3. Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem.

(a) Minimize w = 4y_{1} + 5y_{2} +
7y_{3}

Subject to: y_{1} + y_{2} + y_{3} ≥
18

2y_{1} + y_{2} + 2y_{3} ≥ 20

y_{1} + 2y_{2} + 3y_{3} ≥ 25

y_{1}, y_{2}, y_{3} ≥ 0

(b) Making use of shadow costs, if the 2^{nd} original
constraint changed to

2y_{1} + y_{2} + 2y_{3} ≥ 24, now what
will the minimum of w be? Explain clearly.

(c) Making use of shadow costs, if the 1^{st} original
constraint changed to

y_{1} + y_{2} + y_{3} 21, now what will
the minimum of w be? Explain clearly.

In: Advanced Math

Write a MATLAB code for discrete least squares trigonometric polynomial S3(x), using m = 4 for f(x) = e^x * cos(2x) on the interval [-pi, pi]. Compute the error E(S3).

In: Advanced Math

1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 = 0 (a) Convert the equation into a first-order system in terms of x and v, where v = dx/dt. (b) Find all of the equilibrium points of the first-order system. (c) Make an accurate sketch of the direction field of the first-order system. (d) Make an accurate sketch of the phase portrait of the first-order system. (e) Briefly describe the behavior of the first-order system

In: Advanced Math

Cadbury is preparing a special edition of its famous
egg-fondant. The new design of the chocolate shell of the small egg
is created from the following two paraboloids: z =
2−2x^{2}−2y^{2} and z = x^{2} +
y^{2}−1. The x, y and z coordinates are given in
centimeters. **Answer the following questions using triple
integrals and show steps.**

a) Determine the volume of the egg using the **rectangular
coordinates**

b) Knowing that the density of the fondant inside the egg (in g
/ cm3) at a point (x, y, z) is 3 times the distance from this point
to the Oz axis, determine the mass of the egg using **the
cylindrical coordinates**. (We neglect here the mass of the
chocolate shell.)

c) You share this egg with your teacher by cutting it with the
horizontal plane z = c. Determine the value of the constant c to
separate your egg into two pieces of equal volumes.**Use
rectangular coordinates**

d) Determine the mass of each of the two pieces found in (c)
using the **cylindrical coordinates**. Which piece
should you keep to have the one with the most fondant?

*** fondant is the chocolate white milk inside the egg ****

In: Advanced Math

Qualitative,
Quantitative, Discrete, Continuous.

In: Advanced Math

a. Assuming a low-informative prior probability distribution,
find the posterior distribution of left-handed students in the
population. Summarize your results with an estimation of the mean,
median, mode, and a 95% credible interval. Plot your posterior
probability distribution.

b. According to the literature, 5 to 20% of people are
left-handed. Take this information into account in your prior
probability and calculate a new posterior probability distribution.
Summarize your results with an estimation of the mean, median,
mode, and a 95% credible interval. Plot your posterior probability
distribution.

b. According to the literature, 5 to 20% of people are
left-handed. Take this information into account in your prior
probability and calculate a new posterior probability distribution.
Summarize your results with an estimation of the mean, median,
mode, and a 95% credible interval. Plot your posterior probability
distribution.

In: Advanced Math

Please explain in the most simple way possible what Bipolar coordinates are and what each coordinate represent in them compared to cartesian coordinates. A reference book would be great too.

In: Advanced Math

1. ¬B∨(G↔J), H→(B&C) ∴(H&J)→G

2. A∨B, C↔¬(B∨D) ∴C→A

3. (A&B) ↔ (F→G), (A&F) & B∴(G→R)→R

4. T→¬B, T→¬D ∴ T→¬(B∨D)

5. ¬(M∨¬S), S→(R→M) ∴A → (¬R∨T)

6. (F&G) → I, (I∨J) → K ∴F→(G→K)

7. ¬U, O→G, ¬(O∨G) →U ∴G

Prove that the arguments are valid by constructing a dedication using the rules MP, MT, DN, Conj, Simp, CS, Disj, DS, DM, CP, HS, BE, and DL. Use CP if needed.

In: Advanced Math

3. True or false? All vectors below are in R^{n} for
some n. If your answer is “True”, explain why. If your answer is
“False”, give a counterexample. Please specify for all if the given
statement is true or false, thank you!

(1) If two vectors are linearly independent, then they are orthogonal.

(2) If x is orthogonal to both u and v, then x must be orthogonal to u − v.

(3) If W is a subspace of R^{n}, then W and W^⊥(W
transpose) have no vectors in common.

(4) If z is orthogonal to v_{1} and v_{2} and if
W =span(v_{1},v_{2}), the z must be in W^⊥(W
transpose) .

(5) ∥cv∥ = c∥v∥ for all scalars c and vectors v in R^{n}
.

In: Advanced Math

1. For each of the following statements indicate if it
is true or false. If the answer is

false, briefly explain why.

(a) (2 points) Let V be a vector space and consider the subspace W
= Span{v1, v2, v3, v4}.

If v1 = 2v2 + v3, then {v2, v3, v4} is a basis for W.

(b) (2 points) If A and B are invertible n × n matrices, then A is
row equivalent to B.

(c) (2 points) Let P3 be the vector space of all polynomials of
degree less than or equal

to 3. If {p1, p2, p3} are linearly independent in P3, then they are
a basis of P3.

(d) (2 points) If A is an invertible n × n matrix, then det(A3)
> 0.

In: Advanced Math

Find the number of r-permutations of the multiset
{∞?1, ∞?2, … , ∞??} such that in

every such permutation each type of an element of the multiset
appears at least

once. (You do not need to provide a short answer. Assume r ≥
n.)

In: Advanced Math

(8) Suppose T : R 4 → R 4 with T(x) = Ax is a linear transformation such that • (0, 0, 1, 0) and (0, 0, 0, 1) lie in the kernel of T, and • all vectors of the form (x1, x2, 0, 0) are reflected about the line 2x1 − x2 = 0.

(a) Compute all the eigenvalues of A and a basis of each eigenspace.

(b) Is A invertible? Explain.

(c) Is A diagonalizable? If yes, write down its diagonalization (you can leave it as a product of matrices). If no, why not?

In: Advanced Math

1.critical analisys of the movie Donald in mathmatic land

2what is the central idea of the movie Donald in mathmatic
land?

3.conclusion of the movie Donald in mathmatic land

4.history of the pictogram

In: Advanced Math

Linear Algebra: Explain what a vector space is and offer an example that contains at least five (5) of the ten (10) axioms for vector spaces.

In: Advanced Math

a. Consider a non-equilateral triangle. Try to create a tessellation around a point as you did before. Be sure you have no gaps or overlaps. Do you think any triangle with tessellate? Why or why not? Defend your reasoning.

In: Advanced Math