Answer:
[tex]m=27[/tex]
Step-by-step explanation:
When something is directly proportional, it means that: [tex]a=kb[/tex], where [tex]k[/tex] is some constant (number).
We are given that [tex]m[/tex] is directly proportional to [tex]n^2[/tex], and [tex]m=75[/tex] when [tex]n=5[/tex].
So, we have...
[tex]a=kb[/tex]
[tex]m=kn^2[/tex]
[tex]75=k(5)^2[/tex]
[tex]75=25k[/tex]
[tex]k=3[/tex]
So the full equation is:
[tex]m=3n^2[/tex]
Now, to find the answer when [tex]n=3[/tex], simply put 3 into the equation.
Which gives:
[tex]m=3(3)^2[/tex] [tex]m=9(3)[/tex] [tex]m=27[/tex]
Final answer: m=27.
