n = 1