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Question

If r varies directly with s and t, and r= 20 when s = 2 and t = 5, what is the value of t when r = 40 and s = 5


please explain how to do this

Answer 1

Hi,

If r varies DIRECTLY with s and t then they are both in the numerator on the other side, multiplied together. There is also always a coefficient of variation, k. So the general formula for this direct joint variation is:

r = kst

When we let r = 20, s = 2, and t = 5, then you can solve and find the value of "k".

20 = k(2)(5)

so k = 2

Now that we know "k" = 2, the new formula is:

r = 2st

Plugging in our new values of r = 40 and s = 5, we can find the value of "t".

40 = 2(5)t
4 = t <== This is your answer.

I hope this helps you!! :-)

Answer 2

r = Kts

where K is a constant,

given r=20 when s=2 and t=5,

substitute,

20 = K(5)(2)

K = 20/10 = 2

Hence the equation is,

r = 2ts

So the value of t when r=40 and s=5 is

40 = 2(t)(5)

t = 40/10

t = 4

Answer 3

Varying directly means that it's proportional to s and t, so if s goes up by a factor of 2.5 and r has only gone up by a factor of 2, then t must have gone down by a factor of 2/2.5 = .8, so t = 0.8 *5 = 4

Answer 4

r/2s=t
so...
40/10=4