and the geometric mean of non-negative quantities and are shown. Based on the diagram, which inequality is correct?The arithmetic mean
If the sum of two positive numbers is 18, what is the largest possible value of their product?
Hint. For non-negative numbers and the Arithmetic Mean - Geometric Mean Inequality implies that and
For values of such that and are positive, what is the maximum possible value of
Hint. Apply the Arithmetic Mean - Geometric Mean Inequality.
If the sum of two legs of a right triangle is 20, what is the smallest possible value of the hypotenuse?
Hint. The quadratic mean, or root-mean-square of non-negative numbers and is greater than or equal to their arithmetic mean, i.e.
with equality happening when
What is the quadratic mean of the four values and
Note. The quadratic mean, or root-mean-square, of non-negative numbers is