Number 8 , what are the coordinates of point c below segment ac that is partitioned at point b in a ratio of 2 to 5.

Step-by-step explanation:

From the given figure it is clear that the coordinates of points are A(5,0) and B(8,0).

Let the coordinates of C are (a,b).

Section formula:

If a point K divides a line segment PQ in m:n and end point of segment are and , then the coordinates of point K are

It is given that point B divides the line AC in 2:5.

Using section formula the coordinates of B are

We know that B(8,0).

On comparing both sides we get

Similarly,

Therefore, the coordinates of C are .

1 number

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.