Discuss modern mathematical theories such as dynamical systems theory, chaos theory, hyperbolic geometry, fractal geometry, spherical geometry.
In: Advanced Math
In about 250 words discuss the history of foundations of mathematics as proposed in the late 19th and early 20th centuries.
In: Advanced Math
Discuss the ideas of any three of the following:
In: Advanced Math
let R be a ring; X a non-empty set and (F(X, R), +, *) the ring of the functions from X to R. Show directly the associativity of the multiplication of F(X, R). Assume that R is unital and commutative. show that F(X, R) is also unital and commutative.
In: Advanced Math
Consider the ODE u" + lambda u=0 with the boundary conditions u'(0)=u'(M)=0, where M is a fixed positive constant. So u=0 is a solution for every lambda,
Determine the eigen values of the differential operators: that is
a: find all lambda such that the above ODE with boundary conditions has non trivial sol.
b. And, what are the non trivial eigenvalues you obtain for each eigenvalue
In: Advanced Math
Which one of the following rectangular regions guarantees the uniqueness of a solution to the I. V. P. (10 x-13y) y′= 2x, y(26)=0.
In: Advanced Math
Frank, Sofia, Eldridge, and Jake are the four qualifiers for a charity raffle with two $500 prizes. One of their names will be drawn for the first prize then replaced, at which point the second prize winner will be drawn. Draw a tree diagram to determine the sample space and find the probability that (a) One person wins both prizes. (b) There are two different winners. (c) Sofia wins at least one prize. (d) Frank wins both prizes. (e) The two winners are Jake and Eldridge.
In: Advanced Math
6. For many applications of matchings, it makes sense to use bipartite graphs. You might wonder, however, whether there is a way to find matchings in graphs in general.
Please keep straight to the point and short if possible, I give good ratings on good legible writings and correctness. THANKS!!
In: Advanced Math
In: Advanced Math
Problem 10-07 (Algorithmic)
Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in Los Angeles, Tulsa, and Seattle. The following table shows Aggie Power Generation's major residential markets, the annual demand in each market (in megawatts or MWs), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW).
Distribution Costs | ||||
City | Los Angeles | Tulsa | Seattle | Demand (MWs) |
---|---|---|---|---|
Seattle | $364.25 | $601.75 | $67.38 | 958.00 |
Portland | $367.25 | $604.75 | $189.13 | 842.25 |
San Francisco | $166.13 | $463.00 | $284.88 | 2363.00 |
Boise | $341.25 | $460.00 | $281.88 | 578.75 |
Reno | $241.50 | $479.00 | $360.25 | 954.00 |
Bozeman | $428.63 | $428.63 | $309.88 | 506.15 |
Laramie | $367.25 | $426.63 | $367.25 | 1198.50 |
Park City | $375.25 | $375.25 | $494.00 | 622.25 |
Flagstaff | $238.13 | $535.00 | $653.75 | 1178.19 |
Durango | $363.25 | $303.88 | $600.75 | 1472.25 |
In: Advanced Math
Consider the system of equations
2x-5y=a
3x+4y=b
2x- 4y=c
where a, b, c are constants. Because there are 3 equations and 3 unknowns, there are no possible values of a, b and c for which the system of equations has a unique solution. True or false?
In: Advanced Math
Prove using the principle of mathematical induction:
(i) The number of diagonals of a convex polygon with n vertices is n(n − 3)/2, for n ≥ 4,
(ii) 2n < n! for all n > k > 0, discover the value of k before doing induction
In: Advanced Math
This exercise requires the use of technology.
Four sectors of the U.S. economy are (1) livestock and livestock
products, (2) other agricultural products, (3) forestry and fishery
products, and (4) agricultural, forestry, and fishery services.
Suppose that in 1977 the input-output table involving these four
sectors was as follows (all figures are in millions of
dollars).
Determine how these four sectors would react to an increase in
demand for livestock (Sector 1) of $1,000 million, how they would
react to an increase in demand for other agricultural products
(Sector 2) of $1,000 million, and so on. (Round your answers to two
decimal places. Let the columns of the matrix be given in millions
of dollars.)
To | 1 | 2 | 3 | 4 |
From 1 | 11,937 | 9 | 109 | 855 |
2 | 26,649 | 4,285 | 0 | 4,744 |
3 | 0 | 0 | 439 | 61 |
4 | 5,423 | 10,952 | 3,002 | 216 |
Total Output | 97,795 | 120,594 | 14,642 | 47,473 |
Answer is a 4x4 Matrix and is NOT 0.182 or 0.878 for the first box in the matrix answer
In: Advanced Math
Solve the LP problem. If no optimal solution exists because
there is no Solution Set, enter EMPTY. If no optimal solution
exists because the region is unbounded, enter UNBOUNDED.
Note that an unbounded region can still have an optimal
solution while a bounded region is guaranteed to have optimal
solutions. HINT [See Example 1.]
Minimize c = 2x − 2y subject to
|
≤ | y | ||||||
y | ≤ |
|
||||||
x | + | y | ≥ | 10 | ||||
x | + | 2y | ≤ | 35 | ||||
x ≥ 0, y ≥ 0. |
c=
(x, y)=
In: Advanced Math
Solve the LP problem. If no optimal solution exists because
there is no Solution Set, enter EMPTY. If no optimal solution
exists because the region is unbounded, enter UNBOUNDED.
Note that an unbounded region can still have an optimal
solution while a bounded region is guaranteed to have optimal
solutions. HINT [See Example 1.]
Maximize and minimize p = x + 2y subject
to
x | + | y | ≥ | 4 |
x | + | y | ≤ | 10 |
x | − | y | ≤ | 4 |
x | − | y | ≥ |
−4. |
Minimum
P=
(x, y)=
Maximum
P=
(x, y)=
In: Advanced Math