Which just means that the square of the hypotenuse, or longest side of a triangle is equal to the sum of the squares of the two other sides...
Often it is just called the "distance formula" because it is used so often in that context...
In this case we wish to know the distance between two points and the equation becomes...
d^2=81, since d>0
i cant see the graph
if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that
where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.
in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.