The mechanical resistance $S$ of a wooden beam, in the form of a rectangular parallelepiped, is directly proportional to its width (b) and to the square of its height (d) and inversely proportional to the square of the distance between the beam's supports, which coincides with its length ($x$), as illustrated in the figure. The constant of proportionality k is called the resistance of the beam. The expression that translates the resistance S of this wooden beam is (A) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}^{2}}$ (B) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}}{\mathrm{x}^{2}}$ (C) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}}$ (D) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b}^{2} \cdot \mathrm{d}}{\mathrm{x}}$ (E) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot 2\mathrm{d}}{2\mathrm{x}}$
The mechanical resistance $S$ of a wooden beam, in the form of a rectangular parallelepiped, is directly proportional to its width (b) and to the square of its height (d) and inversely proportional to the square of the distance between the beam's supports, which coincides with its length ($x$), as illustrated in the figure. The constant of proportionality k is called the resistance of the beam.
The expression that translates the resistance S of this wooden beam is\\
(A) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}^{2}}$\\
(B) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}}{\mathrm{x}^{2}}$\\
(C) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot \mathrm{d}^{2}}{\mathrm{x}}$\\
(D) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b}^{2} \cdot \mathrm{d}}{\mathrm{x}}$\\
(E) $\mathrm{S} = \dfrac{\mathrm{k} \cdot \mathrm{b} \cdot 2\mathrm{d}}{2\mathrm{x}}$