The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.

f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f(1) = -2.

The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).

The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).

The determinant of the identity matrix is always 1.

The van 't Hoff factor (i) for a non-electrolyte solute is 1, as it does not dissociate into ions.

Glucose does not dissociate in solution, so the van 't Hoff factor (i) = 1.

Na2SO4 dissociates into 3 ions (2 Na⁺ and 1 SO4²⁻), so i = 3.

Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (10 / 11) * P0 ≈ 0.909 P0.

Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (9 / 10) * P0 = 0.9 P0.

Vapor pressure of solution = (moles of solvent / total moles) * P0 = (3 / (2 + 3)) * P0 = 0.6 P0.

Vapor pressure lowering = (moles of solute / total moles) = 2 / (2 + 4) = 2/6 = 1/3. Thus, vapor pressure is 1/2 of pure solvent.

Vapor pressure = (moles of solvent / total moles) * P0 = (4 / (2 + 4)) * P0 = (4/6) * P0 = 0.67 P0.

The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.

The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.

Using Ohm's law, V = I * R = 2A * 10Ω = 20V.

Using Ohm's law, V = IR = 3A * 10Ω = 30V.

Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.

Using Ohm's law, V = IR = 3A * 12Ω = 36V.

Using Ohm's law, V = IR = 3A * 5Ω = 15V.

Using Ohm's law, V = IR = 3A * 5Ω = 15V.

Using Ohm's law, V = I * R = 2A * 10Ω = 20V.

Using Ohm's law, V = I * R = 4A * 3Ω = 12V.

Using the formula M1V1 = M2V2, (0.1 M)(0.25 L) = (0.2 M)(V2). V2 = 0.125 L = 125 mL.

Volume = moles / molarity = 0.5 moles / 1 M = 0.5 L.

At STP, 1 mole of an ideal gas occupies 22.4 liters.

Volume (L) = moles / molarity = 4 moles / 2 M = 2 L.

Volume = side³ = 3³ = 27 cubic units.

Volume = side³ = 4³ = 64 cubic units.

Volume = πr²h = π(2²)(5) = 20π cubic units.