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.

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

The discriminant is b² - 4ac = (-12)² - 4*3*12 = 144 - 144 = 0.

The discriminant is b² - 4ac = (-12)² - 4*3*9 = 0.

The distance from the center to a point on the circumference is the radius, which is 8 cm.

The distance from the center to a point on the circumference is the radius, which is 12 cm.

Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.

Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.

Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

According to Boyle's Law, increasing pressure on a gas at constant temperature results in a decrease in volume.

Chemisorption is an exothermic process, and increasing temperature generally decreases the extent of chemisorption.

According to Charles's Law, increasing the temperature of a gas at constant pressure increases its volume.

Capacitive reactance Xc = 1/(2πfC), so increasing frequency decreases Xc.

For most solid solutes, increasing the temperature increases their solubility in water.

Chemisorption typically decreases with an increase in temperature because it involves the formation of stronger chemical bonds, which are less favorable at higher thermal energies.

According to the Nernst equation, the cell potential generally increases with temperature.

Efficiency = 1 - (T_c/T_h) = 1 - (300/600) = 0.5.

Efficiency = 1 - (T2/T1) = 1 - (300/500) = 0.4 or 40%.

The efficiency (η) of a Carnot engine is given by η = 1 - (T2 / T1), where T1 is the higher temperature and T2 is the lower temperature.

E = k * |q| / r^2 = (9 × 10^9) * (3 × 10^-6) / (0.3)^2 = 90 N/C.

V = k * q / r = (9 × 10^9) * (5 × 10^-6) / 0.4 = 112.5 V.

Chromium (Cr) has the electron configuration [Ar] 3d5 4s1 due to stability of half-filled d-orbitals.

Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.