9 × 9 = 81 and 5 × 5 = 25, so 81 - 25 = 56.

9 × 9 = 81, then 81 - 7 = 74.

The discriminant must be negative: 4² - 4*1*k < 0, which gives k > 4, so the minimum value is -6.

For equal roots, the discriminant must be zero: k² - 4*1*16 = 0, thus k² = 64, k = ±8. The value of k can be -8.

For no real roots, the discriminant must be negative: k² - 4*1*9 < 0, thus k² < 36, hence k < -6 or k > 6.

For no real roots, the discriminant must be less than zero: k² - 4*1*16 < 0, which gives k > 8.

Setting the determinant to zero: \( 1*x - 2*3 = 0 \) gives \( x - 6 = 0 \) or \( x = 6 \).

Setting y = 0 in the equation gives 5x + 10 = 0, thus x = -2. The x-intercept is -2.

Setting x = 0 in the equation gives y = 8. Therefore, the y-intercept is 8.

The integral is (5/5)x^5 + C = x^5 + C.

The integral is (6/3)x^3 - 4x + C = 2x^3 - 4x + C.

The integral is (6/6)x^6 + C = x^6 + C.

The integral of e^x is e^x + C.

For a monatomic ideal gas, γ = C_p/C_v = 5/3 = 1.67.

At constant volume, no work is done (W=0), and the heat added equals the change in internal energy (Q=ΔU).

Using t = 1 / (k[A₀]) * (1/[A] - 1/[A₀]), t = 1 / (0.02 * 0.5) * (1/0.25 - 1/0.5) = 25 s.

Using the Arrhenius equation, k = Ae^(-Ea/RT). Calculate k using the given values.

Increasing the temperature generally increases the rate of reaction significantly due to higher kinetic energy.

For a zero-order reaction, t = [A₀ - A] / k. Here, t = (0.5 - 0.2) / 0.1 = 3 s.

For a zero-order reaction, t = [A₀] / k. Here, t = 0.5 M / 0.1 M/s = 5 s.

In an isobaric process, the work done is calculated using the formula W = PΔV, where P is pressure and ΔV is the change in volume.

The Ideal Gas Law (PV = nRT) relates pressure (P), volume (V), and temperature (T) for an ideal gas.

The discriminant must be non-negative: 4² - 4*1*k ≥ 0, thus k ≤ 4.

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, which gives k ≤ 9, so the minimum value is -9.

The discriminant must be non-negative: 6² - 4*1*k ≥ 0, thus k ≤ 9.

For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants.

For an exothermic reaction, increasing the temperature shifts the equilibrium to the left, favoring the reactants, as the system tries to absorb the added heat.

According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium to the left, favoring the reactants.

The vertex x-coordinate is given by -b/(2a) = -4/(2*-1) = 2.

The vertex x-coordinate is found using x = -b/(2a) = -6/(-2) = 3.