What is the magnitude of the current \( i \) in the given circuit?
Kirchhoff's Current Law states that at any junction, the sum of currents entering equals the sum of currents leaving.
Using Kirchhoff’s Current Law (KCL), the sum of currents entering a junction equals the sum of currents leaving it:
\[ i = (6 \, \text{A} + 3 \, \text{A}) - (10 \, \text{A} + 3 \, \text{A}) = 4 \, \text{A}. \]The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:
Let \( S \) denote the set of all subsets of integers containing more than two numbers. A relation \( R \) on \( S \) is defined by:
\[ R = \{ (A, B) : \text{the sets } A \text{ and } B \text{ have at least two numbers in common} \}. \]
Then the relation \( R \) is:
The centre of the hyperbola \(16x^2 - 4y^2 + 64x - 24y - 36 = 0\) is at the point:
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $