Explanation

To find the divergence, calculate:

div(f) = ∂/∂x (3x^2) + ∂/∂y (5xy) + ∂/∂z (xyz^3)

= 6x + 5x + 3xyz^2

At (1, 2, 3):

div(f) = 6(1) + 5(1) + 3(1)(2)(3)^2

= 6 + 5 + 54

= 65

Explanation

Explanation

Clear nights are cooler than cloudy nights because of radiation. Here's why:

• On a clear night, the Earth's surface rapidly loses heat by radiating it into space, a process known as radiative heat loss. This causes the temperature to drop.
• On a cloudy night, the clouds act as an insulating blanket, trapping heat and preventing it from escaping into space. This reduces radiative heat loss and keeps the temperature warmer.

Explanation

The demand curve is downward sloping due to the law of demand,

Which states that as the price of a good or service decreases, the quantity demanded generally increases, and vice versa.

This inverse relationship between price and quantity demanded results in a downward-sloping curve on a graph.

Explanation

In an isothermal process, the temperature of the system remains constant throughout.

Since this expansion occurs at a constant temperature, the internal energy is not changed (for an ideal gas, internal energy is dependent only on temperature).

The work done by the gas during expansion is not zero, and as the gas expands, the pressure decreases.

Explanation

When a police car with its siren on moves towards a stationary listener, the frequency of the sound perceived by the listener increases.

This phenomenon is known as the Doppler effect.

Explanation

The Hay Bridge is used for the measurement of inductance.

It is specifically designed to measure the inductance of coils with high accuracy.

Explanation

An inductor stores energy in the form of a magnetic field when current flows through it.

The energy is stored due to the magnetic field created around the inductor's coil.

Explanation

As the value of AWG increases, the thickness of the wire decreases.

The American Wire Gauge (AWG) system assigns smaller numbers to thicker wires and larger numbers to thinner wires.

Explanation

The magnetic effect of electric current is the basis of relays, motors, and generators.

It involves generating a magnetic field that interacts with other magnetic fields to produce mechanical motion or electrical effects.