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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?

User Xueke
by
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2 Answers

4 votes

Answer:


b=(3cd)/(e)

Explanation:

b ∝ c d*
(1)/(e)


b=(kcd)/(e)

Now substitute the values to find k


18=(k*4*9)/(6) \\36k=108\\k=(108)/(36) \\k=3

The relationship will be:


b=(kcd)/(e)\\b=(3cd)/(e)

User Ye Shiqing
by
8.1k points
3 votes

Answer:

constant of variation = 3

Explanation:

we know that b varies jointly with c and d

so:

b∝c∝d

and b varies inversely with e, so

b∝
(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(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(cd)/(e)\\ 18=k((4)(9))/(6)

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


18=k(36)/(6)\\ 18=6k\\(18)/(6)=k\\ 3=k

the constant of variation is 3.

User Denis Voloshin
by
8.2k points
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