Explanation

The sound level β (in dB) is given by:

β = 10 log(I / I₀)

where I₀ is the threshold intensity (faintest audible sound). Given I = I₀:

β = 10 log(1) = 0 dB

Explanation

Step 1: Add the two equations to eliminate y

(x + y) + (x - y) = 10 + 10

2x = 202x = 10

Step 2: Solve for x

x = 20/2x = 10

Explanation

The argument of the product of two complex numbers is the sum of their arguments.

This property comes from the multiplication of complex numbers in polar form.

Explanation

A quadratic equation has the form ax² + bx + c = 0, and it typically has two roots. 

These roots can be real or complex, and they can be distinct or repeated (in the case of a double root).

Explanation

Explanation

A matrix has an inverse only if its determinant is non-zero, meaning it is non-singular.

Singular matrices (with determinant = 0) do not have an inverse.

Explanation

This is an example of the associative property of multiplication:

  a × (b × c) = (a × b) × c

So, 8 × (6 × 7) = (8 × 6) × 7

Explanation

The differential equation (1 - x²)y'' - 2xy' + n(n + 1)y = 0 is known as Legendre's equation.

It arises in problems with spherical symmetry, such as solutions to Laplace’s equation in spherical coordinates.

Explanation

a^2 (-2b)^2 = a^2 × 4b^2 = 4a^2b^2

Explanation

To determine the type of conic section, rewrite the equation in standard form:

9x² + 4y² = 36

Divide by 36:

x²/4 + y²/9 = 1

Since 9 > 4, the major axis is vertical.