The distance from the center to any point on the circumference is always the radius, which is 15 cm.

Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.

Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.

Distance = |(2 + 3 + 4 - 10) / √(1² + 1² + 1²)| = |(-1)/√3| = 1/√3.

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Using the distance formula, d = √((5 - 2)² + (7 - 3)²) = √(9 + 16) = √25 = 5.

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.

Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.

Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.

Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.

Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0/√2 = 0

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

A catalyst lowers the activation energy of a reaction, thereby increasing the reaction rate.

Inserting a dielectric material increases the capacitance of a capacitor by reducing the electric field within it.

Adding a common ion decreases the solubility of a salt due to the common ion effect, which shifts the equilibrium to the left.

Adding a non-volatile solute increases the boiling point due to boiling point elevation.

Adding a non-volatile solute decreases the vapor pressure of the solvent due to the solute particles occupying space at the surface.

Adding a non-volatile solute to a solvent increases the boiling point of the solution due to the colligative property of boiling point elevation.

When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances, thus it increases.

Cortisol is a steroid hormone that helps reduce inflammation and is involved in the stress response.

Deforestation leads to habitat loss, which significantly decreases biodiversity as many species lose their homes.

Deforestation increases carbon dioxide levels in the atmosphere as trees that absorb CO2 are removed.

Introducing a dielectric material between the plates of a capacitor increases its capacitance by a factor equal to the dielectric constant (κ) of the material.

Inductive reactance is directly proportional to frequency; as frequency increases, inductive reactance increases.

Gibberellins promote seed germination by breaking dormancy and stimulating the growth of the embryo.

Heavy metals can be toxic to organisms, leading to bioaccumulation and harmful effects on ecosystems.