A={1,3,4},B={2,3}

Check ALL of the Cartesian products to which the following elements belong:

(1,1)
A. A×A
B. A×B
C. B×B
D. B×A

(3,3)
A. B×B
B. A×A
C. B×A
D. A×B

(3,1)
A. B×B
B. B×A
C. A×B
D. A×A

(1,2)
A. A×A
B. B×A
C. A×B
D. B×B

Use variation of parameters to solve the following differential equations

y''-5y'-6y=tln(t)

prove the following statement: If the augmented matrices of two linear systems are row equivalent, then those systems are equivalent.

(To do this, start with a solution to one of the systems and show that it is still a solution of the other system under each of the three elementary row operations.)

Suppose all even-indexed linear transformations in the chain complexC•are 0 transformations and all odd-indexed transformations are bijections.Compute the homology of this complex

From the time of early studies by Sir Francis Galton in the late nineteenth century linking it with mental ability, the cranial capacity of the human skull has played an important role in arguments about IQ, racial differences, and evolution, sometimes with serious consequences. (See, for example, S.J. Gould, "The Mismeasure of Man," .) Suppose that the mean cranial capacity measurement for modern, adult males is cc (cubic centimeters) and that the standard deviation is cc. Complete the following statements about the distribution of cranial capacity measurements for modern, adult males. (a) According to Chebyshev's theorem, at least ? of the measurements lie between 565 cc and 1481 cc. (b) According to Chebyshev's theorem, at least 36% of the measurements lie between and . (Round your answer to the nearest integer.) (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the measurements lie between and . (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ? of the measurements lie between 565 cc and 1481 cc.

Verify that the three eigenvectors found for the two eigenvalues of the matrix in that example are linearly independent and find the components of the vector i = ( 1 , 0 , 0 ) in the basis consisting of them. Using

\begin{vmatrix}1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4\end{vmatrix}

Which of these is the answer?

(2,−5,2)(2,−5,2)

(−1,3,23)(−1,3,23)

(1,−3,32)(1,−3,32)

Solve the following differential equation using Linear operators and the Annihilator approach as needed.

y''+2y'+y=x^2-3x

Does {1,2,3} ,{3,4,5}, {1,4}, {1,5}, {2,4}, {2,5} form an incidence geometry? If so do any of the parallel postulates hold (Elliptic, Euclidean, Hyperbolic parallel postulates)?

Interpret the meaning of a loading function

I just need an exemple

Suppose that e(t) is a piecewise defined function

e (t) = 0 if 0 ≤ t < 3

and

e(t) = 1 if 3 ≤ t

Solve

y’’+ 9y = e(t)

y(0) = 1 y’(0) = 3

y=fx1, ……..,x5)

St:

c1=w1(x1, ……..,x5)

c2=w2(x1, ……..,x5)

By using the signs of the principal minors Hj

1-Derive the second- order-sufficient condition for maximum.

2-Derive the second order-sufficient condition for minimum

A round-robin tournament is an event wherein every competing team plays every other team once and only once. Assuming no ties, every game can be depicted on a graph G using a directed edge (x, y), where team x has defeated team y.

(a) Assuming n teams participate in a round-robin tournament, how many vertices and edges will graph G depicting the tournament have?

(b) Is it preferable to be a source or a sink in graph G?

(c) Can G have multiple sources and/or sinks? Explain why or why not.

(d) Assuming G has a cycle, can it have a sink? Explain why or why not.

a) 8t*dydt+y=t^3, t>0
Put the problem in standard form.
Then find the integrating factor, μ(t)=________

b) 5(sin(t)dydt+cos(t)y)=cos(t)sin6(t), for 0<t<π and y(π/2)=18.

Put the problem in standard form.

find y(t)=___________

c)   13(t+1)dydt−9y=36t, for t>−1 with y(0)=18
Put the problem in standard form.

find y(t)=_______

d) x^2−4xy+x*dydx=0

Put the problem in standard form.

Find the integrating factor, ρ(x)=

6. The function f(t) =

0 for − 2 ≤ t < −1

−1 for − 1 ≤ t < 0

0 for t = 0

1 for 0 ≤ t < 1

0 for 1 ≤ t ≤ 2

can be extended to be periodic of period 4. (a) Is the extended function even, odd, or neither? (b) Find the Fourier Series of the extended function.(Just write the final solution.)

A beam is embedded at the left end and free at the other end with a constant loadw0=48EI uniformly distributed across its length. (6pts)

and L =1.

(a)Is this an initial value problem? Explain.

(b) Write and solve the beam deflection equation. Find the deflection when L=1/2