The sum of the coefficients is found by substituting x=1. So, (1 + 2)^5 = 3^5 = 243.

(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.

The sum of the roots is given by -b/a = 4/2 = 2.

The symbol for Gold is Au.

To convert Kelvin to Celsius, use the formula: °C = K - 273. Therefore, 273 K - 273 = 0°C.

Temperature in Kelvin (K) = Temperature in Celsius (°C) + 273.15 = 25 + 273.15 = 298.15 K.

The term containing x^2 is given by C(6,2) * (4)^4 * (x)^2 = 15 * 256 * x^2 = 3840.

A saturated solution is one that contains the maximum amount of solute that can dissolve at a specific temperature.

The heat of fusion is the energy required to change a substance from solid to liquid.

Desorption energy is the energy required to separate an adsorbate from an adsorbent.

The maximum amount of solute that can be adsorbed on a surface is referred to as the adsorption capacity.

Adsorption is the process where a solid attracts and holds molecules of a liquid or gas on its surface.

Using the formula Q = kA(T1-T2)t, we find k = Q / (A(T1-T2)t) = 100 J / (1 m² * 20°C * 10 s) = 0.5 W/m°C.

Using Ohm's law, I = V/R = 9V / 3Ω = 3A.

Total resistance R = 5Ω + 5Ω = 10Ω; I = V/R = 15V / 10Ω = 1.5A.

Z = √(R² + Xl²) = √(20² + 30²) = √(400 + 900) = √1300 = 36.06 ohms. I = V/Z = 240/36.06 = 6.66 A.

In a parallel circuit, the total current (I_total) is the sum of the currents in each branch: I_total = 3A + 5A = 8A.

Total current in parallel = I1 + I2 = 5A + 3A = 8A.

Total impedance Z = √(R² + (ωL)²) = √(10² + (2π(50)(20))²). Calculate to find current.

At maximum displacement, the total mechanical energy of a simple harmonic oscillator is at its maximum, as all energy is potential.

At the highest point of a projectile's trajectory, the kinetic energy is minimum (zero at the peak) and potential energy is maximum, thus total mechanical energy is maximum potential energy.

Moles = Molarity * Volume = 3 mol/L * 2 L = 6 moles.

Total resistance R = 10Ω + 10Ω = 20Ω. Power P = V²/R = 20² / 20 = 20W.

Total resistance R = 5Ω + 5Ω = 10Ω; Power P = V²/R = 30²/10 = 90W.

In series, R_eq = R1 + R2 = 10Ω + 20Ω = 30Ω.

In a series circuit, total resistance (R_total) is the sum of individual resistances: R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω.

For parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6. Finding a common denominator gives R_eq = 2.4Ω.

The Tyndall effect is the scattering of light by colloidal particles, making the path of the light visible.

The unit of electric charge is Coulomb (C).

The unit of electrical conductivity is Siemens (S).