Write a Fourier series equations solved example.
add bibliography reference.
In: Advanced Math
Properties and characteristic of the Fourier series equations.
In: Advanced Math
determine the range and domain of the following: the function k defined by k(x)= square root x-3
In: Advanced Math
y''+ 3y'+2y=e^t
y(0)=1
y'(0)=-6
Solve using Laplace transforms.
Then, solve using undetermined coefficients.
Then, solve using variation of parameters.
In: Advanced Math
A small dairy wants to make sure that their butter mill is producing bricks of butter that do not differ from the labelled weight by too much. The machine produces 30 bricks of butter per minute and runs for 4 hours Monday, Tuesday, and Wednesday mornings. If the weights of the bricks of butter are deemed to be too high or too low then that afternoon will be dedicated to recalibrating the machines.
Question 1.
Use a hypothesis test to determine if Monday's sample indicates we should recalibrate the butter mill.
Question 2.
On Tuesday the sample yielded an average of weight differences of -2.71 g and a sample standard deviation of 9.87 g. Use a hypothesis test to determine if Tuesday's sample indicates we should recalibrate the butter mill.
Need Codes for R program
This was the code block given
normalplot<-function(m,sd,region=0){
x<-seq(m-3.5*sd,m+3.5*sd,length=1000)
y<-dnorm(x,m,sd)
plot(x,y,type="l",xlab="",ylab="")
z<-x[x>region[1]]
z<- z[z<region[2]]
polygon(c(region[1],z,region[2]),c(0,dnorm(z,m,sd),0),col="gray")
}
In: Advanced Math
This problem is a complex financial problem that requires several skills, perhaps some from previous sections. Clark and Lana take a 30-year home mortgage of $127,000 at 7.1%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1100 per month. (a) Find their regular monthly payment. (Round your answer to the nearest cent.) $ (b) Find the unpaid balance when they begin paying the $1100. (Round your answer to the nearest cent.) $ (c) How many payments of $1100 will it take to pay off the loan? Give the answer correct to two decimal places. monthly payments (d) Use your answer to part (c) to find how much interest they save by paying the loan this way. (Round your answer to the nearest cent.)
In: Advanced Math
Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $55,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 17%, while the Blue Chip fund has a projected annual return of 7%. The investment advisor requires that at most $30,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 220.
(a) | Formulate a linear programming model to find the best investment strategy for this client. | ||||||||||||||||||||||||||||||||||||||||||
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If required, round your answers to two decimal places. If an amount is zero, enter “0”. If the constant is "1" it must be entered in the box. | |||||||||||||||||||||||||||||||||||||||||||
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(b) | Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? | ||||||||||||||||||||||||||||||||||||||||||
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What is the annual return for the portfolio? | |||||||||||||||||||||||||||||||||||||||||||
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(c) | Suppose that a second client with $55,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 310. What is the recommended investment portfolio for this aggressive investor? | ||||||||||||||||||||||||||||||||||||||||||
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(d) | Suppose that a third client with $55,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 150. Develop the recommended investment portfolio for the conservative investor. If an amount is zero, enter “0”. | ||||||||||||||||||||||||||||||||||||||||||
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In: Advanced Math
Find the solution of the initial-value problem. y'' + y = 3 + 5 sin(x), y(0) = 5, y'(0) = 8
In: Advanced Math
Into how many parts can n circles divide the plane, maximum and minimum?
In: Advanced Math
4.- Show the solution:
a.- Let G be a group, H a subgroup of G and a∈G. Prove that the coset aH has the same number of elements as H.
b.- Prove that if G is a finite group and a∈G, then |a| divides |G|. Moreover, if |G| is prime then G is cyclic.
c.- Prove that every group is isomorphic to a group of permutations.
SUBJECT: Abstract Algebra
(18,19,20)
In: Advanced Math
Exercise 31: (General definition of a topology) Let X be a set and O ⊂ P(X), where P(X) := {U ⊂ X}. O is a topology on X iff O satisfies
(i) X∈O and ∅∈O;
(ii) ?i∈I Ui ∈ O where Ui ∈ O for all i ∈ I and I is an arbitrary
index set;
(iii) ?i∈J Ui ∈ O where Ui ∈ O for all i ∈ J and J is a finite
index set.
In a general topological space O on some X a sequence (xn) ⊂ X
converges to x ∈ X iff
for all neighborhoods x ∈ U ∈ O there exists N such that xn ∈ U for all n ≥ N. Show
a) O = ?{a},{b,c},{a,b,c},{∅}? defines a topology on X = {a,b,c}.
b) Write down all possible topologies on X = {a, b, c}.
c) Oc = ?U ⊂ R : R\U isatmostcountableorallofX? defines a topology onX = R. Moreover, show that a sequence (xn) ⊂ R equipped with the topology Occonverges if and only if (xn) is eventually constant, i.e. xn = x for all n ≥ N for some N.
In: Advanced Math
For matrices A ∈ Rn×n and B ∈ Rn×p, prove each of the following
statements:
(a) rank(AB) = rank(A) and R(AB) = R(A) if rank(B) = n.
(b) rank(AB) = rank(B) and N (AB) = N (B) if rank(A) = n.
In: Advanced Math
For an arbitrary ring R, prove that a) If I is an ideal of R, then I[ x] forms an ideal of the polynomial ring R[ x]. b) If R and R' are isomorphic rings, then R[ x] is isomorphic to R' [ x ].
In: Advanced Math
1. Rolling two D20
Consider what hapens when we roll two 20-sided dice d1 and d2 (so the sample space is S={(d1,d2):d1,d2∈{1,2,3,…,20}} and Pr(ω)=1/|S| for each ω∈S). Consider the following events:
Use the definitions of independence and conditional probability to answer these two questions:
In: Advanced Math
A stock sells for $84 and pays a continuously compounded 3% dividend. The continuously compounded risk-free rate is 5%.
a. What is the price of a pre-paid forward contract for one share to be delivered six months (.5 year) from today?
b. What is the price of a forward contract that expires six months from today?
c.Describe the transactions you would undertake to use the stock and bonds (borrowing and lending) to construct a synthetic long forward contract for one share of stock.
In: Advanced Math