1) The hypotenuse of a right triangle is divided by the altitude into two segments with a ratio of \(3:5\). Find the ratio of the legs of the triangle.
2) Find the arithmetic and geometric mean of the following pairs of numbers.
a) \(3\) and \(48\)
b) \(\Large\frac{1}{2}\) and \(\Large\frac{1}{8}\)
c) \(20\) and \(-5\)
d) \(3\sqrt{6}\) and \(5\sqrt{22}\)
2) Find the arithmetic and geometric mean of the following pairs of numbers.
a) \(3\) and \(48\)
b) \(\Large\frac{1}{2}\) and \(\Large\frac{1}{8}\)
c) \(20\) and \(-5\)
d) \(3\sqrt{6}\) and \(5\sqrt{22}\)