Activation energy is the minimum energy required to initiate a chemical reaction.

The number of games played is given by n(n-1)/2. For 12 players, it is 12(12-1)/2 = 66 games.

The number of games played is given by n(n-1)/2. For 10 players, it is 10(10-1)/2 = 45.

The number of games played is given by n(n-1)/2. For 12 players, it is 12(12-1)/2 = 66 games.

The number of games played is given by the combination formula n(n-1)/2. For 10 players, it is 10(10-1)/2 = 45 games.

The inscribed angle is half the measure of the central angle that subtends the same arc. Therefore, the inscribed angle measures 80/2 = 40 degrees.

Using the formula: radius² = (distance from center to chord)² + (half of chord length)². Here, radius² = 5² + (12/2)² = 25 + 36 = 61, so radius = √61, which is approximately 7.81.

Using the formula: radius² = (distance from center to chord)² + (half of chord length)². Thus, radius² = 5² + (12/2)² = 25 + 36 = 61, so radius = √61 ≈ 7.81.

Using the formula: chord length = 2√(radius² - (half of chord length)²). Here, half of chord length = √(9² - 0) = 9, so chord length = 2 * 9 = 18.

The angles subtended by the same chord at the circumference are equal.

A radius that is perpendicular to a chord at its endpoint bisects the chord.

The angle subtended by the chord at the center is twice the angle between the tangent and the chord, so it is 2 * 30° = 60°.

The angle subtended at the circumference is half the angle subtended at the center. Therefore, the angle at the circumference is 80/2 = 40 degrees.

The angle subtended at the circumference is half the angle subtended at the center. Therefore, it is 80/2 = 40 degrees.

The angle subtended at the circumference is half of that at the center, so it is 80/2 = 40 degrees.

The angle subtended at the circumference is half of that at the center, so it is 30 degrees.

The angle subtended at the circumference is half of that at the center, so it is 30 degrees.

The angle in radians is given by the formula θ = s/r, where s is the arc length. Thus, θ = 10/5 = 2 rad.

Using the formula: distance = √(radius² - (chord length/2)²) = √(10² - (8/2)²) = √(100 - 16) = √84 ≈ 9.17.

Using the formula d = √(r^2 - (c/2)^2), where r = 5 and c = 6, we get d = √(5^2 - 3^2) = √(25 - 9) = √16 = 4.

Using the formula d = √(r^2 - (c/2)^2): d = √(5^2 - (8/2)^2) = √(25 - 16) = √9 = 3.

Using the formula d = √(r² - (c/2)²): d = √(8² - (12/2)²) = √(64 - 36) = √28 ≈ 5.29.

If the radius is doubled, the area increases by a factor of four (since area is proportional to the square of the radius).

If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.

If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.

The segments of the chords are proportional to each other according to the intersecting chords theorem.

Voltage drop across R2 = (R2 / (R1 + R2)) * Vtotal = (6 / (3 + 6)) * 10 = 6.67V.

In a parallel circuit, the voltage across each resistor is the same as the source voltage. Therefore, both resistors have 10V across them.

Using the voltage divider rule, V3 = (R3 / (R2 + R3)) * Vtotal = (3 / (2 + 3)) * 10 = 6V.

Total resistance R_total = R1 + R2 = 2Ω + 3Ω = 5Ω. Current I = V / R_total = 10V / 5Ω = 2A.