Let S = {x : x 3 < 1}.

(a) Find supS

(b) Is S bounded?

Thank you!

Convert from rectangular to polar form and vice versa:

a. ?6

b. 2√5∠135∘

c. −2 − ?2√3

d. √2∠45∘

Please show your steps because I need to understand how we reached the solution

Thank you

(a) Patty Stacey deposits $2200 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 6%, compounded annually. (Round your answer to the nearest cent.) (b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $2200 deposits at the end of each of the next 15 years. If the interest rate is 6%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.)

How many non-isomorphic 5-vertex connected planar graphs are there? Use Sage
to produce / depict them. Include your Sage code. A number alone will receive no
credit.

x' = -3x + 2y,

y' = -10x + 5y +2e^t/cos 2t

Solve the system by variation of parameters

Determine whether each set of vectors is linearly dependent or linearly independent.

a) (1,1,0,1), (1,0,1,1), (0,1,1,1)

b) (1,0,1,0), (0,1,0,1), (1,-1,1,-1), (1,-1,0,0)

Find the value of the digit indicated with a question mark . ISBN value 0-321-50230-?

CRT and solving linear congruences (No credit will be given for simply guessing and proving that your answer is correct): (a) Solve the system of linear congruences: x ≡ [1, 2, 3] (mod [3, 5, 7]). (b) If 3x ≡ 2 (mod 7) and 5x ≡ 3 (mod 13), find a solution for x modulo 91 if it exists. (c) Solve for x if 3x ≡ 15 (mod 18) and 4x ≡ 5 (mod 15), if it exists. (d) Solve for x if 3x ≡ 15 (mod 18) and 4x ≡ 6 (mod 15), if it exists.

Show that every sequence contains a monotone subsequence and explain how this furnished a new proof of the Bolzano-Weierstrass Theorem.

Consider the linear transformation T: R^4 to R^3 defined by T(x, y, z, w) = (x +2y +z, 2x +2y +3z +w, x +4y +2w)

a) Find the dimension and basis for Im T (the image of T)

b) Find the dimension and basis for Ker ( the Kernel of T)

c) Does the vector v= (2,3,5) belong to Im T? Justify the answer.

d) Does the vector v= (12,-3,-6,0) belong to Ker? Justify the answer.

Use the simplex method to solve the following linear programming problems. Clearly indicate all the steps, the entering and departing rows and columns and rows, the pivot and the row operations used. An investor has up to N$450,000 to invest in three types of investments. Type A pays 6% annually and has a risk factor of 0. Type B pays 10% annually and has a risk factor of 0.06. Type C pays 12% annually and has a risk factor of 0.08. To have a well-balanced portfolio, the investor imposes the following conditions. The average risk factor should be no greater than 0.05. Moreover, at least one-half of the total portfolio is to be allocated to Type A investments and at least one-fourth of the portfolio is to be allocated to Type B investments. How much should be allocated to each type of investment to obtain a maximum return?

solve using MATLAB.
Title: Numerical differentiations.

Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/4 using step sizes of h₁ = π/3 and h₂ = π/6. Employ centered differences of O(h²) for the initial estimates.

solve using MATLAB.

What are the eigenvalues and eigenvectors of a diagonal matrix? Justify your answer (explain)

These questions follow the exercises in Chapter 4 of the book, Scientic Computing: An Introduction, by Michael Heath. They study some of the properties of eigenvalues, eigenvectors, and some ways to compute them.

x^2*y''+x*y'+(x^2-1)y=0 what is the solution by using Frobenius method