A point M on a segment with endpoints X (1, −2) and Y (10, 3) partitions the segment in a 5:1 ratio. Find M. You must show all work to receive credit.

Step-by-step explanation:

Since segment XY is divided in the ratio 5:1, it is divided into 6 equal sections. (6 = 5+1)

As we move along XY from X to Y, x increases by 9 and y increases by 5  M is the point on XY that is 5/6 of the way from X to Y.  .

x-coordinate of M = 1 + (5/6)(9) = 1 + 7.5 = 8.5

y-coordinate of M = -2 + (5/6)(5) = -2 + 4 1/6 = 2 1/6

So, M = (8 1/2, 2 1/6)

h df tyjgtyj ttd y ytkgfty ty

step-by-step explanation:

tyty jry j y yj yttj yhgtyj y ghyj ytthj

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.