The vertex occurs at x = -b/(2a) = 4/(-2) = 2. f(2) = -2^2 + 4*2 + 1 = 6.

The magnetic quantum number m_l can take values from -l to +l. For l = 3, m_l can be -3, -2, -1, 0, +1, +2, +3, giving a maximum value of 3.

The vertex form gives the maximum value at x = 2, f(2) = 5.

The vertex form gives the maximum value at x = 3, f(3) = -3^2 + 6*3 - 8 = 4.

Maximum voltage = Potential gradient × Length = 0.1 V/m × 20 m = 2 V.

The maximum wavelength λ_max can be calculated using λ_max = hc/E, where E = 2.0 eV = 3.2 x 10^-19 J. Thus, λ_max = (6.63 x 10^-34 * 3 x 10^8) / (3.2 x 10^-19) = 620 nm.

Maximum wavelength (λ) = hc/φ. λ = (1240 eV.nm) / 4.0 eV = 310 nm.

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.

Mean = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.2, rounded down to 5.

Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Mean = (1 + 1 + 1 + 1 + 1) / 5 = 5 / 5 = 1.

Mean = (2 + 4 + 6 + 8 + 10 + 12) / 6 = 42 / 6 = 7.

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Mean = (4 + 8 + 12 + 16 + 20) / 5 = 60 / 5 = 12.

Mean = (4 + 8 + 12 + 16) / 4 = 40 / 4 = 10.

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