H(t)= -16t^2 + 87t. find the average rate of change of the height of the ball from 2 to 4.5 seconds

  -17 ft/s

Step-by-step explanation:

The average rate of change is the difference in height on the interval, divided by the difference in time.

  m = (h(4.5) -h(2))/(4.5 -2) . . . . . . . . definition of rate of change on [2, 4.5]

  h(4.5) = (-16·4.5 +87)(4.5) = 67.5

  h(2) = (-16·2 +87)(2) = 110

Then ...

  m = (67.5 -110)/(2.5) = -17

The average rate of change on the interval from 2 to 4.5 seconds is -17 ft/s.

Check

The slope of the curve is given by its derivative:

  h'(t) = -32t +87

The midpoint of the interval is (2+4.5)/2 = 3.25.

The slope at the midpoint is ...

  h'(3.25) = -32(3.25) +87 = -17 . . . . average rate of change on [2, 4.5]

For a quadratic function. the average rate of change on an interval is the slope of the function at the midpoint of the interval. This calculation confirms that.

correct answer is option b.

step-by-step explanation:

the true statement about geometric figure is option b that is one line can be drawn through all three points.

if three points are on the same plane, they can be connected by a line.

answer:   c ?

step-by-step explanation: