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
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?

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, $$\displaystyle{J}=√\frac{{3}}{{4}}{\left(√{6}\right)}{\left({8}\right)}$$
$$\displaystyle{J}={2}√{18}$$
$$\displaystyle{J}={2}√{9}\cdot{2}$$
$$\displaystyle{J}={2}\cdot{3}√{2}$$
$$\displaystyle{J}={6}√{2}$$

2021-10-10

Answer is given below (on video)