The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.

The derivative f'(x) = d/dx(5x^4) = 20x^3.

Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).

The derivative f'(x) = d/dx(x^3 - 4x + 6) = 3x^2 - 4.

The derivative f'(x) = d/dx(x^3 - 4x) = 3x^2 - 4.

The derivative f'(x) = d/dx(x^4 + 2x^3 - x + 1) = 4x^3 + 6x^2 - 1.

Det(G) = 1(2*6 - 3*3) - 1(1*6 - 1*3) + 1(1*3 - 1*2) = 1(12 - 9) - 1(6 - 3) + 1(3 - 2) = 3 - 3 + 1 = 1.

Det(G) = 1(5*9 - 6*8) - 2(4*9 - 6*7) + 3(4*8 - 5*7) = 1(45 - 48) - 2(36 - 42) + 3(32 - 35) = -3 + 12 - 9 = 0.

Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.

Det(G) = (2*2) - (1*1) = 4 - 1 = 3.

Det(G) = (2*2) - (2*2) = 4 - 4 = 0.

The determinant of G is (3*4) - (2*1) = 12 - 2 = 10.

The determinant of H is calculated as (3*4) - (1*2) = 12 - 2 = 10.

The determinant of H is (3*4) - (2*1) = 12 - 2 = 10.

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

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

The determinant of J is (5*3) - (4*2) = 15 - 8 = 7.

Det(I) = (1*1) - (0*0) = 1 - 0 = 1.

The determinant of E is calculated using the rule of Sarrus or cofactor expansion, resulting in -14.

The determinant of G is (2*3) - (4*1) = 6 - 4 = 2.

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.

The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).

Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.

Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.

Diameter = 2 * radius = 2 * 9 cm = 18 cm.

Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.