Explanation

Boyle's Law:

• Pressure ($P$) is inversely proportional to volume ($V$) at constant temperature.
• Formula: $PV=k$.

Explanation

Given: y = (2x + 3)⁴  

Using the chain rule:  

dy/dx = 4(2x + 3)³ * d/dx(2x + 3)  

= 4(2x + 3)³ * 2  

= 8(2x + 3)³  

Explanation

 The specific gravity of water is taken as 1, as it is the standard fluid with a specific gravity of 1.

Specific gravity is a dimensionless ratio comparing the density of a substance to the density of a reference, with pure water at 4C typically used as the reference for liquids

Explanation

Avogadro's number represents the number of particles (atoms, molecules, or formula units) in one mole of a substance

Its approximate value is 6.022 × 10²³

Explanation

The hardest substance in the world is diamond.

Its hardness is due to the strong covalent bonding between its carbon atoms.

This making it the most resistant to scratching.

Category: Native minerals

Cleavage: 111 (perfect in four directions)

Crystal class: Hexoctahedral (m3m); H-M symbol: (4/m 3 2/m)

Crystal habit: Octahedral

Crystal system: Cubic

Dana classification: 1.3.6.1

Density: 3.5–3.53 g/cm3 3500–3530 kg/m3

Explanation

STP is defined as 1.00 atm and 0°C, or 273 K.

One mole of a gas at STP has a volume of 22.4 liters.

Explanation

Limestone consists of calcium carbonate,

which has the chemical formula CaCO3.

Calcium carbonate is a chemical compound.

It is a common substance found in rocks as the minerals calcite.

Explanation

To convert 0.00416 into scientific notation:  

Move the decimal 3 places to the right → 4.16 × 10⁻³.

Explanation

Complete combustion of a hydrocarbon (like methane or fuel) in the presence of sufficient oxygen produces carbon dioxide and water, releasing energy.  

Example reaction:  

CH₄ + 2O₂ → CO₂ + 2H₂O + heat

Explanation

Efficiency of a machine is never 100% because some energy is always lost due to friction between moving parts, heat, or sound.

This reduces the amount of useful output energy.