Suppose that r varies directly with s and inversely with t, and r = 2 when s = 3 and t = 12. What is the value of r when s = 5 and t = 4? (1 point) Responses Image with alt text: two over five Image with alt text: thirty-two over five 10 10 20
To solve this problem, we can use the formula for direct and inverse variation:
r = k(s/t)
where k is the constant of variation.
We can plug in the given values of r = 2, s = 3, and t = 12 to find k:
2 = k(3/12)
2 = k(1/4)
k = 8
Now we can use the value of k to find the value of r when s = 5 and t = 4:
r = 8(5/4)
r = 40/4
r = 10
So the value of r when s = 5 and t = 4 is 10.