[tex]\quad[/tex]JOINT VARIATION
[tex]\qquad[/tex]z varies directly as x and y
[tex]\\[/tex]
[tex]\bold {EQUATION:}[/tex][tex]\boxed{\tt z=kxy}[/tex] where k is the constant of the variation.
[tex]\bold {GIVEN:}[/tex]
- z = 90 when x =3 and y = 6
[tex]\bold {UNKNOWN:}[/tex]
- constant of the variation k
- z when x =4 and y = 8
[tex]\bold {SOLUTION:}[/tex]
First, we will find the value of k,
[tex] \begin{array}{c} \large\tt z = kxy \\ \\ \large \tt 90 = k(3)(6) \\ \\ \large \tt 90 = 18k \\ \\ \Large \tt \frac{90}{18} = \frac{18k}{18} \\ \\ \large \tt \boxed{ \tt k = 5} \end{array}[/tex]
Now, we will substitute the value of k to find z when x = 4 and y = 8.
[tex] \begin{array}{l} \large \tt z = kxy \\ \\ \large \tt z = (5)(4)(8) \\ \\ \large \red{ \boxed{ \tt z = 160}}\end{array}[/tex]
[tex]\\[/tex]
[tex]\therefore\boxed{\textsf{z = 160 when x = 4 and y = 8.}}[/tex]
[tex]\\ \\[/tex]
#CarryOnLearning
