CI = P(1 + r)^n - P = 1500(1 + 0.12)^2 - 1500 = 1500(1.2544) - 1500 = $381.60.

Mass of KCl = 0.5 moles × 74.5 g/mol = 37.25 g. Concentration = 37.25 g / 1.5 L = 24.83 g/L.

Moles of NaCl = 58.5 g / 58.5 g/mol = 1 mole. Molarity = 1 mole / 1 L = 1 M.

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Molarity (M) = moles of solute / liters of solution = 0.5 moles / 1.5 L = 0.33 M.

PPM = (mass of solute in grams / volume of solution in liters) * 10^6 = (1 g / 1 L) * 10^6 = 1000 ppm.

Molarity (M) = moles of solute / liters of solution = (10 g / 58.5 g/mol) / 0.5 L = 0.34 M.

Moles of NaOH = 5 g / 40 g/mol = 0.125 mol. Molarity = 0.125 mol / 0.25 L = 0.5 M.

[H+] = 10^(-pH) = 10^(-3) = 0.001 M

Concentration of H+ = 10^(-pH) = 10^(-3) = 0.001 M.

[H+] = 10^(-pH) = 10^(-4) = 0.0001 M.

A system is critically damped when the damping coefficient equals the square root of the product of mass and spring constant.

The condition for a Wheatstone bridge to be balanced is R1/R2 = R3/R4.

The condition for balance is R1/R2 = R3/R4.

In a Wheatstone bridge, the bridge is in equilibrium when the ratio of the resistances in one branch is equal to the ratio in the other branch, i.e., R1/R2 = R3/R4.

For rotational equilibrium, the net torque acting on the object must be zero.

Constructive interference occurs when the path difference between the two waves is an even multiple of the wavelength (nλ, where n is an integer).

For constructive interference, the condition is 2t = mλ, where t is the thickness of the film and m is an integer.

Constructive interference occurs when the path difference is nλ, where n is an integer.

Critical damping occurs when the damping coefficient equals twice the mass times the natural frequency of the system.

Critical damping occurs when the damping coefficient equals the mass times the natural frequency.

Light is completely polarized when it is reflected at Brewster's angle, which is given by θ_B = arctan(n2/n1).

Light is polarized by reflection when the angle of incidence equals Brewster's angle.

The condition for rolling without slipping is that the linear velocity v of the center of mass is equal to the product of the radius R and the angular velocity ω, i.e., v = Rω.

The first minimum occurs at a = λ, where 'a' is the slit width and 'λ' is the wavelength.

Both lines can be rewritten in slope-intercept form. The first line has slope -2/3 and the second line has the same slope, hence they are parallel.

The condition for the lines to be parallel is given by h^2 = ab.

The lines are coincident if the discriminant D of the quadratic equation is zero.

The condition for parallel lines is that the determinant of the coefficients must be zero.

Two lines are parallel if their coefficients of x and y are proportional, which means c1 must equal c2.