Given that the value of the integral \[ \int_1^9 (x^2 - 2)\, dx \] calculated using the Simpson's 1/3 rule with four uniform subintervals over the interval [1,9] is given by \[ f(1) + \alpha^2 + \frac{8}{3}, \] then the possible value of \( \alpha \) is _______
If \( F = F(x, y, z) = \dfrac{x^2 y^2 z^2}{x^2 + y^2 + z^2} \), \( G = G(x, y, z) = \log\left(\dfrac{xy + yz + zx}{x^2 + y^2 + z^2}\right) \), and \( H = F + G \), then \[ x \dfrac{\partial H}{\partial x} + y \dfrac{\partial H}{\partial y} + z \dfrac{\partial H}{\partial z} = \text{...........} \]
The supply voltage magnitude \( |V| \) of the circuit shown below is ____ .
A two-port network is defined by the relation
\(\text{I}_1 = 5V_1 + 3V_2 \)
\(\text{I}_2 = 2V_1 - 7V_2 \)
The value of \( Z_{12} \) is: