Explanation

Prime factors:

 • 36 = 2² × 3²

 • 54 = 2 × 3³

 • 360 = 2³ × 3² × 5

Common prime factors are 2 × 3² = 18.

Explanation

The Laplace equation is a 2nd order partial differential equation, given by:

∇²u = 0 or ∂²u/∂x² + ∂²u/∂y² + ∂²u/∂z² = 0

Explanation

Variance measures the spread of data around the mean.

For a constant number, all values are the same, so there is no variation, making variance 0.

Explanation

A sequence is a function whose domain is the set of natural numbers (1, 2, 3, ...).

Each natural number input gives a specific term in the sequence.

Explanation

In an arithmetic progression, the sum of n terms between a and b is given by: Sum = n(a+b)/2

This formula uses the first and last terms to find the total of evenly spaced values.

Explanation

To find the sum, we need to calculate each term:

i^101 = i (since i^1 = i and the powers repeat every 4 terms)

i^102 = i^2 = -1

i^103 = i^3 = -i

i^104 = i^4 = 1

Now, let's add them up:

i + (-1) + (-i) + 1 = 0

Explanation

The square root of any prime number is not a perfect square.

Therefore, √𝑝 is irrational, meaning it cannot be expressed as a fraction of two integers.

Explanation

To find the range, subtract the smallest value from the largest value:

Maximum value = 28

Minimum value = 20

Range = Maximum value - Minimum value

= 28 - 20

= 8

Explanation

Extrapolation is the process of estimating a value outside the range of known data points.

In contrast, interpolation refers to estimating a value within the known range.

Explanation

Given:

Side length of square = 31 meters

Perimeter formula: P = 4 × side

P = 4 × 31

P = 124 meters