Let G be a Group. The center of, denoted by Z(G), is defined to be the set of all elements of G that with every element of G. Symbolically, we have

Z(G) = {x in G | ax=xa for all a in G}.

(a) Prove that Z(G) is a subgroup of G.

(b) Prove that Z(G) is an Abelian group.

The cutting ratio in an orthogonal cutting model is given by To/Tc = sinϕ/Cos(ϕ-α)

What is:

ϕ = ?

α = ?

Several years ago Brant, Inc., sold $960,000 in bonds to the public. Annual cash interest of 9 percent ($86,400) was to be paid on this debt. The bonds were issued at a discount to yield 12 percent. At the beginning of 2016, Zack Corporation (a wholly owned subsidiary of Brant) purchased $160,000 of these bonds on the open market for $181,000, a price based on an effective interest rate of 7 percent. The bond liability had a carrying amount on that date of $930,000. Assume Brant uses the equity method to account internally for its investment in Zack.

1. a. & b. What consolidation entry would be required for these bonds on December 31, 2016 and December 31, 2018?

PLEASE SOLVE IN EXCEL.

Consider a cash flow profile in which $3000 is received at t=1, spent at t=2, and received at t=5, and $3000 is received at t=3. Suppose the interest rate is 3% the first 2 periods, 5% the next two periods and is 7% the 5th period. ( Note: t denotes end of period t.) Create a cashflow and present value table. Find the equivalents for the cash flow profile for the following items. a) Present worth b) Uniform series equivalent c) Geometric Series Equivalent (j = 1% for the entire period) • Show your calculation in detail and explain how the results are obtained.

Find the (a) amplitude, (b) period, (c) phase shift (if any), (d) vertical translation(if any), and (e) range of each function. then graph the function over at least one period.

1) y=-1/4 sin(3/4x+180degrees/8)

2)y=-3+3sin1/2x

3)y=2/3cos(x=180degrees/2)

x^2=ln(cy^2) Find the perpendicular orbits of the family of curves

Linear Optimization (Math 423) Problem, prove an analog of the follow theorem:

Thm 2.4: Consider the constraints Ax = b and x ≥ 0 and assume
that the m X n matrix A has linearly independent rows. A vector
x ∈ Rⁿ is a basic solution if and only if we have Ax = b, and there
exist indices B(1), ... , B(m) such that:
(a} The columns A_B(1),...,A_B(m) are linearly independent;
(b} If i ≠ B(1),...,B(m), then x_i = 0.

How can bias change results in a study? How can bias influence a person who wants to conduct a study? What key things can you look for when conducting a study to eliminate bias?

prove by epsilon-delta definition that f:R->R given by f(x)=x^3 is continuous at x=2

Let (Xn) be a monotone sequence. Suppose that (Xn) has a Cauchy subsequence. Prove that (Xn) converges.

Differential equations-Cengel 2.98
A spherical tank of radius R is initially filled with water. Now a hole of radius r is opened at the bottom of the tank and the water is let out. According to Torricelli's law, water comes out of the opening at a velocity v = (2gy) ^ 1/2, where y is the height of the water over the hole at a given moment, and g is the acceleration of gravity. Obtain a relation for the depth of the water with function of time t, and determine how long it takes to empty.
Explain your procedure

Give an example of a set A subset the real numbers for which both A and the complement of A are unbounded.

The phone company calculates a customer’s monthly cell phone bill as follows: monthly service charge: $35 voice charges:

First 100 minutes: $0.018 per minute

Second 100 minutes: $0.034 per minute

Additional minutes: $0.055 per minute

a. What is the charge for a month in which 158 minutes were used?

b. What is the charge for a month in which 311 minutes were used?

c. Construct a piecewise function that gives the monthly charge for x minutes of usage.