Question

If t varies as v, and t = 2 4/7 when v = 13/14 , find v when t = 2 1/4.. v=. Direct variation. .

Answer 1

13/16

Explanation:

"t varies as v" => t(v) = kv, where k is the constant of proportionality.

If t = kv, then this is true: 2 4/7 = k(13/14), or

18/7 = (13/14)k

Solving for k, we get:

(14/13)(18/7) = k = 36/13

Therefore, our equation is t = (36/13)v.

Now let t = 2 1/4 or 9/4, and find the corresponding v:

9/4 = (36/13)v, or v = (9/4)(13/36) = 0.8125 = 13/16

v = 13/16 when t = 2 1/4.

Answer 2

13/16

Explanation:

Direct variation is when one variable is equal to a constant times another variable. In this case, t varies as v, so, t = k*v, where k is a constant. We know that t = 2 4/7 = 18/7 when v = 13/14, then:

18/7 = k*13/14

18/7*(14/13) = k

36/13 = k

Replacing in the formula with t = 2 1/4 = 9/4, we get:

9/4 = 36/13*v

9/4*(13/36) = v

13/16 = v