Z varies directly as x². If z=8 when x=2, find z when x=7

98

Step-by-step explaination:

For this question, it is a direct variation. Hence, the equation would be formed accordingly, and the constant k would also be used.

z varies directly as x²

z= kx² where k is the constant

z = 8

x = 2

Putting the figures in the equation, we have

8=2²(k)

8= 4k

Dividing both sides by 4, we have

k = 8/4

k = 2

Solving for z now, we substitute k with 2. And x with 7

z=kx²

z = 2(7²)

z= 2(49)

z= 98

If it were indirect variation, the constant would have been 1/k. We also have other types of variation, Indirect variation, partial variation and joint variation.

answer:

sometimes

*i think

- "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."