Binomial Expansions

Find the following. (Questions held on attachment) Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of x^3yz^4 in the expansion of c) The coefficient of x^3 in the expansion of d) The coefficient of x^5 in the expansion of is equal to the coefficient of x^4 in the ...continues

Arithmetic / Geometric Progressions

Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers? b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are con ...continues

Solve for x

How would you go about solving for x, when x to the tenth power = 2.533836? Thanks! x^10= 2.533836

Permutation

Find the number of inversions in the following permutation: (3, 2, 1)

Determinants

Find the value of each of the third-order determinants:  2 0 -2   1 1 5  (this is a  3 4 5  3x3 matrix)

Tangent plane

Find every point on the given surface z = f(x, y) at which the tangent plane is horizontal: z = 10 + 8x - 6y - x^2 - y^2

Maximum volume

Find the maximum possible volume of a rectangular box if the sum of the lengths of its 12 edges is 6 meters.

Find and classify the critical points in the function

Find and classify the critical points in the function: f(x, y) = x^2 + 4xy + 2y^2 + 4x - 8y + 3

Critical points

Find and classify the critical points in the function: f(x, y) = x^3 + 6xy + 3y^2

Financial Accounting 363 (II)

1. What are the benefits for an organization to raise capital by issuing stocks as opposed to issuing bonds?