Question

A quantity b varies jointly with c and d and inversely with eWhen b is 18, c is 4, d is 9, and e is 6What is the constant of variation?

Answer 1

Answer:

$b=\frac{3cd}{e}$

Step-by-step explanation:

b ∝ c d*  $\frac{1}{e}$

$b=\frac{kcd}{e}$

Now substitute the values to find k

$18=\frac{k*4*9}{6} \\36k=108\\k=\frac{108}{36} \\k=3$

The relationship will be:

$b=\frac{kcd}{e}\\b=\frac{3cd}{e}$

Answer 2

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∝$\frac{1}{e}$

and i will call the constant of variation k, this way we can make an equation for b in the following form:

$b=k\frac{cd}{e}$

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:

$b=18\\c=4\\d=9\\e=6$

substituting this in our equation for b:

$b=k\frac{cd}{e}\\ 18=k\frac{(4)(9)}{6}$

and we solve operations and clear for the constant of variation k:

$18=k\frac{36}{6}\\ 18=6k\\\frac{18}{6}=k\\ 3=k$

the constant of variation is 3.