The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.

The linear velocity v of the center of the wheel is related to the angular velocity ω by the equation v = Rω.

The linear velocity v of the center of the wheel is related to the angular velocity by v = Rω.

Using the equation of motion for rotation, ω = ω₀ + αt.

Let the cost price be x. Selling Price = x + 20% of x = 1.2x. Thus, 1.2x = 1200, so x = 1000.

Let the cost price be x. Selling Price = Cost Price + Profit = x + 0.25x = 1.25x. Setting this equal to $400 gives 1.25x = $400, so x = $400 / 1.25 = $320.

Wholesaler's selling price = Cost Price + 20% of Cost Price = $200 + $40 = $240. Retailer's selling price = $240 - 10% of $240 = $240 - $24 = $216.

Let the cost price be x. Selling Price = x + (20% of x) = 1.2x. Therefore, 1.2x = $200, x = $200 / 1.2 = $166.67.

40% of 300 hectares = 0.40 * 300 = 120 hectares of grassland.

1.5 MW * 24 hours = 36 MWh

R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10.4 ohms.

R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10(1.32) = 13.2 Ω.

R = R0(1 + α(T - T0)) = 10(1 + 0.004(100 - 20)) = 10(1 + 0.32) = 10(1.32) = 13.2 Ω.

A = ρ * (L / R) = 3 x 10^-6 * (4 / 12) = 1 mm².

Resistance R is proportional to length; if length doubles, resistance also doubles to 24 Ω.

R = R0(1 + α(T - T0)) = 5(1 + 0.004(100 - 20)) = 6.4 Ω.

Resistance is directly proportional to resistivity; hence, wire B with higher resistivity will have higher resistance.

Resistance R = ρ(L/A). For wire A, R_A = ρ(2L/(A/2)) = 4ρ(L/A) = 4R_B.

Resistivity ρ = R * (A / L) = 3 * (2 x 10^-6 / 10) = 1.5 x 10^-6 Ω·m.

The extension of the wire can be calculated using the formula: extension = (F * L) / (A * Y).

The elongation ΔL of a wire is given by ΔL = (F * L) / (A * Y), where Y is Young's modulus.

The elongation ΔL of a wire is given by ΔL = FL / (AE), where E is Young's modulus.

Stress = Force / Area. Halving the diameter increases the area by a factor of 1/4, thus stress quadruples.

Elongation is inversely proportional to the area. Halving the diameter reduces the area to a quarter, thus elongation quadruples.

Stress (σ) = Force (F) / Area (A). Halving the diameter increases the area by a factor of 4, thus stress quadruples.

Elongation is inversely proportional to the area. Doubling the diameter increases the area by a factor of 4, thus elongation becomes L/4.

Elongation (ΔL) = (F * L) / (A * Y), where A is the cross-sectional area and Y is Young's modulus.

B's cat can be in the same room as D's parrot since A and C cannot be together.

B has a cat, which is confirmed by the information given.

Since A has a dog, B has a cat, C has a bird, and E has a rabbit, D must have the fish.