If \(x^2+y^2+-2x-6y+5 =0\), evaluate dy/dx when x=3 and y=2.
Evaluate\({1_0^∫} x^2(x^3+2)^3\)
Given \(\begin{vmatrix} 2 & -3 \\ 1 & 4 \end{vmatrix} \begin{vmatrix} -6 \\ k \end{vmatrix} \begin{vmatrix} 3 \\ -26 \end{vmatrix} = 15\). Solve for k.
A linear transformation T is defined by T: (x,y) → (3x - y, x + 4y). Find the image of (2, -1) under T.
