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

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

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.

According to Boyle's Law, increasing pressure on a gas at constant temperature results in a decrease in volume.

Chemisorption is an exothermic process, and increasing temperature generally decreases the extent of chemisorption.

According to Charles's Law, increasing the temperature of a gas at constant pressure increases its volume.

Increasing capacitance increases the current in a capacitive AC circuit, as current I = V/Xc.

Increasing the current in a coil increases the magnetic field produced by the coil.

Increasing the current in a solenoid increases its magnetic field strength, as the magnetic field is directly proportional to the current.

Capacitive reactance Xc = 1/(2πfC), so increasing frequency decreases Xc.

The impedance of a capacitor decreases with increasing frequency.

The total impedance can increase or decrease depending on the relationship between R, XL, and XC as frequency changes.

For most solid solutes, increasing the temperature increases their solubility in water.

Chemisorption typically decreases with an increase in temperature because it involves the formation of stronger chemical bonds, which are less favorable at higher thermal energies.

Chemisorption typically decreases with an increase in temperature because it involves the formation of stronger chemical bonds, which are less favorable at higher thermal energies.

According to the Nernst equation, the cell potential generally increases with temperature.

Fringe separation is directly proportional to the distance from the slits to the screen. Increasing this distance increases the fringe separation.

Removing a resistor from a series circuit decreases the total resistance since the sum of the remaining resistances is less.

Efficiency = 1 - (T_c/T_h) = 1 - (300/600) = 0.5.

Efficiency = 1 - (T2/T1) = 1 - (300/500) = 0.4 or 40%.

Efficiency (η) = 1 - (T_c/T_h) = 1 - (300/600) = 0.5 or 50%.

Efficiency (η) = 1 - (T2/T1) = 1 - (300/500) = 0.4 or 40%.