an LTIC system is specified by the equation (D2 +4D + 4)y(t) = Dx(t) with initial condition y'(0) = -4... How do I find the other initial condition?
In: Advanced Math
Write down the chromatic polynomials of
(i)the complete graph K7;
(ii)the complete bipartite graph K1,6.
In how many ways can these graphs be coloured with ten colours?
In: Advanced Math
Find the solution of the system
x′=−4y, y′=3x,
where primes indicate derivatives with respect to t, that satisfies the initial condition x(0)=1, y(0)=−1.
In: Advanced Math
find the appropriate series solution or solutions, using the frobenius method, about the origin (x_0 = 0)
2x(x+2)y'' + y' -xy = 0
In: Advanced Math
Show by induction that if a prime p divides a product of n numbers, then it divides at least one of the numbers.
Number theory course. Please, I want a clear and neat and readable answer.
In: Advanced Math
In: Advanced Math
5. Another equation that has been used to model population growth is the Gompertz equation dP /dt = rP ln (K P ) , where r and K are positive constants, and P(t) > 0.
(a) Sketch a clearly labeled graph of f(P), where dP/dt = f(P) (state the main facts you used to obtain your answer).
(b) Draw the phaseline. Next to it, sketch a set of integral curves in the t − P plane.
(c) State and classify all equilibria.
(d) (Extra Credit) For 0 < P < K, find P 00(t) and determine where the graph of P(t) is concave up and where it is concave down. Enter the inflection point in your graph in (a). (Enter your answer in an attached blank page.)
In: Advanced Math
For each part below, find a binary relation on the set S = {1,2,3,4} that satisfies the given combination of properties
a) reflexive, symmetric, and transitive
b) not reflexive, but symmetric and transitive
c) not symmetric, but reflexive and transitive
d) not transitive, but reflexive and symmetric
e) neither reflexive nor symmetric, but transitive
f) neither reflexive nor transitive, but symmetric
g) neither symmetric not transitive, but reflexive
h) not reflexive, not symmetric, and not transitive
In: Advanced Math
A student has 10 tickets to the show but she has 20 friends who want to see the show. Find the number of ways she can choose ten to give the tickets to, where:
a. There are no restrictions. Simplify your answer to a final number.
for questions b and c Do not simplify your answers. Leave in Combinatorics format.
b. Two of the friends are twins so if you invite one you have to invite the other
c. Two of the friends do not like each other so if you invite one you cannot invite the other.
In: Advanced Math
Explain if the set below is a vector space given standard
operations.
The set of all even functions defined on R with addition and scalar
multiplication defined as follows:
1.) (f+g)(x) = f(x) + g(x) (addition)
2.) (cf)(x) = cf(x)
In: Advanced Math
Write the greatest common divisor over the given filed as a linear combination of the given polynomials. That is, given f(x) and g(x), find a(x) and b(x) so that d(x) = a(x)f(x) + b(x)g(x), where d(x) is the greatest common divisor of f(x) and g(x).
(a) x^10 − x^7 − x^5 + x^3 + x^2 − 1 and x^8 − x^5 − x^3 + 1 over Q.
(b) x^5 + x^4 + 2x^2 − x − 1 and x^3 + x^2 − x over Q.
(c) x^3 − 2x^2 + 3x + 1 and x^3 + 2x + 1 over Z5.
(d) x^5 + x^4 + 2x^2 + 4x + 4 and x^3 + x^2 + 4x over Z5.
I know the GCD's are
a. x^3-1 b. 1 c. 1 d.1
Please help me write them as a linear combination.
In: Advanced Math
Explain what truncating a Fourier series expansion and Fourier Integral does
In: Advanced Math
The Lifang Wu Corporation manufactures two models of industrial robots, the Alpha 1 and the Beta 2. The firm employs 5 technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (that is, all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor-hours to assemble each Alpha 1 robot and 25 labor-hours to assemble each Beta 2 model. Wu wants to see at least 10 Alpha 1s and at least 15 Beta 2s produced during the production period. Alpha 1s generate a $1,200 profit per unit, and Beta 2s yield $1,800 each.
a. Determine the most profitable number of each model of robot to produce during the coming month.
b. What is the total profit?
c. What if there was a reduction in 50 hours, what impact, in terms of profit, would this decision have?
In: Advanced Math
Use the method of Undetermined Coefficients to find a general solution of this system X=(x,y)^T
Show the details of your work:
x' = 6 y + 9 t
y' = -6 x + 5
Note answer is: x=A cos 4t + B sin 4t +75/36; y=B cos 6t - A sin 6t -15/6 t
In: Advanced Math