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Answer:
Answer:
The value of t when m = 24 and n = 6 is 128.
Step-by-step explanation:
Mathematical Sentence:
t=\frac{mk}{n^2}t=
n
2
mk
Solution for the constant of variation or k:
Given: t=32t=32 , m=16m=16 , n=4n=4
Find: k=?k=?
Formula: t=\frac{mk}{n^2}t=
n
2
mk
Solution:
\begin{gathered}t=\frac{mk}{n^2}\\32=\frac{16k}{(4)^2}\\32=\frac{16k}{16}\\32=k\end{gathered}
t=
n
2
mk
32=
(4)
2
16k
32=
16
16k
32=k
Solution for t:
Given: k=32k=32 , m=24m=24 , n=6n=6
Find: t=?t=?
Formula: t=\frac{mk}{n^2}t=
n
2
mk
Solution:
\begin{gathered}t=\frac{mk}{n^2}\\t=\frac{24(32)}{6}\\t=4(32)\\\boxed{t=128}\end{gathered}
t=
n
2
mk
t=
6
24(32)
t=4(32)
t=128