Question

If J is jointly proportional to G and V, and J = √3 when G = √2 and V = √8, what is J when G = √6 and V = 8?

Trigonometric equation and identitie
ANSWERED
asked 2021-06-02
If J is jointly proportional to G and V, and J = √3 when G = √2 and V = √8, what is J when G = √6 and V = 8?

Expert Answers (2)

2021-06-03

We are given that J is jointly proportional to G and V so: J=kGV
Solve for k when \(\displaystyle{J}=√{3}\), \(G=√2\), and \(\displaystyle{V}=√{8}\): \(\displaystyle√{3}={k}{\left(√{2}\right)}{\left(√{8}\right)}\)
\(\displaystyle√{3}={k}√{16}\)
\(\displaystyle√{3}={4}{k}\)
\(\displaystyle√\frac{{3}}{{4}}={k}\)
So, the equation becomes: \(\displaystyle{J}={\left(√\frac{{3}}{{4}}\right)}{G}{V}\)
When \(\displaystyle{G}=√{6}\) and V=8, \(\displaystyle{J}=√\frac{{3}}{{4}}{\left(√{6}\right)}{\left({8}\right)}\)
\(\displaystyle{J}={2}√{18}\)
\(\displaystyle{J}={2}√{9}\cdot{2}\)
\(\displaystyle{J}={2}\cdot{3}√{2}\)
\(\displaystyle{J}={6}√{2}\)

17
 
Best answer
2021-10-10

Answer is given below (on video)

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