# ðŸ“¢ Shares

## Calculate the determinant of a 4x4 matrix.

November 12, 2024

The determinant of the given 4x4 matrix is calculated using cofactor expansion along the fourth row, resulting in a determinant of -21.

## Calculate the determinant of a 2x2 matrix.

November 12, 2024

The determinant of the 2x2 matrix [[2, 2], [3, 5]] is calculated as (2 * 5) - (2 * 3) = 4.

## Solving an equation with absolute value and exponent

November 12, 2024

The equation (x-1)^(|x|-4) = 1 has solutions x = -4, 0, 2, and 4.

## Calculate the difference of 100 squared and 99 squared.

November 12, 2024

The difference of squares formula is used to evaluate the expression 100^2 - 99^2, resulting in 199.

## Find the smallest possible values of A and B for the number 645A2879B8 to be divisible by both 8 and 9.

November 11, 2024

To find the smallest possible values for A and B in a 10-digit number divisible by both 8 and 9, the last three digits (9B8) must be divisible by 8, and the sum of all digits must be divisible by 9. This leads to B=2 and A=3 as the smallest possible values.

## Solving a quadratic equation by factoring

November 11, 2024

The equation x^2 - 2x = 0 has two solutions, x = 0 and x = 2, not just x = 2.

## Find the value of b in the equation 2^b^2+2 = 64

November 9, 2024

The solution for b in the equation 2^(b^2+2) = 64 is b = 2.

## Find the value of 2^(m+n)

November 9, 2024

To find 2^(m+n), solve for m and n in the equations 2^m = 1 and 2^n = 16, then substitute the values into the expression.

## Evaluating Zero to the Power of Zero

November 7, 2024

The expression 0^0 is considered an indeterminate form in calculus because different approaches to evaluating it yield different potential values. While some approaches suggest a value of 1 and others suggest 0, the limit does not have a single, well-defined value. In some contexts, like combinatorics, it is defined as 1 for convenience.

## Evaluate the absolute value of a vector.

November 6, 2024

The magnitude of the given row vector is calculated, resulting in 3.