Find the determinant of the given matrix. [5 4][8 -2] = a.-42 b.-22 c.22 d.42

Find the gradient of f(x,y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

If the perimeter of the square equals the perimeter of the regular pentagon. each side of a pentagon is 16cm long. how long is each side of the square?

In chemistry,n molecules of an ideal gas have pressure, volume, and tempersture that stand inthe following relation, where r is constant. solve the equation for n,the number of molecules. pv=nrt