Let sequence an be a bounded sequence and let E be the set of subsequential limits of an. prove that E is bounded and contains both sup E and inf E

Computational Geometry:

Let E be an unsorted set of n segments that are the edges of a convex polygon. Describe an O(nlogn) algorithm that computes from E a list containing all vertices of the polygon, sorted in clockwise order.

Don't copy other peoples wrong answer or you get down-voted.

Let ?V be the set of vectors in ?2R2 with the following definition of addition and scalar multiplication:
Addition: [?1?2]⊕[?1?2]=[0?2+?2][x1x2]⊕[y1y2]=[0x2+y2]
Scalar Multiplication: ?⊙[?1?2]=[0??2]α⊙[x1x2]=[0αx2]
Determine which of the Vector Space Axioms are satisfied.

A1. ?⊕?=?⊕?x⊕y=y⊕x for any ?x and ?y in ?V
? YES NO

A2. (?⊕?)⊕?=?⊕(?⊕?)(x⊕y)⊕z=x⊕(y⊕z) for any ?,?x,y and ?z in ?V
? YES NO

A3. There exists an element 00 in ?V such that ?⊕0=?x⊕0=x for each ?∈?x∈V
? YES NO

A4. For each ?∈?x∈V, there exists an element  −?−x in ?V such that ?⊕(−?)=0x⊕(−x)=0
? YES NO

A5.  ?⊙(?⊕?)=(?⊙?)⊕(?⊙?)α⊙(x⊕y)=(α⊙x)⊕(α⊙y) for each scalar ?α and any ?x and ?y ?V
? YES NO

A6. (?+?)⊙?=(?⊙?)⊕(?⊙?)(α+β)⊙x=(α⊙x)⊕(β⊙x) for any scalars ?α and  ?β and any ?∈?x∈V
? YES NO

A7. (??)⊙?=?⊙(?⊙?)(αβ)⊙x=α⊙(β⊙x) for any scalars ?α and  ?β and any ?∈?x∈V
? YES NO

A8. 1⊙?=?1⊙x=x for all ?∈?x∈V
? YES NO

Please someone assist me with the following problem please!

5. K-nearest-neighbor

Given the training data set shown below

Predict the label for a sample, [2, 2] by using

1) 1-nearest neighbor. Show steps.

2) 3-nearest neighbor. Show steps.

6. K-means

Given six data points,

X1: (1, 1)

X2: (5, 5)

X3: (1, 2)

X4: (4, 4)

X5: (2, 2)

X6: (4, 5)

1) Plot all the points on a two-dimensional plane.

2) Supposing initial centroids are (5, 3) and (2, 4), group six points into two clusters by using L1 norm distance measure. Show steps.

Solve the linear programming problem by the method of corners.

Consider the parabolas y=x^2 and y=a(x-b)^2+c, where a,b,c are all real numbers

(a) Derive an equation for a line tangent to both of these parabolas (show all steps with a proof, assuming that such a line exists)

(b) Assume that the doubly-tangent line has an equation y+Ax+B. Find an example of values of a,b,c (other than the ones given here) such that A,B ∈ Z

Based on Euler's identity, show the linear superposition of the eigenfunctions

A series circuit has a capacitor of 1.6×10−6 F and an inductor of 2.5 H. If the initial charge on the capacitor is 0.11×10−6C and there is no initial current, find the charge Q on the capacitor at any time t.

Enter an exact answer. Do not use thousands separator in the answer field.

Enclose arguments of functions in parentheses. For example, sin(2x).

Q(t) = ?

Find the appropriate series solutions about the origin.

for 2x(x+2)y''+y'-xy

Write the first three non-zero terms of the Taylor series of sin x near x0 = 3π/2. Sketch a plot of the curves for sin x and your approximation.

If n>=2, prove the number of prime factors of n is less than 2ln n.

Eight students (Anna, Brian, Carol, ...) are to be seated around a circular table with eight seats, and two seatings are considered the same arrangement if each student has the same student to their right in both seatings.(a) How many arrangements of the eight students are there?(b) How many arrangements of the eight students are there with Anna sitting next to Brian?(c) How many arrangements of the eight students are there with Brian sitting next to both Anna and Carol?(d) How many arrangements of the eight students are there with Brian sitting next to either Anna or Carol?

please explain how u got the numerical answer for each part, like what you multiplied to get it

The diploma ceremony process was as follows. Students lined up to be hooded. Professors Venkataraman and Rodriguez performed the actual hooding ceremony. Together, they could hood 12 students per minute, on average. After hooding, students waited at the top of the steps to the stage until a Faculty Marshal called their name. This past year, Professor Allayannis read the names of the Global MBA for Executives (GEMBA) students, Professor Wilcox read the names of the MBA for Executives (EMBA) students, and Professors Frank and Parmar read the names of the residential MBA students. There were 29 GEMBA students, 65 EMBA students, and 315 residential MBA students. Once their name was called, students walked across the stage to Dean Bruner, who handed out their diploma. Then they continued on across the rest of the stage and returned to their seat. The administration had set a target of finishing the diploma ceremony in 60 minutes. The Marshals called names at the rate of one every 7 seconds. It took students an average of 8.2 seconds to walk across the stage, shake the Dean’s hand, and receive their diploma. After the handshake, it took students an additional 2 seconds to depart from the stage. There were approximately five students on the stage at any given time (one being hooded, two waiting for their names to be called, one in the process of receiving the diploma and congratulatory handshake, and one finishing the walk across the stage.)

1. What is the takt time for the diploma ceremony? Answer in seconds.

2. What is the cycle time for the process? Answer in seconds.

3. What is the throughput time for a student from the time he/she begins the hooding process until he/she walks off the stage? Answer in seconds.

4. What is the throughput rate? Answer in students per hour.

5. Could the goal of a 60-minute diploma ceremony be met? Yes or no?why.

Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,

A)Find the Laplace transform of the solution Y(s).Y(s). Write the solution as a single fraction in s.

Y(s)= ______________

B) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form (c/(s-p)), where c is a constant and the root p is a constant. Both c and p may be complex.

Y(s)= ____ + ______ +______

C) Find the inverse transform of Y(s). The solution must consist of all real terms.

L−1{Y(s)} = _______________________

Define the greatest lower bound for a set A ⊂ R. Let A and B be two non-empty subsets of R which are bounded below. Show glb(A ∪ B) = min{glb(A), glb(B)}.