Suppose that a subset S of an ordered field F is not bounded above in F. Let T be a subset of F satisfying the property that, for each x ∈ S, there exists y ∈ T such that x ≤ y. Prove that T is not bounded above in F.
In: Advanced Math
A company must meet (on time) the following demands quarter 1|30 units; quarter 2|20 units; quarter 3|40 units. Each quarter, up to 27 units can be produced with regular-time labor, at a cost of $40 per unit. During each quarter, an unlimited number of units can be produced with overtime labor, at a cost of $60 per unit. Of all units produced, 25% are unsuitable and cannot be used to meet demand. Also, at the end of each quarter, 10% of all units on hand spoil and cannot be used to meet any future demands. After each quarter's demand is satisfied and spoilage is accounted for, a cost of $15 per unit is assessed against the quarter's ending inventory. Formulate an LP that can be used to minimize the total cost of meeting the next three quarters' demands. Assume that 20 usable units are available at the beginning of quarter 1. (Hint: Define inventory variables to keep track of the number of usable units.)
In: Advanced Math
Find Eigenvalues and eigenvectors
6 -2 2
2 5 0
-2 0 7
In: Advanced Math
The Swiss mathematician Leonard Euler pronounced, Oiler, who lived from 1707 to 1783. Do some research and write two paragraphs on something you found out about this mathematician. It could be about his mathematical career, his life, etc.
In: Advanced Math
A projective plane is a plane (S,L ) satisfying the following four axioms. P1. For any two distinct points P and Q there is one and only one line containing P and Q. P2. For any two distinct lines l and m there exists one and only one point P belonging to l∩m. P3. There exist three noncollinear points. P4. Every line contains at least three points.
Let π be a projective plane. Using P1 − P4, show that π contains two distinct lines l and m and a point P such that P does not lie on l or m.
In: Advanced Math
In how many ways you can triangulate a simple polygon with n vertices. Give both qualitative and quantitative answer.
In: Advanced Math
1. The differential equation y''+4y=f(t) and y'(0)=y(0)=0
a. Find the transfer function and impulse response.
b. If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplace techniques. u(t) is unit step function.
c. If f(t)= cos(t) ; find the y(t) by convolution and Laplace techniques.
2. The differential equation y''+3y'+2y=e^(-3t) and y'(0)=y(0)=0
a. Find the system transfer function and impulse response.
b. Find the y(t) by convolution and Laplace techniques.
3. y''+3y'+2y=f(t) and y'(0)=y(0)=0
Plot y(t) without any calculations and write down your reasons!
4. y''-4y'+3y=f(t) and y'(0)=y(0)=0
If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplace techniques. u(t) is unit step function.
Define:
a. f(t)'s system input, and y(t)'s system output. How to define Transfer function? Find the transfer function.
b. Find y(t) by Laplace Transformation Technique.
In: Advanced Math
Calculate the OC curve of the 2.5-sigma C-chart to control the number of defects per engine assembly at nine. Use c values of 3, 5, 7, 9, 10, 15, and 20.
In: Advanced Math
Use the Function Design Recipe (FDR) to design, code and test the definition of a new function named distance. This function returns the distance between two points, given by the coordinates (x1, y1) and (x2, y2). The function parameters are the x and y values.
Need help. Thank you
In: Advanced Math
Create a one page table to show the major similarities and differences between public and private sector. This should cover all areas not just finance e.g. HR, technology etc
In: Advanced Math
Let p be the prime number (2^20)*(3^7)5 + 1 = 11466178561. Solve for x such that 2^x ≡ 2376886429 (mod p) Explain your method carefully.
In: Advanced Math
4. (a) Use the Euclidean algorithm to find the greatest common divisor of 21 and 13, and the greatest common divisor of 34 and 21.
(b) It turns out that 21 and 13 is the smallest pair of numbers for which the Euclidean algorithm requires 6 steps (for every other pair a and b requiring 6 or more steps a > 21 and b > 13). Given this, what can you say about 34 and 21?
(c) Can you guess the smallest pair of numbers requiring 8 Euclidean algorithm steps?
(d) Is there a pattern here? Do the numbers which keep coming up have a name?
In: Advanced Math
Describe a real-world prediction problem using urban data for which accuracy is paramount and interpretability may be less important, and for which it might be preferable to use random forests rather than decision trees. Argue why this is the case.
In: Advanced Math
1.Is there evidence of multicollinearity? Perform Factor analysis by extracting four factors and name for those factors.
Problem needs to solved using R
| ID | ProdQual | Ecom | TechSup | CompRes | Advertising | ProdLine | SalesFImage | ComPricing | WartyClaim | OrdBilling | DelSpeed | Satisfaction |
| 1 | 8.5 | 3.9 | 2.5 | 5.9 | 4.8 | 4.9 | 6 | 6.8 | 4.7 | 5 | 3.7 | 8.2 |
| 2 | 8.2 | 2.7 | 5.1 | 7.2 | 3.4 | 7.9 | 3.1 | 5.3 | 5.5 | 3.9 | 4.9 | 5.7 |
| 3 | 9.2 | 3.4 | 5.6 | 5.6 | 5.4 | 7.4 | 5.8 | 4.5 | 6.2 | 5.4 | 4.5 | 8.9 |
| 4 | 6.4 | 3.3 | 7 | 3.7 | 4.7 | 4.7 | 4.5 | 8.8 | 7 | 4.3 | 3 | 4.8 |
| 5 | 9 | 3.4 | 5.2 | 4.6 | 2.2 | 6 | 4.5 | 6.8 | 6.1 | 4.5 | 3.5 | 7.1 |
| 6 | 6.5 | 2.8 | 3.1 | 4.1 | 4 | 4.3 | 3.7 | 8.5 | 5.1 | 3.6 | 3.3 | 4.7 |
| 7 | 6.9 | 3.7 | 5 | 2.6 | 2.1 | 2.3 | 5.4 | 8.9 | 4.8 | 2.1 | 2 | 5.7 |
| 8 | 6.2 | 3.3 | 3.9 | 4.8 | 4.6 | 3.6 | 5.1 | 6.9 | 5.4 | 4.3 | 3.7 | 6.3 |
| 9 | 5.8 | 3.6 | 5.1 | 6.7 | 3.7 | 5.9 | 5.8 | 9.3 | 5.9 | 4.4 | 4.6 |
7 |
In: Advanced Math
Solve using Laplace Transform
ty'' + 2(t-1)y'-2y = 0 y(0)=0, y'(0)=0, Y(s) = C/(s^2+2s)^2 (C is arbitrary)
In: Advanced Math