Explanation

The differential equation xy' = y can be rewritten as y'/y = 1/x.

This equation has a unique solution when x ≠ 0, since dividing by zero is undefined.

The solution exists on the region defined by either x > 0 or x < 0.

Explanation

Orbital electrons have specific, quantized energy levels depending on their orbit.

They cannot have arbitrary energy values — only fixed amounts allowed by quantum rules.

Explanation

In Simple Harmonic Motion (SHM), instantaneous velocity is maximum when displacement is zero.

This occurs when the phase angle is 90° with respect to displacement (since velocity leads displacement by 90° in SHM).

Explanation

To find g(3), substitute t = 3 into the equation:

g(3) = (3)³ + (3)² - 9(3) - 9

= 27 + 9 - 27 - 9

= 0

Explanation

The direction of the induced emf is predicted by Lenz's Law.

It states that the induced emf always acts to oppose the change causing it.

Explanation

An electric generator converts mechanical energy (like rotation from a turbine) into electrical energy using electromagnetic induction.

The mechanical movement causes a conductor to cut magnetic field lines, generating electric current.

Explanation

Given dt/dx = xy^(1/2)

Separate variables:

dt/y^(1/2) = x dx

Integrate both sides:

∫y^(-1/2) dy = ∫x dx

2y^(1/2) = (x²)/2 + C

y^(1/2) = x²/4 + C'

Square both sides:

y = (x²/4 + C')²

For simplicity, let's assume C' = 0:

y = (x²/4)² = x⁴/16

Explanation

A scalar quantity has only magnitude and no direction.

Examples include mass, time, temperature, and speed.

Explanation

Cohesion is the attractive force between molecules of the same substance.

It is strongest in solids due to tightly packed molecules.

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.