Sketch the given region of integration r and evaluate the integral over r using polar coordinates. modifyingbelow integral from nothing to nothing integral from nothing to nothing with upper r startfraction 1 over startroot 16 minus x squared minus y squared endroot endfraction da∫∫r 1 16−x2−y2 da; requals=startset (x comma y ): x squared plus y squared less than or equals 1 comma x greater than or equals 0 comma y greater than or equals 0 endset

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

- "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."

step-by-step explanation: