The sum of the roots is given by -b/a = -12/3 = -4.

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) * (3x)^2 * (-4)^(6-2) = 15 * 9 * 256 = -1440.

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

The term containing x^5 occurs when k = 5. Using the binomial theorem, the term is C(6,5) * (2x)^5 * 3^1 = 6 * 32 * 3 = 576.

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.

The term independent of x is given by C(8,4) * (2x)^4 * (-3)^4 = 70 * 16 * 81 = -256.

The term independent of x occurs when k = 3. Using the binomial theorem, the term is C(6,3) * (3x)^3 * (-2)^(6-3) = 20 * 27 * -8 = -4320.

The term 'adsorption capacity' refers to the maximum amount of solute that can be adsorbed on a surface under specific conditions.

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 parallel circuits, the total current is the sum of the currents in each branch: I_total = 3A + 2A = 5A.

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.

The total mechanical energy E is given by E = (1/2)kA². Therefore, E = (1/2)(100)(0.1)² = 0.5 J.

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.