7^2 = 7 × 7 = 49.

9 squared (9^2) = 9 * 9 = 81.

Cotangent is the reciprocal of tangent. Since tan 60° = √3, cot 60° = 1/√3.

Cosecant is the reciprocal of sine. Since sin 30° = 1/2, csc 30° = 1 / (1/2) = 2.

The discriminant must be non-negative: (2k)^2 - 4(1)(16) ≥ 0. This gives 4k^2 - 64 ≥ 0, leading to k^2 ≥ 16, so k ≥ 4.

The discriminant must be less than zero. Thus, k^2 - 4*1*16 < 0 leads to k^2 < 64, giving k < 8 and k > -8.

For the roots to be equal, the discriminant must be zero. Thus, k^2 - 4*1*16 = 0, which gives k^2 = 64, so k = ±8.

For equal roots, the discriminant must be zero. Thus, k^2 - 4*1*4 = 0, which gives k^2 = 16, so k = ±4.

For both roots to be negative, k must be negative and greater than the square root of the discriminant. Thus, k < -6.

The sum of the roots is 3 + 3 = 6, so k = 6.

The sum of the roots is 3 + 3 = 6, so k = 6.

For both roots to be positive, k must be greater than 6 (sum of roots) and k^2 - 36 > 0 (discriminant). Thus, k > 6 and k < 12.

For both roots to be negative, k must be negative and |k| > 8. Thus, k = -8.

For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

Using Vieta's formulas, the sum of the roots is 0, so k = -0 = 0. The product of the roots is 9, confirming k = 6.

For both roots to be positive, k must be negative and k^2 > 36. Thus, k < -6.

For both roots to be negative, k must be positive and k^2 > 4(1)(9). Thus, k > 6.

The sum of the roots is -2 + -2 = -4, so k = 4.

The discriminant must be less than zero: k^2 - 4*1*9 < 0 leads to k^2 < 36, hence k < 0 or k > 0.

For the roots to be equal, the discriminant must be zero. Thus, (-5)^2 - 4(1)(k) = 0. Solving gives k = 6.25.

For the roots to be real and distinct, the discriminant must be positive: k^2 - 64 > 0, leading to k > 8 or k < -8.

The sum of the roots is 2 + 4 = 6, so k = 6.

The sum of the roots is 3 + 3 = 6, so k = 6.

For the roots to be real and distinct, the discriminant must be greater than zero: k^2 - 4(1)(9) > 0, which simplifies to k^2 > 36, hence k < -6 or k > 6.

log_10(0.01) = log_10(10^-2) = -2.

log_2(1/8) = log_2(2^-3) = -3.

log_4(16) = log_4(4^2) = 2.

log_5(1) = 0 because 5^0 = 1.

log_5(25) = 2, so log_5(25) + log_5(4) = 2 + log_5(4).