When we have a number that is jointly proportional to two other numebrs, the formula is:
[tex]a=kcb[/tex]
This means "a is jointly proportional to c and b with a factor of k"
Then, we need to find the factor k.
In this case z is jointly proportional to x² and y³
This is:
[tex]z=kx^2y^3[/tex]
Then, we know that z = 115 when x = 8 and y = 3. We can write:
[tex]115=k\cdot8^2\cdot3^3[/tex]
And solve:
[tex]\begin{gathered} 115=k\cdot64\cdot27 \\ 115=k\cdot1728 \\ k=\frac{115}{1728} \end{gathered}[/tex]
NOw we can use k to find the value of z when x = 5 and y = 2
[tex]z=\frac{115}{1728}\cdot5^2\cdot2^3=\frac{115}{1728}\cdot25\cdot8=\frac{2875}{216}\approx13.31[/tex]
To the nearest hundreth, the value of z when x = 5 and y = 2 is 13.31
