Doubling the intensity of light increases the number of photons incident on the surface, which in turn increases the number of emitted electrons, assuming the frequency is above the threshold frequency.

Doubling the intensity of light doubles the number of photons, thus doubling the number of photoelectrons emitted.

If the internal resistance of a cell is negligible, it increases the accuracy of the potentiometer measurement as it does not affect the voltage being measured.

The potential gradient is calculated as V/L = 12 V / 6 m = 2 V/m.

The volume of a cube is given by V = a³. If the side length a is doubled, the new volume is (2a)³ = 8a³, which is 8 times the original volume.

Volume of a cube is given by V = a³. If a is doubled, V becomes (2a)³ = 8a³, hence volume increases by 8 times.

Volume V = L³. The maximum error in volume can be calculated using the formula: ΔV = 3L²ΔL. Here, ΔL = 0.1 m, L = 2.0 m, so ΔV = 3(2.0)²(0.1) = 1.2 m³.

Volume = side³ = (2.5 cm)³ = 15.625 cm³. Considering significant figures, it is reported as 16.0 cm³.

Volume = (2.5 cm)³ = 15.625 cm³. The uncertainty in volume can be calculated using the formula for propagation of uncertainty.

Young's modulus is a material property and does not change with the dimensions of the wire.

Resistance is directly proportional to length; doubling the length doubles the resistance.

If the length is doubled, the area increases by a factor of four (A = length²).

If the length is doubled, the volume increases by a factor of 2^3 = 8, since volume is proportional to the cube of the length.

Increasing the length of the potentiometer wire while keeping the voltage constant will increase the balance point length for the same EMF.

Increasing the length of the potentiometer wire increases the maximum measurable voltage due to a larger potential gradient.

The distance between the foci is given by 2c, where c = √(a^2 - b^2). Here, c = √(5^2 - 3^2) = √16 = 4, so the distance is 2c = 8.

Torque is directly proportional to the lever arm; if the lever arm is doubled, the torque also doubles.

Set y = 0 in the equation: 3x = 12 => x = 4. The point is (4, 0).

Set y = 0 in the equation: 3x = 12 => x = 4.

Rearranging gives y = -3/4x + 3. The slope is -3/4.

Rearranging gives y = -3/4x + 3. The y-intercept is 3.

The slope of the line is given by -A/B = -3/-4 = 3/4. Parallel lines have the same slope.

Rearranging gives y = (3/4)x + 3, so the slope is -3/4.

Rearranging gives y = -5/12 x + 5, so the slope is -5/12.

Setting x = 0 in the equation gives 2y = 10, hence y = 5.

Reflecting about the x-axis changes the sign of y-coefficient: 5x + 2y + 10 = 0.

Slope of 2x + 3y = 6 is -2/3, so m = 3/2 (negative reciprocal).

The lines intersect if the discriminant D = b^2 - 4ac > 0.

The sum of the slopes of the lines can be found using the relation -b/a, which gives -3.

Using the formula for the angle between two lines, we can derive the coefficient of xy that satisfies the angle condition.