The 5th term is given by C(6,4) * (3x)^4 * (-2)^2 = 15 * 81 * 4 = -4860.

The azimuthal quantum number l for d orbitals is 2.

The azimuthal quantum number (l) for a p-orbital is 1.

The coefficient of x^4 is C(6,4) * (-2)^2 = 15 * 4 = -60.

The coefficient of x^5 is given by 8C5 * (1/2)^3 = 56 * 1/8 = 7.

The coefficient of x^5 is given by 7C5 * (2)^2 = 21 * 4 = 84.

Determinant of B = (2*7) - (3*5) = 14 - 15 = -1.

Determinant of B = (5*3) - (1*2) = 15 - 2 = 13.

The discriminant D = b² - 4ac = 6² - 4*3*2 = 36 - 24 = 12.

The discriminant D = b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.

The discriminant is b² - 4ac = (-2)² - 4*1*1 = 0.

The discriminant is b² - 4ac = (-4)² - 4*1*4 = 0.

The term containing x^4 is C(8,4) * (1/2)^4 = 70 * 1/16 = 4.375.

The term containing x^5 is C(8,5)(1/2)^3 = 56 * 1/8 = 7.

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 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 = 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 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.