Sum of the numbers = Average × Number of items = 30 × 5 = 150.

Let the integers be (x-1), x, and (x+1). Their average is (x-1 + x + x+1) / 3 = x.

The azimuthal quantum number l = 1 corresponds to p orbitals, which have a dumbbell shape.

The emf is calculated as V = potential gradient × length = 4 V/m × 0.5 m = 2 V.

The potential gradient is V/L = 2V/0.4m = 5 V/m.

The bar graph shows that History had the least sales among the listed genres.

A drop in sales could be attributed to increased competition in the market.

If the sales increased by 50%, then the sales figure for 2021 was 200 units.

In base 'b', '10' represents 'b'. In base 'b+1', it becomes '11'.

The term containing x^2 is C(4,2) * x^2 * 2^2 = 6 * x^2 * 4 = 24x^2.

Capacitive reactance XC = 1/(ωC). If capacitance C increases, XC decreases.

Capacitance C is defined as C = Q/V. If C is doubled and Q remains constant, then V must halve to maintain the equation.

The capacitance C of a parallel plate capacitor is given by C = εA/d. If the distance d is doubled, the new capacitance will be C/2.

The radius is 5 (distance from (0,0) to (3,4)), so the equation is x² + y² = 5² = 25.

The radius is the distance from the center to the point, which is √(3² + 4²) = √25 = 5.

The electric field inside a non-conducting sphere with linearly increasing charge density varies linearly with radius.

At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.

The electric field inside a non-uniform charge distribution varies quadratically with radius due to the increasing charge density.

According to Gauss's law, the electric flux is directly proportional to the enclosed charge, so it doubles.

Capacitance C = Q/V. If Q is doubled and V remains constant, C must also double.

Capacitance C = Q/V; if Q is doubled and V remains constant, C must halve.

The energy stored in a capacitor is given by U = 1/2 * C * V^2. If the charge is doubled, the energy stored quadruples.

The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.

Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.

Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Circumference = 2πr. Therefore, r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.

Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.