Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.

Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.

Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².

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.

Linear velocity v = rω, so if r is halved and ω remains constant, v also halves.

The focal length (f) of a concave mirror is given by f = R/2, where R is the radius of curvature. Thus, f = 20 cm / 2 = 10 cm.

The focal length f of a lens is given by f = R/2. Therefore, f = 20 cm / 2 = 10 cm.

The focal length (f) of a mirror is given by f = R/2. For a convex mirror, R is positive, so f = 20 cm / 2 = 10 cm.

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 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.

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

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, if the resistance (R) is doubled and the voltage (V) remains constant, the current (I) will be halved (I = V/R).

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.