The fractional compression \(\frac{\Delta V}{V}\) is given by:
\[ \frac{\Delta V}{V} = -\frac{\Delta P}{B} \]
The pressure \(\Delta P\) at the bottom of the ocean is:
\[ \Delta P = \rho gh = 1000 \times 10 \times 4000 = 4 \times 10^7 \, \text{Pa} \]
Thus,
\[ \frac{\Delta V}{V} = -\frac{4 \times 10^7}{2 \times 10^9} = -2 \times 10^{-2} \]
Therefore, \(\alpha = 2\).
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: