If a set K that is a subset of the real numbers is closed and bounded, then it is compact.

Show that (0, 1) and (−1, 1) have the same cardinality.

Let set E be defined as E={?∙?? +? | [?]∈R2}, where ?? is the natural exponential?

function, please show E is a vector space by checking all the 10 axioms. (Notice: you may use the properties of vector addition and scalar multiplication in R2)

If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 9 lb/in is suddenly set in motion at t=0 by an external force of 99cos(20t) lb, determine the position of the mass at any time. Assume that g=32 ft/s2. Solve for u in feet.

Suppose I is an interval in R. Prove from the definition of outer Lebesgue measure that m^∗ (I) = I.

Bonus Problem:

Find the number of spanning trees in K_m,n.

Note: I need how to get the right formula-not just oh this is the formula you need.

Cucina Corp. signed a new installment note on January 1, 2018, and deposited the proceeds of $51,000 in its bank account. The note has a 3-year term, compounds 6 percent interest annually, and requires an annual installment payment on December 31. Cucina Corp. has a December 31 year-end and adjusts its accounts only at year-end

1. Use an online application, such as the loan calculator with annual payments at mycalculators.com, to generate an amortization schedule. Enter that information into an amortization schedule with the following headings: Year, Beginning Notes Payable, Interest Expense, Repaid Principal on Notes Payable, and Ending Notes Payable.
2. Prepare the journal entries on (a) January 1, 2018, and December 31 of (b) 2018, (c) 2019, and (d) 2020.
3. If Cucina Corp.’s year-end were March 31, rather than December 31, prepare the adjusting journal entry would it make for this note on March 31, 2018?

(1) In each part, decide whether or not the described relation is an equivalence relation.

Explain your answers.

(a)

A

is the set of all residents of the United States. The relation

∼

on

A

given by:

x

∼

y

if

x, y

are in the same state at noon on November 3rd.

(b)

U

is the set of all undergraduates at the University of Oregon. The relation

∼

on

U

given by:

x

∼

y

if

x, y

are in a class together.

(c)

P

is the set of all people on Earth. The relation

∼

on

P

given by:

x

∼

y

if

x

and

y

have birthdays on the same day.

(d)

P

is the set of all people on Earth. The relation

∼

on

P

given by:

x

∼

y

if

x

and

y

have birthdays on the same day of June.

1) What permutation group is pentagon D5 a subgroup of ?why?

2) What is a generating set of pentagon D5? Why? Is it a minimal generating set?Why or why not?

3) What is not a generating set of pentagon D5? Why?

Write a procedure that implements the Fermat factorization method done in Mathematica.

write a procedure that implements the Pollard rho factorization method in Mathematica.

May I know the how to solve this question?

Consider the two functions f(x) = ?|x| − 1 and g(x) = 1/(x2 − 1) defined on the maximal set of real numbers x for which each formula is defined.

1. (a) Identify the domains and ranges for both f and g, giving analytical reasons for your answers. (Drawing the graph alone is not sufficient).

2. (b) Determine an expression (in terms of x) for the composite function (g ◦ f ) and identify its domain and range, justifying your answer. Simplify the expression for (g ◦ f) as much as possible for values of x within that domain.

Let V be a vector space of dimension 1 over a field k and choose a fixed nonzero element voe V, which is therefore a basis. Let W be any vector space over k and let woe W be an arbitrary vector. Show that there is a unique linear transformation T: V → W such that T(v)= wo. [Hint: What must T(Avo) be?)

Explain the process of using Laplace transforms for solving a difference equation with an initial condition. You may illustrate with an example, but you don’t have to solve the whole thing out.