Suppose S varies directly as the cubed root of T, and tha $$\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96$$ .
A) 64
B) 1
C) 4
D) 24

Question

Quizplus · Accepted Answer

Since S varies directly as the cubed root of T, we can write the relationship as $S = k\sqrt[3]{T}$, where k is the constant of variation. Given $S = 24$ when $T = 1$, we find $k = 24$. For $S = 96$, we substitute $k = 24$ into the equation to get $96 = 24\sqrt[3]{T}$, which simplifies to $\sqrt[3]{T} = 4$, leading to $T = 64$.

Suppose S Varies Directly as the Cubed Root of T S=24 when T=1. Find T when S=96\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96S=24 when T=1. Find T when S=96

Suppose S Varies Directly as the Cubed Root of T $\mathrm { S } = 24 \text { when } \mathrm { T } = 1 . \text { Find } \mathrm { T } \text { when } \mathrm { S } = 96$