Question

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?
A. 2/5
B.32/5
C.10
D.20

Answer 1

The statement suppose that r varies directly with s and inversely with t is best represented as:

r α s/t

To make it into equality, we insert a proportionality constant, k:

r = ks/t

Using the initial conditions, we solve for k.

r = ks/t
r = 2 when s = 3 and t = 12

2 = k(3)/12
k = 8

Thus, when s = 5 and t = 4,

r = 8(5)/4
r = 10 -----> OPTION C

Answer 2

A correct option is an option (c)

Given values are,

$r = 2$ when $s = 3 , t = 12$

According to the given question, the relation is,

$r\propto \frac{s}{t}\\r=k\frac{s}{t}...(1)$

Substituting the values $r = 2$ when $s = 3 , t = 12$ into equation (1)

$2=\frac{3k}{12} \\k=\frac{24}{3} \\k=8$

Since we have to find the value $r$ again from equation (1)

$r=\frac{8\times5}{4} \\r=10$

So, the required value r is 10.

Learn More:https://brainly.com/question/2827452