The vertex of the quadratic equation is given by the point (-b/2a, f(-b/2a)).

Plutonium is widely used in nuclear reactors and weapons due to its fissile properties.

Neodymium is used in making strong permanent magnets, known as neodymium magnets.

Uranium is commonly used as fuel in nuclear reactors.

Uranium is commonly used in the production of nuclear reactors due to its fissile properties.

The British colonial policies, particularly in agriculture, led to widespread poverty due to exploitative land revenue systems and neglect of rural development.

The weakness of the Delhi Sultanate allowed the Mughals to establish their dominance, as they capitalized on the discontent among the local rulers and the fragmented political landscape.

All of the above factors contributed to the agricultural decline in the Roman Empire, including overreliance on slave labor, technological stagnation, and climate change.

The nature of the solvent does not directly affect Gibbs Free Energy; it is primarily influenced by temperature, pressure, and concentration.

Density does not directly affect surface tension; it is influenced by temperature, impurities, and the nature of the liquid.

The color of the wire does not affect the accuracy of a potentiometer; however, temperature, length, and material do.

The color of the adsorbent does not affect its adsorption capacity; factors like surface area, temperature, and nature of the adsorbate do.

The color of the solid does not affect the adsorption of a gas; however, temperature, pressure, and surface area do.

The color of the adsorbent does not affect the adsorption process; however, temperature, pressure, and surface area do.

The color of the adsorbent does not affect the adsorption process; factors like temperature, surface area, and nature of adsorbate do.

Raoult's Law is primarily affected by the nature of the solute, temperature, and mole fraction of the solvent, but not by the pressure of the system.

The average kinetic energy of gas molecules is dependent only on the temperature of the gas, not on the mass or type of gas.

The buoyant force depends on the density of the fluid, the volume of the object submerged, and the acceleration due to gravity, but not on the depth of the object.

The buoyant force depends on the volume of fluid displaced, the density of the fluid, and the acceleration due to gravity, but not on the shape of the object.

The coefficient of friction is independent of the surface area in contact; it depends on the materials and their surface roughness.

The coefficient of kinetic friction is generally independent of the speed of sliding, while it depends on surface roughness, normal force, and material.

While temperature, pressure, and composition affect fluid density, volume does not directly affect density.

The enthalpy change of a reaction is independent of the pathway taken, as it is a state function.

While temperature, volume, and the nature of the substance affect entropy, pressure does not directly affect the entropy of a system in a significant way.

The equilibrium constant K is only affected by temperature. Changes in concentration or pressure will shift the position of equilibrium but not change the value of K.

The equilibrium constant K is only affected by temperature. Changes in concentration or pressure will shift the position of equilibrium but not change the value of K.

The equilibrium constant is only affected by temperature; changes in concentration or pressure do not affect it.

While temperature, pressure, and concentration of reactants affect Gibbs Free Energy, the nature of the solvent does not directly affect ΔG.

The gravitational force depends on the masses of the objects and the distance between them, but not on the speed of the satellite.

The gravitational force depends on the masses and the distance, but not on the speed of the satellite.