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∝[tex]\frac{1}{e}[/tex]
and i will call the constant of variation k, this way we can make an equation for b in the following form:
[tex]b=k\frac{cd}{e}[/tex]
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:
[tex]b=18\\c=4\\d=9\\e=6[/tex]
substituting this in our equation for b:
[tex]b=k\frac{cd}{e}\\ 18=k\frac{(4)(9)}{6}[/tex]
and we solve operations and clear for the constant of variation k:
[tex]18=k\frac{36}{6}\\ 18=6k\\\frac{18}{6}=k\\ 3=k[/tex]
the constant of variation is 3.
Answer:
[tex]b=\frac{3cd}{e}[/tex]
Step-by-step explanation:
b ∝ c d* [tex]\frac{1}{e}[/tex]
[tex]b=\frac{kcd}{e}[/tex]
Now substitute the values to find k
[tex]18=\frac{k*4*9}{6} \\36k=108\\k=\frac{108}{36} \\k=3[/tex]
The relationship will be:
[tex]b=\frac{kcd}{e}\\b=\frac{3cd}{e}[/tex]
