Answer:
constant of variation = 3
Step-by-step explanation:
we know that b varies jointly with c and d
so:
b∝c∝d
and b varies inversely with e, so
b∝![\frac{1}{e}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Be%7D)
and i will call the constant of variation k, this way we can make an equation for b in the following form:
![b=k\frac{cd}{e}](https://tex.z-dn.net/?f=b%3Dk%5Cfrac%7Bcd%7D%7Be%7D)
this satisfy that b varies jointly with c and d (if b increases, c and d also increase) and inversely with e (if b increases, e decreases)
we know that when b is 18, c is 4, d is 9, and e is 6:
![b=18\\c=4\\d=9\\e=6](https://tex.z-dn.net/?f=b%3D18%5C%5Cc%3D4%5C%5Cd%3D9%5C%5Ce%3D6)
substituting this in our equation for b:
![b=k\frac{cd}{e}\\ 18=k\frac{(4)(9)}{6}](https://tex.z-dn.net/?f=b%3Dk%5Cfrac%7Bcd%7D%7Be%7D%5C%5C%2018%3Dk%5Cfrac%7B%284%29%289%29%7D%7B6%7D)
and we solve operations and clear for the constant of variation k:
![18=k\frac{36}{6}\\ 18=6k\\\frac{18}{6}=k\\ 3=k](https://tex.z-dn.net/?f=18%3Dk%5Cfrac%7B36%7D%7B6%7D%5C%5C%2018%3D6k%5C%5C%5Cfrac%7B18%7D%7B6%7D%3Dk%5C%5C%203%3Dk)
the constant of variation is 3.