Please, give an example of at least 1 case where rational functions can be used in each of the next careers:
-Photography
-Economics
-Medicine
-Music
Which one uses them the most?
In: Advanced Math
Consider the nonhomogenous heat equation with time dependent sources ut = uxx + xt, an initial condition u(x, 0) = x2 and inhomogenous boundary conditions ux(0, t) = 2t and ux(1, t) = 4. Use eigen function expansion to find the solution u(x, t).
In: Advanced Math
Select a 12 ft cantilever beam with p = 0.012, to support a dead load of 2k/f (including self weight) and Live load of 3 k/ft. fy= 60000 psi, fc'= 3500 psi (hint your answer should be Width = XXXX, Effective depth= XXXXX, Area of reinforcement = XXXXX)
In: Advanced Math
Vector Error Correction Models (VECM) provide a useful way to find the co-integration vector between two or more series, please explain it with the help of equations. What is an Error Correction term? and why do we call it so?
In: Advanced Math
Let ?+?+?=7 where ?,?,?∈ℝ. Prove that ?^2+?^2+?^2≥7/3
In: Advanced Math
In: Advanced Math
Building on Group Theory #1(topics of "Operators and Postulates" under Group Theory) for the following 3 postulates:
1) Commutative, 2) Distributive, 3) Associative: Give 2 examples for each not provided on the website (Tutorial point) with your own explanation and only own answer appreciated.
In: Advanced Math
Solve each of the following IVP’s:
y'' - y' - 3y = 0, y(0) = 0, y'(0) = -1
y'' + 4y' + 2y = 0, y(0) = 1, y'(0) = 0
y'' + 11y' + 30y = 0, y(0) = -2, y'(0) = 0
y'' + 3y' = 0, y(0) = 1, y'(0) = 0
y'' - 16y = 0, y(0) = 1, y'(0) = 2
In: Advanced Math
V = $40,000B - $1000B2
Where B is the number of boats engaged in fishing. The cost of running one fishing boat for one month is $18,000, giving the total cost of running B fishing boats as $16,000B
In: Advanced Math
______________________people
(Note: once diseases become widespread, they start to behave more like logistic growth, but don't worry about that for the purpose of this exercise)
2 . A population grows according to an exponential growth model. The initial population is P0=10, and the growth rate is r=0.45.
Then:
P1 =
P2 =
Find an explicit formula for Pn. Your formula should involve n.
Pn =
Use your formula to find P12
P12 =
Give all answers accurate to at least one decimal place
3 . Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 240% per year.
If the starting population is given by p0=500, then after one breeding season the population of the pond is given by
p1 =
After two breeding seasons the population of the pond is given by
p2 =
In: Advanced Math
Give 2 examples for each using postulates. (Group theory)
1)Semi_Group, 2)Monoid, 3)Group with your own explanation and own answers are appreciated. Do not copy and paste.
In: Advanced Math
consider the relation where each elements of the domain are the vowels of the alphabet. If the elements of the range are all the elements of the subset of {P,Q,R} and each domain element is associated with an image, can this relation be a function? Can it be one to one, justify your answer.
In: Advanced Math
a) Find the Fourier Cosine Transform of ?(?) = sin ? ; 0 < ? < ?.
b) Solve, by using Laplace Transform: ?" + ? = 3 ??? 2?; ?(0) = 0, ?′(0) = 0.
In: Advanced Math
In order to grow a certain crop, it is recommended that each square foot of the ground be treated with 10 units of phosphorus, 9 units of potassium and 19 units of nitrogen. Suppose that there are three brands of fertilizer on the market - X, Y and Z. One pound of X contains 2, 3, 5 units of phosphorus, potassium and nitrogen respectively. One pound of Y contains 1, 3, 4 units of phosphorus, potassium and nitrogen respectively. One pound of Z contains 1, 0, 1 units of phosphorus, potassium and nitrogen respectively. Using matrixes:
(i) Determine whether or not it is possible to meet exactly the recommendations by applying some combination of the three brands of fertilizer?
(ii) Take into account that a negative number of pounds of any brand cannot be applied, and suppose that each brand is sold only in integral amounts. Under these conditions, determine all possible combinations of the three brands that can be applied to satisfy the recommendations exactly.
(iii) Suppose X costs $1 per pound, Y costs $6 per pound and Z costs $3 per pound. Determine the least expensive solution that will satisfy the recommendations exactly as well as the constraints in (ii).
In: Advanced Math
I need Q1,2 and 3 ASAP please, thanks
1. Identify three applications of integration.
2. Give two specific examples of how we use integration to solve real-world problems.
3. Write a paragraph about how integration is applied in non-STEM disciplines.
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In: Advanced Math