Explanation

Ext(A) denotes the exterior of the set A, which is defined as the interior of the complement of A, i.e., Int(A^c).

Explanation

The extraction of a cube root of a given number is a binary operation.

Explanation

Explanation

Reflex angle: an angle whose measure is greater than 180∘and less than 360∘is called a reflex angle

Explanation

The extraction of a square root of a given number is a unary operation because it takes only one operand (the number) and returns a value (the square root).

Explanation

• The word ARGENTINA has 9 letters, and some of these letters are repeated (2Ns, 2Ts, and 2As). To calculate the number of unique words that can be formed using these letters, we need to divide the total number of permutations (9!) by the number of repetitions: 9! / (2! × 2! × 2!)
• This formula accounts for the repetitions of the N, T, and A letters, and gives us the total number of unique words that can be formed using the letters of the word ARGENTINA.

Explanation

1. Center:

To check for symmetry, we first need to identify the center of the graph.

The equation is in the form of a circle, x^2 + y^2 = 1, which has its center at the origin (0,0).

2. x-axis symmetry:

A graph is symmetric about the x-axis if replacing y with -y in the equation does not change the equation.

Let's test this:

x^2 + (-y)^2 - x = 1

x^2 + y^2 - x = 1

As we can see, the equation remains the same, so the graph is symmetric about the x-axis.

Explanation

Plane geometry has two dimensions

It deals with shapes like lines, circles, and polygons that exist on a flat plane.

Explanation

The combination formula is:

nCr = n! / (r!(n-r)!)

Given that nC12 = nC6, we can equate the two expressions:

n! / (12!(n-12)!) = n! / (6!(n-6)!)

Simplifying the equation, we get:

12!(n-12)! = 6!(n-6)!

Since 12! = 12 × 11 × 10 × 9 × 8 × 7 × 6!, we can cancel out the 6! terms:

12 × 11 × 10 × 9 × 8 × 7 = (n-6)(n-7)(n-8)(n-9)(n-10)(n-11)

This equation is true when n = 18.

Therefore, the correct answer is 18.

Explanation

The given equation y = Asin(x) + Bcos(x) is a general solution to the differential equation y'' + y = 0, where A and B are arbitrary constants.