Assess the symmetry of your body measurements by computing the proportions of your body using phi. Do the same with your facial measurements. (you may upload camera image).

Consider the cities B,C,D,E,F,G
The costs of the possible roads between cities are given below:

c(B,F) = 11
c(B,G) = 10
c(C,G) = 8
c(D,E) = 12
c(D,F) = 13
c(E,F) = 9
c(E,G ) = 7

What is the minimum cost to build a road system that connects all the cities?

Solve each of the following equations by finding an integrating factor:

x dy + y dx + 3x^3y^4 dy = 0

Consider a formula of propositional logic consisting of a conjunction of clauses of the form (±p⊕±q), where p and q are propositional variables (not necessarily distinct) and ±p stands for either p or ¬p. Consider the graph in which the vertices include p and ¬p for all propositional variables p appearing in the formula, and in which there is an edge (1) connecting p and ¬p for each variable p, and (2) connecting two literals if their exclusive-or is a clause of the formula. Prove that the formula is satisfiable if and only if the graph is 2-colorable.

Please formulate and solve each of the following problems. For each problem, you should include the final SOLVER printout (either your final spreadsheet or an answer report), as well as (1) clear and precise definitions for all decision variable; (2) your objective function indicating whether it is to be maximized and minimized; (3) all constraints, including non-negativity and integrality (if necessary); and (4) what the optimal decision is (in words) and what outcome will be produced.

1. A manufacturer of stereos has plants in Atlanta, New Haven and Dallas, and distributions centers in San Francisco, Boston, Washington, D.C., and Cleveland. The tables show weekly production capacities, demand requirements, and unit transportation costs (in dollars).

                                                                                Cleveland                                       65

The goal is to minimize total transportation costs.

3. A company has five jobs, each of which must be assigned to a single machine. The table shows the dollar costs for each possible job-machine assignment:

JOB                                                    MACHINE

                                    A                     B                     C                     D                     E

1                                  138                  127                  118                  121                  143

2                                  157                  138                  129                  132                  160

3                                  143                  129                  131                  130                  172

4                                  111                  119                  123                  107                  120

5                                  102                  120                  100                  119                  100     

Find the set of assignments with the lowest possible total cost.

prove that every integer is either even or odd but never both.

Please examine and make an assessment on Ford over the last five years compared to the auto industry? [200 words or more][Will give thumbs up]

a) y''(x)-3y'(x)=8e^3x+4sinx

b) y''(x)+y'(x)+y(x)=0

c) y^(iv)(x)+2y''(x)+y(x)=0

Matrix:

Ax b
[2 1 0 0 0 | 100]
[1 1 -1 0 -1 | 0]
[-1 0 1 0 1 | 50]
[0 -1 0 1 1 | 120]
[0 1 1 -1 1 | 0]

Problem 5
Compute the solution to the original system of equations by transforming y into x, i.e., compute x = inv(U)y.
Solution:
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I have not Idea how to do this. Please HELP!

The Goodsmell perfume company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to contain at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and the corresponding surface are and volume.

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod p), i.e., the number of elements (x,y), x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)

Consider the following graphs. Select the graphs that are planar. There are 3 correct answers out of 5.

A. The wheel graph, W6.

B. The complete bipartite graph, K3,3.

C. The 4-cube graph, Q4.

D. The complete graph, K4.

E. The cycle graph, C5.

Use power series approximations method to approximate the solution of the initial value problem: y"− (1+ x) y = 0 y(0) = 1 y'(0) = 2 (Write all the terms up to the power ). x^4