##### 3. Solve the following linear programming problem. You must use the dual. First write down the...

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 = 4y1 + 5y2 + 7y3

Subject to: y1 + y2 + y3 ≥ 18

2y1 + y2 + 2y3 ≥ 20

y1 + 2y2 + 3y3 ≥ 25

y1, y2, y3 ≥ 0

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

2y1 + y2 + 2y3 ≥ 24, now what will the minimum of w be? Explain clearly.

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

y1 + y2 + y3 21, now what will the minimum of w be? Explain clearly.

##### Write a MATLAB code for discrete least squares trigonometric polynomial S3(x), using m = 4 for...

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).

##### 1. Consider the following second-order differential equation. d^2x/dt^2 + 3 dx/dt + 2x − x^2 =...

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

##### Cadbury is preparing a special edition of its famous egg-fondant. The new design of the chocolate...

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 = 2−2x2−2y2 and z = x2 + y2−1. 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 ****

##### Qualitative, Quantitative, Discrete, Continuous. Required: (a) List 5 qualitative variables and 5 quantitative variables seen around...

Qualitative, Quantitative, Discrete, Continuous.

Required:

(a) List 5 qualitative variables and 5 quantitative variables seen around the home.

(b) List 5 discrete and 5 continuous variables found at home, at work, on TV or any other location.

##### a. Assuming a low-informative prior probability distribution, find the posterior distribution of left-handed students in the...

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.

##### Please explain in the most simple way possible what Bipolar coordinates are and what each coordinate...

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.

##### 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....

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.

##### 3. True or false? All vectors below are in Rn for some n. If your answer...

3. True or false? All vectors below are in Rn 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 Rn, then W and W^⊥(W transpose) have no vectors in common.

(4) If z is orthogonal to v1 and v2 and if W =span(v1,v2), the z must be in W^⊥​​​​​​​(W transpose) .

(5) ∥cv∥ = c∥v∥ for all scalars c and vectors v in Rn .

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

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.

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

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.)

##### (8) Suppose T : R 4 → R 4 with T(x) = Ax is a linear...

(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?

##### 1.critical analisys of the movie Donald in mathmatic land 2what is the central idea of the...

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