Answer:
The value of z when x = 6 and y = 9 is [tex]\boxed{\frac{18}{5}}[/tex] or [tex]\boxed{3\frac{3}{5}}[/tex].
Step-by-step explanation:
Mathematical Sentence:
[tex]z=xyk[/tex]
Solution for the constant of variation or k:
Given: [tex]z=3[/tex], [tex]x=3[/tex], [tex]y=15[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]z=xyk[/tex]
Solution:
[tex]z=xyk\\3=(3)(15)k\\\frac{3}{(3)(15)}=\frac{(3)(15)k}{(3)(15)}\\k=\frac{1}{15}[/tex]
Final solution for z:
Given: [tex]k=\frac{1}{15}[/tex], [tex]x=6[/tex], [tex]y=9[/tex]
Find: [tex]z=?[/tex]
Formula: [tex]z=xyk[/tex]
Solution:
[tex]z=xyk\\z=(6)(9)(\frac{1}{15})\\z=(2)(9)(\frac{1}{5})\\z=(18)(\frac{1}{5})\\\boxed{z=\frac{18}{5}\:\:or\:\:3\frac{3}{5}}[/tex]
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