Area change = π[(r-2)² - r²] = π[-4r + 4] = 3.14 * (-4r + 4).

Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.

Circumference = 2πr; If r is halved, new circumference = πr; Factor = 1/2.

Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.

Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.

Area increases by a factor of (3r)²/r² = 9.

Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.

Gravitational force is inversely proportional to the square of the radius. If radius is doubled, F becomes F/4.

Weight is inversely proportional to the square of the radius. If radius increases by 50%, weight decreases by 25%.

Gravitational acceleration g = GM/R². If R increases, g decreases.

Gravitational acceleration is inversely proportional to the square of the radius. If radius increases, g decreases.

If the radius increases while mass remains constant, g decreases because g = G * M / r^2.

Using the Arrhenius equation, if the rate doubles for a 10°C increase, Ea is approximately 40 kJ/mol.

The order of the reaction is third because the rate is proportional to the concentration raised to the power of 3.

The reaction is second-order because the rate depends on the square of the concentration of A.

Using Ohm's law, I = V/R = 5 V / 10 ohms = 0.5 A.

According to Ohm's law, I = V/R. If R is doubled, I will be halved.

Max revenue occurs at x = -b/(2a) = 100/(2*2) = 25.

R'(x) = 20 - x = 0 gives x = 20. This maximizes revenue.

Max revenue occurs at x = -b/(2a) = -50/(2*-0.5) = 50.

Using the sum and product of roots: 1 + (-3) = -2 and 1 * (-3) = -3, thus k = 3.

The discriminant must be greater than zero: 2² - 4*1*k > 0, which simplifies to k < 1.

The sum of the roots is given by -b/a = -5/1 = -5.

Using the product of roots: k = (-2)(-3) = 6.

Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.

The discriminant must be greater than zero: 5² - 4*1*k > 0, thus k < 25.

Using the product of roots: q = 1 * 4 = 4.

Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find k = 12.

Using the product of roots, k = 1*6 = 6.

Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find p = 12.