Amodel for a company's revenue from selling a software package is r(p) = -2.5p² + 500p, where p is the price in dollars of the software. what price will maximize revenue? find the maximum revenue. the price $ maximizes the revenue. the maximum revenue is $

p = $100,  R = $25,000

Step-by-step explanation:

The maximum is the y-value of the Vertex.

Step 1: Use the Axis-Of-Symmetry (AOS) formula to find x:

R(p) = -2.5p² + 500p

        a=-2.5  b=500

Step 2: Find the maximum by plugging the p-value (above) into the given equation.

R(100) = -2.5(100)² + 500(100)

          = -25,000 + 50,000

          = 25,000

It's a quadratic function

If a < 0, then the function has a maximum value in vertex.

The vertex (h, k), where:

We have:

Substitute:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."