Questions
We consider the Boundary Value Problem : u'(x)+u(x)=f(x), 0<x<1 u(0)-eu(1)=a ,a is real number kai f...

We consider the Boundary Value Problem :

u'(x)+u(x)=f(x), 0<x<1

u(0)-eu(1)=a

,a is real number kai f is continue in [0,1].

1. Find a a necessary and sufficient condition ,that Boundary value problem is solvabled.

2. Solve the Boundary value problem with a=0.

In: Advanced Math

(1 point) Consider the initial value problem my′′+cy′+ky=F(t), y(0)=0, y′(0)=0 modeling the motion of a spring-mass-dashpot...

(1 point) Consider the initial value problem my′′+cy′+ky=F(t), y(0)=0, y′(0)=0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=80cos(8t) Newtons. Solve the initial value problem. y(t)= Determine the long-term behavior of the system. Is limt→∞y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t)≈

In: Advanced Math

For a cube -describe the type of groups of a rectangle -describe the orders of the...

For a cube

-describe the type of groups of a rectangle

-describe the orders of the groups

-describe the structure of the groups

-describe the elements of the groups (make sure to name all the elements and describe them as a group of permutations on the vertices)

- describe each group as subgroups of permutation groups

-describe all possible orders, types and generators for each subgroup of the group

-are any of these groups cyclic and or abelian?

-are any of these subgroups cyclic and or abelian?

-are there subgroups of every possible order?

-which subgroups are isomorphic and how do you know?

In: Advanced Math

Let X be an uncountable set, let τf be the finite complement topology on X, and...

Let X be an uncountable set, let τf be the finite complement topology on X, and let τc be the countable complement topology; namely, we have
τf ={U⊂X : X\U is finite}∪{∅},

τc={U⊂X : X\U is countable}∪{∅},

where “countable” means that the set is either finite or countably infinite (in bijection with the natural numbers).

(a) What are the compact subspaces of (X, τf )? Are all compact subspaces closed in (X, τf )?

(b) What are the compact subspaces of (X,τc)? Are all compact subspaces closed in (X,τc)?

(c) What have we learned about the nature of compact subspaces when (X,τ) is not Hausdorff ?

In: Advanced Math

This problem involves a periodic system: while t can be any real number, the dependent variable...

  1. This problem involves a periodic system: while t can be any real number, the dependent

    variable θ(t) ∈ [0, 2π). Consult chapter 4 of Strogatz. Consider the equation

    θ ̇ = μ + sin θ.
    (a) Draw phase portraits for different values of μ, find the bifurcation values of μ, and

    describe the fixed points and their stability in each regime.

    (b) Now consider specifically the case where μ is just slightly less than 1: what is true about the fixed point(s) you found above now? The equation in this case is an example of an “excitable system,” which means it has a single attracting rest state, but a sufficiently large stimulus can cause the system to make a large excursion before returning to its rest state. Think of the initial conditions as different stimuli. Explain why this is an excitable system.

    (c) Write a program to solve the system using the backward Euler method. Plot various trajectories θ(t) for different initial conditions on the same plot. On a second graph, plot V (t) = cos[θ(t)] for each of the same initial conditions. This is a very simple model for the response function of a neuron to a stimulus (see the Wikipedia page on the “Kuramoto model.” )

In: Advanced Math

Consider the universal context to be U = Z. Let P(x) be the proposition 1 ≤...

Consider the universal context to be U = Z.
Let P(x) be the proposition 1 ≤ x ≤ 3. Let Q(x) be the proposition ∃x ∈Z, x = 2k. Let R(x) be the proposition x2 = 4. Let S(x) be the proposition x = 1.
For each of the following statements, write out its logical negation in symbolic notation; then, decide which claim (the original or its negation) is True or False, and why.

(a) ∃x ∈ Z, [R(x) ∧ P (x)]
(b) ∀x ∈ Z, ∃y ∈ Z, [(S(x) ∨ Q(x)) ∧ P (y) ∧ ¬Q(y)]

(c)∃x∈Z,[S(x) ⇐⇒ (P(x)∧¬Q(x))]

In: Advanced Math

Hello, I have some datas to fit with by the following equation y = 1/(Ax+B) where...

Hello, I have some datas to fit with by the following equation y = 1/(Ax+B) where A and B are the constant coefficients, and I need to get the values of A and B.
Also I need the plot of the linearized form of the function which is (1/y)=Ax+B, (X=x and Y=1/y), and the function itself together.
I really need help with the code. Thank you.

In: Advanced Math

I need an example of how to solve the Diffie-Hellman protocol if you know Bobs number...

I need an example of how to solve the Diffie-Hellman protocol if you know Bobs number and the padlock combination but you need to find Alice number

In: Advanced Math

2a. The two space curves and r1(t) = <?1 + 5t, 3 − t^2, 2 +...


2a. The two space curves

and

r1(t) = <?1 + 5t, 3 − t^2, 2 + t − t^3> and? r2(s)=< ?3s−2s^2,s+s^3 +s^4,s−s^2 +2s^3>?

both pass through the point P(1,3,2). Find the values of t and s at which the curves pass through this point.

2b. Find the tangent vectors to each curve at the point P (1, 3, 2).

2c. Suppose S is a surface which contains the point P (1, 3, 2), and both r1(t) and r2(s) lie in S. We don’t have an equation for S, but we can still find the equation of the tangent plane to surface S at the point P (1, 3, 2). Use your answers to 2b. to do so:

Find the equation of the tangent plane to S at point P. (Hint: the vectors from 2b. lie in the tangent plane.)

3.

3. The above contour map shows the island of Hawai’i. Suppose that the height above sea level of the island is given by a function z = f(x,y) where (0,0) is at the peak of Mauna Loa and x, y, and z are measured in feet.

3a. If (a, b) is at the point P , determine if each of the following is positive, negative or zero (approximately). Briefly explain your answers. (i) fx (a, b) (ii) fy (a, b) (iii) fxy (a, b) (iv) fxx (a, b)

3b. If Mauna Loa is at a height of 13, 678 feet above sea level, write down the equation of the tangent plane at the point (0, 0).

3c. Approximate the equation of the tangent plane at the point P . Be sure to convert kilometers to feet in your computations!

In: Advanced Math

y"-y'-2y=54xe^2x

y"-y'-2y=54xe^2x

In: Advanced Math

In very dry regions, the phenomenon called Virga is very important because it can endanger aeroplanes....

In very dry regions, the phenomenon called Virga is very important because it can endanger aeroplanes. Virga is rain in air that is so dry that the raindrops evaporate before they can reach the ground.

Suppose that the volume of a raindrop is proportional to the 3/2 power of its surface area; and the rate of reduction of the volume of a raindrop is proportional to its surface area.

(a) Are these suppositions reasonable? Note that raindrops are not spherical, but let's assume that they always have the same shape, no matter what their size may be.

(b) Find a formula for the amount of time it takes for a virga raindrop to evaporate completely, expressed in terms of the constants you introduced and the initial surface area of a raindrop. Check that the units of your formula are correct.

(c) Suppose somebody suggests that the rate of reduction of the volume of a raindrop is proportional to the square of the surface area. Argue that this cannot be correct.

In: Advanced Math

Big-Pear Corp. is considering replacing its existing equipment that is used to produce smart cell phones....

Big-Pear Corp. is considering replacing its existing equipment that is used to produce smart cell phones. This existing equipment was purchase 2 years ago at a base price of $50,000. Installation costs at the time for the machine were $7,000. The existing equipment is considered a 5-year class for MACRS. The existing equipment can be sold today for $40,000 and for $20,000 in 4 years. The new equipment has a purchase price of $140,000 and is also considered a 5-year class for MACRS. Installation costs for the new equipment are $6,000. The estimated salvage value of the new equipment in year 4 is $90,000. This new equipment is more efficient than the existing one and thus savings before taxes using the new equipment are $12,000 a year. Due to these savings, inventories will see a one time reduction of $2,000 at the time of replacement. The company's marginal tax rate is 40% and the cost of capital is 12%.

MACRS 5 year

Year 5-year
1 20.00%
2 32.00%
3 19.20%
4 11.52%
5 11.52%
6 5.76%

For this project, what is the incremental cash flow in year 3?

The answer (incremental cash flow in year 3) is 17,100.

Please help me with the steps/work required to arrive at this value. Thank you.

In: Advanced Math

In very dry regions, the phenomenon called Virga is very important because it can endanger aeroplanes....

In very dry regions, the phenomenon called Virga is very important because it can
endanger aeroplanes. Virga is rain in air that is so dry that the raindrops evaporate before they can reach the ground.
Suppose that

the volume of a raindrop is proportional to the 3=2 power of its surface area; and
the rate of reduction of the volume of a raindrop is proportional to its surface
area.


(a) Are these suppositions reasonable? Note that raindrops are not spherical, but
let's assume that they always have the same shape, no matter what their size may
be.


(b) Find a formula for the amount of time it takes for a virga raindrop to evaporate
completely, expressed in terms of the constants you introduced and the initial
surface area of a raindrop. Check that the units of your formula are correct.


(c) Suppose somebody suggests that the rate of reduction of the volume of a raindrop
is proportional to the square of the surface area. Argue that this cannot be correct.

In: Advanced Math

Assume that lake Hefner has volume billion cubic meters with initial pollutant concentration of, The daily...

Assume that lake Hefner has volume billion cubic meters with initial pollutant concentration of, The daily inflow of water is million cubic meters with a pollutant concentration of, Assume that the water is well mixed in the lake and the water flow out from the lake at the same rate.

(a) How long will it take to reduce pollutant concentration in the lake?

(b) What will be the pollutant concentration in the lake eventually?

In: Advanced Math

Prove the second-order formula for the third derivative f′′′(x) = (f(x−3h)−6f(x−2h)+12f(x−h)−10f(x)+3f(x+h)) / 2h3

Prove the second-order formula for the third derivative

f′′′(x) = (f(x−3h)−6f(x−2h)+12f(x−h)−10f(x)+3f(x+h)) / 2h3

In: Advanced Math