What is the number of permutations of the six digits 123456 in which the strings 123, 234, 345, 456, 654, 543, 432, 321 don't appear?

1) Find y as a function of t if 9y′′+24y′+32y=0,

y(0)=5,y′(0)=8. y(t)=

2) Find y as a function of x if y′′′+16y′=0,

y(0)=−5,  y′(0)=−32,  y′′(0)=−32. y(x)=

3) Find y as a function of t if 9y′′−12y′+40y=0,

y(1)=5,y′(1)=9. y=

What is overmatching versus undermatching? Give an example of overmatching and undermatching (with hypothetical proportions) that might occur on a concurrent VI 20-sec VI 30-sec schedule (which means that you must first work out the expected proportions with these schedules).

JOAN+CAN=START

Solve this addition problem by substituting numbers by the given letters, to find the value of start. Each letter represents a unique digit

1) . Solve the IVP:

y^''+6y^'+5y=0, y(0)=1, y^' (0)=3

2. Find the general solution to each of the following:

a) y^''+2y^'+5y=e^2x

b) y^''+2x/(x^2+1) y'=x

c) y^''+4y=1/(sin⁡(2x)) (use variation of parameters)

3) Cherillee Toys makes a fiberglass tricycle for kids that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat, and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. The company does not have the resources available to manufacture everything needed for the completion of 12,000 tricycles so it has gathered purchase information for each component.

The following table shows relevant information:

Develop a linear programming model to advise the operations manager of Cherillee Toys how many of each component should be manufactured and how many should be purchased in order to provide 12,000 fully completed tricycles at the minimum cost.

PLEASE FINISH THIS PROBLEM USING EXCEL

Consider the linear transformation T : P1 → R^3 given by T(ax + b) = [a+b a−b 2a]

a) find the null space of T and a basis for it

(b) Is T one-to-one? Explain

(c) Determine if w = [−1 4 −6] is in the range of T

(d) Find a basis for the range of T and its dimension

(e) Is T onto? Explain

What is the ^VIX index and why is it so important? How do you explain the solutions and difference of Logarithmic and Polynomial solutions?

Let G = R\{0} and N = (0,∞). Show that G/N is isomorphic to the multiplicative group {1, −1}.

Let f : R → R be a function.

(a) Prove that f is continuous on R if and only if, for every open set U ⊆ R, the preimage f −1 (U) = {x ∈ R : f(x) ∈ U} is open.

(b) Use part (a) to prove that if f is continuous on R, its zero set Z(f) = {x ∈ R : f(x) = 0} is closed.

find the general solution

y'''-y''-4y'+4y=5-e^x-4e^2x

(UNDETERMINED COEFFICIENTS—SUPERPOSITION APPROACH)

Let A = Z and let a, b ∈ A. Prove if the following binary operations are (i) commutative, (2) if they are associative and (3) if they have an identity (if the operations has an identity, give the identity or show that the operation has no identity).

(a) (3 points) f(a, b) = a + b + 1

(b) (3 points) f(a, b) = a(b + 1)

(c) (3 points) f(a, b) = x² + xy + y²

A pharmacist has fluocinolone ointment with50% fluocinolone , and the other contains
15% fluocinolone. How many grams of each may be used to prepare 1950 g of a 20%
fluocinolone ointment?

Compute the nominal annual rate of interest (compounded monthly) at which $250.00 deposited at the end of each month for ten years will amount to $30 000.00.