Let's put a little geometry into geometric series! The spiral in the picture is made from 45° right triangles. The smallest triangle (red) has a side length of
1. You can use the Pythagorean theorem to find that the length of its
hypotenuse is 2. The next (orange) triangle has a side length exactly
matching the hypotenuse of the smallest triangle (which was just mentioned
as being 2). The next (yellow) triangle has a side length of 2; the next
triangle has a side length of 22, and so on.
The areas of the colored triangles, calculated with the formula
2.
• base • height, are 3. 1.2.4, and so on. What is the area of this entire
colorful figure?

what are ur choices?

- "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."

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.