Answer:
The constant of variation (k) is 10, and the equation describing the joint variation is [tex]\LARGE\text{$\boldsymbol{w=10xy}$}[/tex].
Step-by-step explanation:
Mathematical Equation:
[tex]\LARGE\text{$w=kxy$}[/tex]
For the constant of variation (k):
Given: [tex]w=10[/tex], [tex]x=\frac{1}{2}[/tex], [tex]y=2[/tex]
Find: [tex]k=?[/tex]
Formula: [tex]w=kxy[/tex]
Solution:
[tex]w=kxy\\10=(\frac{1}{2})(2)k\\\boxed{\boldsymbol{k=10}}[/tex]
For the equation:
Given: [tex]k=10[/tex]
Solution:
[tex]w=kxy\\\boxed{\boldsymbol{w=10xy}}[/tex]
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