Consider the lattice of real numbers in the interval [0,1] with the relation ≤. Does this lattice have any atoms?

Karon went to the post office and spent $31.57 on 84 stamps. She bought 27¢ stamps for all the postcards, 42¢ stamps for each letter addressed to friends in the U.S., and 94¢ stamps for each letter to England. Karon bought 7 times as many postcard stamps as those for the letters to England. How many postcard stamps did Karon buy? (Hint: Use matrices.)

You need to complete the following SWOT analysis:

Creative Computing sells a tablet computer called the Protab. The $780 sales price of a Protab Package includes the following:

• One Protab computer.
• A 6-month limited warranty. This warranty guarantees that Creative will cover any costs that arise due to repairs or replacements associated with defective products for up to six months.
• A coupon to purchase a Creative Probook e-book reader for $420, a price that represents a 30% discount from the regular Probook price of $600. It is expected that 20% of the discount coupons will be utilized.
• A coupon to purchase a one-year extended warranty for $45. Customers can buy the extended warranty for $70 at other times if they do not use the $45 coupon. Creative estimates that 35% of customers will purchase an extended warranty.
• Creative does not sell the Protab without the limited warranty, option to purchase a Probook, and the option to purchase an extended warranty, but estimates that if it did so, a Protab alone would sell for $760.

Required:
1. & 2. Indicate below whether each item is a separate performance obligation and allocate the transaction price of 100,000 Protab Packages to the separate performance obligations in the contract.
3. Prepare a journal entry to record sales of 100,000 Protab Packages (ignore any sales of extended warranties).

Complete this question by entering your answers in the tabs below.

• Req 1 and 2
• Req 3

Indicate below whether each item is a separate performance obligation and allocate the transaction price of 100,000 Protab Packages to the separate performance obligations in the contract.

• Req 1 and 2
• Req 3

y₁(t) = (1+t)² is a solution to y'' + p(t)y' + q(t)y = 0. Find a second solution that is linearly indepentent of y₁(t).

Prove

1. For each u ∈ R n there is a v ∈ R n such that u + v= 0

2. For all u, v ∈ R n and a ∈ R, a(u + v) = au + av

3. For all u ∈ R n and a, b ∈ R, (a + b)u = au + bu

4.  For all u ∈ R n , 1u=u

[Note that, in this example, the mesh sizes in x and y are identical (h); strictly speaking, this need not be true. In some applications, we may need more resolution along the x- or y-axis; we could then use separate mesh sizes h_x and h_y.]

By definition, the partial derivative of a function f ( x , y ) with respect to x is

∂ f ∂ x = L i m h ⟶ 0 f ( x i + h , y j ) − f ( x i , y j ) h

and the partial derivative with respect to y is

∂ f /∂ y = L i m h ⟶ 0 f ( x i , y j + h ) − f ( x i , y j )/ h

If we applied these formulas to our grid values, we would get the finite difference expressions

∂ f /d x ( x i , y j ) ≅ f ( x i + 1 , y j ) − f ( x i , y j )/ h

Note: To avoid round-off error, retain at least six decimal places in all of your calculations.

• Assume the function f is defined as f(x, y) = 3 tan x cos y
• Use differentiation rules to find the exact partial derivatives ∂ f /∂ x and ∂ f /∂ y , and evaluate those exact partial derivatives at (1.56, -2.1).  
• Use the finite difference formulas to estimate ∂ f /∂ x and ∂ f/ ∂ y at (1.56, -2.1) for three different values of the mesh size
  • h = 0.01
  • h = 0.001
  • h = 0.0001

• Use your calculated values to fill in this table:

Answer the following questions:

• For which partial derivative is the finite difference approximation more accurate?
• Why is the finite difference approximation for the other partial derivative less accurate?  Under what real-world conditions might we see such poor approximations?

1. Prove that there exist infinitely many positive real numbers r such that the equation 2^x + 3^y + 5^z = r has no solution (x,y,z) ∈ Q × Q × Q.

(Hint: Is the set S = {2^x + 3^y + 5^z : (x,y,z) ∈ Q × Q × Q} countable?)

Show that the number of solution to x² - y² ≡ a (p) is p-1 if p not divides a and 2p -1 if p divides a, Use u = x+y and v= x-y

Then show that summation y=0 to p-1 ((y^2 +a)/p) = -1 if p not divides a and

= p-1 if p divides a

Step (D) of the divide-and-conquer strategy (i.e. combine the solutions to smaller instances of the problem to obtain the solution of the original instance) is not a necessary step for this design strategy. Mergesort is an example of such cases.

Select one:

True

False

Example 10.5: Verify the divergence theorem for the vector field F = 2xzi + yzj +z2k and V is the volume enclosed by the upper hemisphere x2 + y2 + z2 = a2, z ≥ 0

Compute the quartic interpolating polynomial for the Hermite interpolation problem

p(0) = 2, p'(0) = -9

p(1) = -4, p'(1) = 4

p(2) = 44

with respect to the Newton basis. Compute the divided differences. Find a quintic interpolating polynomial that additionally satisfies p(3) = 2.

We have already derived the integral formulae for the mass m, the moment My about the y-axis, and the moment Mx about the x-axis, of the region R where a lamina with density ρ(x) resides in the xy-plane. The method we used was to:

-Slice R into n rectangles, where y = f(x) bounded R above and y = g(x) bounded R below, on [a, b].

-Compute the area, mass, and moments (about both the y-axis and the x-axis), of the i th rectangle Ri .

-Take the Riemann sum limit to derive the integral formulae for m, My, and Mx.

There are analogous integral formulae for m, My, and Mx, of R in terms of y (in class we did it in terms of x). Indeed now assume the region R is bounded to the right by x = f(y) and to the left by x = g(y) on [c, d] with density ρ(y).

Adapt the method we did in class to derive the formulae for m, My, and Mx, as y-integrals.

You must label or define relevant variables and quantities, and at the end take the Riemann sum limit.

Note: Only by replacing x with y in the x-integral formulae does not yield the correct y-integral formulae.

please please focus on "note" and it is also for "y integral"

I posted the question earlier but the answer was not the professor is looking for

An individual possesses 5 umbrellas which he employs in going from his home to the office, and vice versa. If he is at home at the beginning of a day and it is raining, then he will take an umbrella with him to the office provided there is one to be taken. Similarly, if he is at the office and at the end of a day it is raining, he will take one to go home (provided there is one to be taken at the office). If it is not raining, then he never takes an umbrella. Assume that, independent of the past, it rains at the beginning or at the end of a day with probability 0.35.

(a)Define a Markov chain for this system by the construction of the one-step transition matrix (Hint: Define the states of the chain as the number of umbrellas the individual has in the place he is at (home or office). Assume that there is a transition each time he changes places (from home to the office or vice versa)

(b)Find the steady state probabilities, by the formulation of the steady state equations.

(c) What fraction of time does the man get wet? Justify your answer.