Any non-zero number raised to the power of 0 is 1.

7^2 = 49 and 3^2 = 9, so 49 + 9 = 58.

7^2 = 7 × 7 = 49.

2 + 3 = 5, so 8 × 5 = 40.

According to BODMAS, 6 × 2 = 12, then 9 + 12 = 21.

Using BODMAS, 3 × 2 = 6, so 9 - 6 = 3.

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

9 × 9 = 81.

9^(1/2) = √9 = 3.

9^2 = 81 and 4^2 = 16, so 81 - 16 = 65.

The standard value of acceleration due to gravity at the surface of the Earth is approximately 9.8 m/s².

cos(0°) = 1.

cos(180°) = -1.

Using the double angle formula cos(2x) = 1 - 2sin^2 x. Since sin x = 1/2, we have cos(2x) = 1 - 2*(1/2)^2 = 1 - 2*(1/4) = 1 - 1/2 = 1/2.

Using the double angle formula cos(2θ) = 1 - 2sin^2 θ. Here, sin θ = 1/2, so cos(2θ) = 1 - 2(1/2)^2 = 1 - 2(1/4) = 1 - 1/2 = 1/2.

cos(60°) = 1/2.

cos(90°) = 0.

cos(π/3) = 1/2.

cos^(-1)(-1) = π, since cos(π) = -1.

cos^(-1)(0) corresponds to the angle where the cosine value is 0, which is π.

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

cot(45°) = 1/tan(45°) = 1/1 = 1

cot(90°) = 1/tan(90°) = 1/0 = undefined.

cot(cos^(-1)(1/2)) = √3

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

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

f''(x) = 24x - 12. At x = 1, f''(1) = 24(1) - 12 = 12.

f(2) = 2^2 - 2(2) + 1 = 4 - 4 + 1 = 1.

The standard value of gravitational acceleration at the Earth's surface is approximately 9.81 m/s².

At height R, g' = g / (2^2) = g / 4.