SOLUTION: if s varies directly as t^2, and s=243 when t=9, find s when t is 8 a. s=216 b.s=72 c.s=192 d.s=27

Question 1120579: if s varies directly as t^2, and s=243 when t=9, find s when t is 8
a. s=216
b.s=72
c.s=192
d.s=27
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
if s varies directly as t^2, and s=243 when t=9, find s when t is 8
s = kt^2
s=243; t= 9
243 = k*9^2
243 = 81k
k = 243/81
k = 3
The equation now
s = 3t^2
when t = 8
s = 3(8^2)
s = 3(64
s = 192
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

If you have to find the value of s for many values of t, then you will want a formula for s in terms of t. To do that, you need to use the given information to find the constant of proportionality, as the other tutor did.

For a problem like this, where you are only finding one other value of s, I think it is easier just to consider how the value of s will change, considering the change in the value of t.

The t value changes fro 9 to 8; it gets multiplied by 8/9.

s varies directly as t^2; so the value of s will get multiplied by (8/9)^2.

243 * (8/9)^2 = 243*64/81 = 64*3 = 192

The value of s when t=8 is 192.
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