Understanding Joint Variation
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Beginner
Start here! Easy to understand
Beginner Explanation
Joint variation is when $z$ depends on both $x$ and $y$ proportionally, using $z = kxy$.
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Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
If $z$ varies jointly as $x$ and $y$, and $z = 12$ when $x = 2$ and $y = 3$, what is $z$ when $x = 4$ and $y = 5$?
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
Imagine your weekly earnings $z$ depend on the hours $h$ you work and the amount $r$ you earn per hour. If you earn $z = 200$ with $h = 10$ and $r = 20$, find your earnings if you work $15$ hours at $r = 20$.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Consider a scenario where $z$ varies jointly with $x$ and $y^2$. If $z = 18$ when $x = 3$ and $y = 2$, find $z$ when $x = 6$ and $y = 1$.
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4
Challenge Quiz
Single Choice Quiz
Advanced
For $z$ varying jointly with $x$ and $y^3$, given $z = 54$ when $x = 2$ and $y = 3$, find $z$ when $x = 4$ and $y = 2$.
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Recap
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