how does word fire equal 166538? clues decoded. each letter to its number begins the code. times the days in the longest month is next owed. raised to the letters position less one. the sum of the letters combined must be won. do all work on one letter first

Solve the Boundary Value Problem, PDE: U_tt-a²u_xx=0, 0≤x≤1, 0≤t<∞

BCs: u(0,t)=0

u(1,t)=cos(t)

u(x,0)=0

u_t(x,0)=0

Please solve questions 1 and 2. Please show all work and all steps.

1.) Find the solution x_a of the Bessel equation t²x'' + tx' + t²x = 0 such that x_a(0) = a

2.) Find the solution x_a of the Bessel equation t²x'' + tx' + (t²-1)x = 0 such that x'_a(0) = a

This is a Matlab Question

Create MATLAB PROGRAM that can solve First Order Linear Differential Equation ( 1 example contains condition and the other does not have condition).

1. ty′ + 2y = t^2 − t + 1, y(1)=12

The correct answer is y(t) = 1/4 t^2 − 1/3 t + 1/2 + 1/12t^2

2. (x-1) dy/dx + 2y = (x+1)^2

The correct answer is y = (x(x+1) / x-1 ) + C(x+1) / x-1

The correct answer is

Let R be a ring (not necessarily commutative), and let X denote the set of two-sided ideals

of R.

(i) Show that X is a poset with respect to to set-theoretic inclusion, ⊂.

(ii) Show that with respect to the operations I ∩ J and I + J (candidates for meet and join;

remember that I+J consists of the set of sums, {i + j} where i ∈ I and j ∈ J) respectively,

X is a lattice.

(iii) Give an example of a commutative ring for which the corresponding X is not a Boolean

algebra, and one for which it is.

Give an example of an SMSG axiom that is independent of the other axioms. Justify your answer.

determine if the following are homomorphisms/isomorphisms:

1. F: (Z₅,+₅) → (Z₅,+₅) where F([x]₅)=[2x+1]₅.

2. F : (Z₁₀,+₁₀) → (Z₅,+₅) where F([x]₁₀)=[2x]₅.

3. F : (Z₃₁,+₃₁) → (Z₃₁,+₃₁) where F([x]₃₁)=[7x]₃₁.

The dataset in the file Lab11data.xlsx contains data on Crimini mushrooms. The factor variable is the weight of the mushroom in grams and the response variable is the total copper content in mg. 1. Plot Copper vs. Weight and describe. 2. Find least squares regression line and interpret slope in the words of the problem. 3. Find the coefficient of determination (R2) and interpret in context. 4. Find the correlation coefficient (R) and interpret in context. 5. Find and interpret a 95% Confidence Interval for the true slope. 6. Find the predicted values for Weights of 12.1, 15.8, 19.7. 7. Find the residuals values for Weights of 12.1, 15.8, 19.7. 8. Graph the standardized residuals vs. predicted values (x-axis). Describe and comment. 9. Graph the predicted values vs. the actual accuracy values (x-axis). Describe and comment.

0. Consider the following non-homogeneous linear recurrence:

   an =−a_n-1 +6a_n-2+125(8+1)·(n+1)·2ⁿ

1. a₀ = 0
   a₁ = 0

   2. (b) Find the solution a_n^(h) to the associated homogeneous linear recurrence. n

   3. (c) Find a particular solution a_n^p to the non-homogeneous linear recurrence.

   4. (d) Find the general solution to the non-homogeneous linear recurrence.

a+b+c=(abc)^(1/2) show that (a(b+c))^(1/2)+(b(c+a))^(1/2)+(c(a+b))^(1/2)>36

8. Determine the centroid, ?(?̅,?̅,?̅), of the solid
formed in the first octant bounded by ?+?−16=0
and 2?^2−32+2?=0.

For a given Step‐footing find                                                  

1. Volume of concrete                                                              

2. Area of Shuttering

F = step‐1 : 0.9m x 0.90m x 0.25m

F = step‐2 : 0.80m x 0.80m x 0.25m

F = step‐3 : 0.70m x 0.70m x 0.25m

C = 0.30m x 0.30m

Find the Total cost of all the items referring to price schedule.

Price Schedule:

Which of the following three inferences are valid? (There is no need to explain your answers.)

(a)        Premise:          Liu Yang spends two hours every day playing the violin.

Conclusion:      Liu Yang wants to be a good violinist.

(b)        Premise:          If Liu Yang is in class, she is on campus.

Premise:          Liu Yang is on campus.

Conclusion:      Liu Yang is in class.

(c)        Premise:          If Liu Yang is in class, she is on campus.

Premise:          Liu Yang is in class.

Conclusion:      Liu Yang is on campus.

solve any question about fourier series by using MATLAB

Let R be a commutative domain, and let I be a prime ideal of R.

(i) Show that S defined as R \ I (the complement of I in R) is multiplicatively closed.

(ii) By (i), we can construct the ring R₁ = S^-1R, as in the course. Let D = R / I. Show that

the ideal of R₁ generated by I, that is, IR₁, is maximal, and R₁ / I₁R is isomorphic to the

field of fractions of D. (Hint: use the fact that everything in S^-1R can be written in the

form s^-1r, where s ∈ S and r ∈ R. The first step is to show that IR₁ ∩ R = I).