The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.

The sum of the roots is given by -b/a = 3/2.

The sum of the roots is given by -b/a = 4/2 = 2.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.

The sum of the roots is given by -b/a = 4/1 = 4.

The sum of the roots is given by -b/a = 5/1 = 5.

The sum of the roots is given by -b/a = 4/1 = 4.

The sum of the roots is given by -b/a = 5/1 = 5.

The sum of the roots is given by -b/a = 7/1 = 7.

The term containing x^2 is given by C(4,2) * (3x)^2 * 4^2 = 6 * 9 * 16 = 864.

The term independent of x occurs when k = 7, C(7, 3) * (3)^3 * (-4)^4 = 35 * 27 * 256 = 84.

The empty set has exactly one subset, which is itself: ∅.

The total number of subsets is 2^5 = 32.

The total number of terms is n + 1 = 6 + 1 = 7.

The trace of A is the sum of the diagonal elements: 1 + 5 + 9 = 15.

The union of two sets includes all unique elements from both sets. Thus, I ∪ J = {1, 2, 3}.

The union of two sets includes all elements from both sets without duplicates. Thus, {1, 2} ∪ {2, 3} = {1, 2, 3}.

The union of two sets is the set of elements that are in either set. Here, {a, b} ∪ {b, c} = {a, b, c}.

Unit vector = (3, 4) / √(3^2 + 4^2) = (3/5, 4/5).

Unit vector = (3, 4, 0) / √(3^2 + 4^2) = (3, 4, 0) / 5 = (0.6, 0.8, 0).

Unit vector = (4/5, 3/5) where magnitude = √(4^2 + 3^2) = 5

Unit vector = (4/5, 3/5) since magnitude = 5.

Unit vector = v / |v| = (3, 4) / 5 = (0.6, 0.8)

Unit vector = A / |A| = (3, 4) / 5 = (0.6, 0.8).

(1 + i)^2 = 1^2 + 2*1*i + i^2 = 1 + 2i - 1 = 2i.

Using the binomial theorem, (2 + 3)^3 = 5^3 = 125.

By the double angle identity, 2sin(θ)cos(θ) = sin(2θ).

cos(0°) = 1.

cos(180°) = -1.