Height = Shadow length * tan(angle) = 10 m * tan(30°) = 10 m * (1/√3) ≈ 5 m.

Increasing the supply voltage does not affect the balance condition; it remains dependent on the resistance ratios.

The surface area of a cube is given by the formula SA = 6a². Setting 6a² = 216, we find a² = 36, thus a = 6 meters.

The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(10 + r), we find r = 5 cm.

The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(5 + r), we find r = 4 cm.

Force = Surface Tension × Length = 0.072 N/m × 0.5 m = 0.036 N.

The second equation is a multiple of the first, indicating that both equations represent the same line.

Using the lapse rate of 6.5°C/km, the temperature drop at 3000 meters is 6.5 * 3 = 19.5°C. Therefore, the temperature at 3000 meters is 30°C - 19.5°C = 10.5°C, which rounds to approximately 15.5°C.

Using the lapse rate of 6.5°C/km, the temperature drop at 1000 meters is 6.5°C. Therefore, 30°C - 6.5°C = 23.5°C, which rounds to 24.5°C.

Using the lapse rate of 6.5°C/km, the temperature drop at 3000 meters is 6.5 * 3 = 19.5°C. Therefore, the temperature at 3000 meters is 30°C - 19.5°C = 10.5°C.

According to Newton's law of cooling, the rate of heat transfer increases with an increase in temperature difference.

According to Charles's Law, volume is directly proportional to temperature at constant pressure. A 10°C increase will result in a 10% increase in volume.

The saturation vapor pressure increases by approximately 6.5 hPa for every 1°C increase in temperature.

Maximum possible temperature = Measured value + Error = 30 + 0.5 = 30.5°C

For most conductors, resistivity increases with temperature due to increased atomic vibrations.

According to Charles's Law, at constant pressure, the volume of a gas is directly proportional to its temperature.

According to Gay-Lussac's law, pressure is directly proportional to temperature at constant volume.

According to Gay-Lussac's Law, if the temperature of a gas is increased while keeping the volume constant, the pressure will also increase proportionally, thus it doubles.

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).

The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).

RMS speed is directly proportional to the square root of temperature. Halving the temperature results in a decrease in RMS speed by sqrt(2).

According to Gay-Lussac's Law, if the temperature of a gas increases at constant volume, the pressure increases.

RMS speed increases by sqrt(4) = 2, since v_rms is proportional to sqrt(T).

RMS speed is proportional to the square root of temperature. Increasing from 300 K to 600 K increases the speed by sqrt(2).

According to Gay-Lussac's Law, if the temperature of a gas is increased while keeping the volume constant, the pressure increases.

The viscosity of a liquid generally decreases with an increase in temperature.

Generally, the Young's modulus of materials decreases with an increase in temperature.

For metals, resistivity increases with temperature due to increased lattice vibrations.

As the temperature of a system increases, the kinetic energy of the particles increases, leading to greater disorder and thus an increase in entropy.

According to Gay-Lussac's law, at constant volume, the pressure of an ideal gas is directly proportional to its absolute temperature. Therefore, if the temperature is doubled, the pressure also doubles.