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