Questions
x^2 y ′′ + xy′ + λy = 0 with y(1) = y(2) and y ′...

x^2 y ′′ + xy′ + λy = 0 with y(1) = y(2) and y ′ (1) = y ′ (2)

Please find the eigenvalues and eigenfunctions and eigenfunction expansion of f(x) = 6.

In: Advanced Math

4. Let a < b and f be monotone on [a, b]. Prove that f is...

4. Let a < b and f be monotone on [a, b]. Prove that f is Riemann integrable on [a, b].

In: Advanced Math

Problem formulation: The company wants to increase the availabel sortiment from 2 types of glasses to...

Problem formulation:
The company wants to increase the availabel sortiment from 2 types of glasses to 3 types. A production
line already produces 2 different types of glasses: 6oz juice glasses and 10oz cocktail glasses and 8oz
champagne glass. Adding a new type is possible but you as a manager should check that it will be cost
effective. The production line can produce 100 cases of 6oz glasses in 6 hours and 100 cases of 10oz glasses
in 5 hours. The production time for the new type, a champagne glass, is 8 hours per 100 cases. A manager
needs to optimize the production while she prefers to operate the line on a schedule of 60 hours per week.
The product is stored in factory’s storage room with the capacity of 15000 cubic feet. A case of 6oz glasses
requires 10 cubic feet and a case of 10oz glasses requires 20 cubic feet. A case of the 8oz champagne glass
requires 10 cuft. A retail customer will buy 6oz glasses for $5.00 per case but can accept only 800 cases per
week and 10oz glasses for $4.50 per case, and 8oz glasses for $6.00 per case and there is no limit on the size
of the order for these two types.

Tasks:
1.Find how how many cases of each type of glass should be produced each week in order to
maximize the profit ?
Note: In the report display the optimal solution and the objective function value clearly in a form of
a table.
2. Is including a new type of glass (the champagne glass) economically attractive ?
3. Determine shadow prices summarize them in a table and associate correct units with them.
4. If you divert resources to produce extra one hundred cases of 8oz champagne glasses how
much would the profit change ? (this quantity is called reduced cost).

In: Advanced Math

A cohort study was undertaken to examine the association between high lipid level and coronary heart...

A cohort study was undertaken to examine the association between high lipid level and coronary heart disease (CHD). Participants were classified as having either a high lipid level (exposed) or a low or normal lipid level (unexposed). Because age is associated with both lipid level and risk of heart disease, age was considered a potential confounder or effect modifier and the age of each subject was recorded. The following data describes the study participants: Overall, there were 11,000 young participants and 9,000 old participants. Of the 4,000 young participants with high lipid levels, 20 of them developed CHD. Of the 6,000 old participants with high lipid levels, 200 of them developed CHD. In the unexposed, 18 young and 65 old participants developed CHD.. Calculate the appropriate crude ratio measure of association combining the data for young and old individuals. 3. Now, perform a stratified analysis and calculate the appropriate stratum-specific ratio measures of association. What are they? 4. Do the data provide evidence of effect measure modification on the ratio scale? Justify your answer.

In: Advanced Math

discrete mathematics 1.  Show that if a | b and b | a, where a and...

discrete mathematics

1. 

Show that if a | b and b | a, where a and b are integers, then a = b or a = -b.  

//Ex. 5, Page 208.

2.

Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd.

//Ex. 6, Page 208. 

3.

What are the quotient and remainder when

a) 44 is divided by 8?

b) 777 is divided by 21?

f) 0 is divided by 17?

g) 1,234,567 is divided by 1001?   

//(a), (b), (f), and (g) Ex. 10, Page 209.

4.

Determine whether each of these integers is a prime.

a) 19

b) 27

e) 107

f) 113

//(a), (b), (e), and (f) Ex. 2, Page 217.

5.

Find the prime factorization of each of these integers.

a) 39

c) 101

d) 143

f) 899

//(a), (c), (d), and (f) Ex. 4, Page 217.

6.

What are the greatest common divisors of these pairs of integers?

a) 23 * 33 * 55 and 25 * 33 * 52

d) 22 * 7 and 53 * 13 

//(a) and (d) Ex. 20, Page 218.

7.

Find gcd(1000, 625) and lcm(1000, 625) and verify that gcd(1000, 625)*lcm(1000, 625) = 1000*625 

//Ex. 24, Page 218.

In: Advanced Math

Show that a graph T is a tree if and only if for every two vertices...

Show that a graph T is a tree if and only if for every two vertices x, y ∈ V (T), there exists exactly one path from x to y.

In: Advanced Math

Draw a sketch of z ∈ C | Im((3 − 2i)z) > 6 . 2. Express...

Draw a sketch of z ∈ C | Im((3 − 2i)z) > 6 .

2. Express z = −i − √ 3 in the form r cis θ where θ = Argz.

3. Use de Moivre’s theorem to find the two square roots of −4i.

In: Advanced Math

Perpetuity A pays $100 at the end of each year. Perpetuity B pays $25 at the end of each quarter.


Perpetuity A pays $100 at the end of each year. Perpetuity B pays $25 at the end of each quarter. The present value of perpetuity A at the effective rate of interest is $2,000. 

What is the present value of perpetuity B at the same annual effective rate of interest i?

In: Advanced Math

A stock expects to pay a dividend of $3.72 per share next year. The dividend is...

A stock expects to pay a dividend of $3.72 per share next year. The dividend is expected to grow at 25 percent per year for three years followed by a constant dividend growth rate of 4 percent per year in perpetuity. What is the expected stock price per share 5 years from today, if the required return is 12 percent?

In: Advanced Math

Solve the following differential equation using the power seriesmethod.(1+x^2)y''-y'+y=0I mean this with respect,...

Solve the following differential equation using the power series method.

(1+x^2)y''-y'+y=0

 

In: Advanced Math

Residents were surveyed in order to determine which flowers to plant in the new public garden....

Residents were surveyed in order to determine which flowers to plant in the new public garden. A total of N people participated in the survey. Exactly 9/14 of those surveyed said that the color of the flower was important. Exactly 7/12 of those surveyed said that the smell of the flower was important. In total, 753 people said that both the color and smell were important. How many possible values are there for N?

Please explain all the steps clearly.
Thank you.

In: Advanced Math

Definition 2.3.2 in our book defines the power set of a set S, denoted by P(S),...

Definition 2.3.2 in our book defines the power set of a set S, denoted by P(S), as the set of all subsets of S, that is P(S) = {A : A ⊆ S}. For example, P({1, 2}) = {∅, {1}, {2}, {1, 2}}, and P(∅) = {∅}. Consider the relation ⊆ on the power set P(Z), i.e. the is-a-subset-of relation defined on sets of integers. In other words, the objects we compare are sets of integers. (a) Prove or disprove: ⊆ is reflexive. (b) Prove or disprove: ⊆ is irreflexive. (c) Prove or disprove: ⊆ is symmetric. (d) Prove or disprove: ⊆ is antisymmetric. (e) Prove or disprove: ⊆ is transitive. (f) Is ⊆ on Z an equivalence relation? Is it a partial order? (g) Which other relation satisfies exactly the same properties?

In: Advanced Math

Let ∼ be the relation on P(Z) defined by A ∼ B if and only if...

Let ∼ be the relation on P(Z) defined by A ∼ B if and only if there is a bijection f : A → B. (a) Prove or disprove: ∼ is reflexive. (b) Prove or disprove: ∼ is irreflexive. (c) Prove or disprove: ∼ is symmetric. (d) Prove or disprove: ∼ is antisymmetric. (e) Prove or disprove: ∼ is transitive. (f) Is ∼ an equivalence relation? A partial order?

In: Advanced Math

partial deffrential equation formula for social networks

partial deffrential equation formula for social networks

In: Advanced Math

You plan to take out a $700,000 mortgage for 30 years with monthly payments. If you...

  1. You plan to take out a $700,000 mortgage for 30 years with monthly payments.
    1. If you don’t have a down payment, they will offer you an interest rate of 5.7%. If you can make a down payment of at least $20,000 they will lower the interest rate to 5.2%. Calculate the monthly payment for each loan.
      1. You would like to see how long it will take you to come up with a down payment. You already have $6,000 and can put away $500 every quarter at 4% interest compounded quarterly. How long will it take you to save up to $20,000?

In: Advanced Math