Algebra Answers

Q. Compute ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt

Let S be the set of all real numbers. Define f: S ~
9.
S by f(s) = S2, and
g: S ~ S by g(s) = s + 1.
(a) Find fog.
(b) Find g 0 f.
(c) Isfog = gof?

What is the answer to: 3/5×2/3+1/4×1/3

Suppose that by midnight the vertex of the front has moved 250 miles south and 210 miles east of Des Moines,
maintaining the same shape. Write the equation for the parabola that would represent the cold front at midnight.
(Remember: both longitudinal and latitudinal distances are measured in hundreds of miles.)

hi , I diagonalize hamiltonian H, then I found by chance , that this basis of eigenstates is also a basis of eigenstates of another operator let's call it "O" , which means that the Hamiltonian commute with that operator , before I diagonalizing in that basis , I have H (NxN matrix ) as will as (NxN) matrix for operator "O" , when I diagonalize the matrix of operator O I found that this operator have just two eigenvalues , two eigenstates as well (no matter what N ) , when I diagonalize H I found that it have N different eigenstates where part of them match the requirement of the first eigenstate of operator "O" and other part match the requirement of the second one , I want to understand mathematically how this match happens for example why would the ground state of the Hamiltonian match the requirement of the first eigenstate of operator O , . I wish that my question was clear , I am not a mathematician

Jo and David picked 92 quarts of berries at King’a Orchard. If David picked 6 more quarts than jo picked, how many quarts did Jo pick?

The cost of 5 boxes of envelopes and 5 packages of notebook paper is 25.95. Two boxes of envelopes and 6 packages of paper cost is 22.38. How much would one box of envelopes cost?

Three points P, Q and R have the position vectors p, q and r respectively where p=7i +10j, q=3i + 12j r= -i + 4j
Show that |QS| = |RS| by finding the PSQ where S is the mid-point of PR

1)The points A, B and x have coordinates (2,3) (6,3) and (5,6) respectively
A)The figure ABCD is a square find coordinates of the point D