Answer:
[tex]r = {(\frac{v}{27} ) } ^{2} \: - p [/tex]
Step-by-step explanation:
[tex]v = {3}^{3} \sqrt{p + r} \\ v = 27 \sqrt{p + r} \\ \frac{v}{27} = \frac{27 \sqrt{p + r} }{27} \\ [/tex]
[tex]\frac{v}{27} = \sqrt{p + r} \\ {(\frac{v}{27} ) }^{2} = p + r \\ {(\frac{v}{27} ) } ^{2} \: - p = r \\ [/tex]
Answer:
[tex]\displaystyle r=\frac{v^2 }{3^{6} }-p[/tex]
Step-by-step explanation:
[tex]v=3^3(\sqrt{p+r} )[/tex]
Divide both sides by 3³.
[tex]\frac{v}{3^3 } =\frac{3^3(\sqrt{p+r} )}{3^3}[/tex]
[tex]\frac{v}{3^3 } =\sqrt{p+r}[/tex]
Square both sides.
[tex](\frac{v}{3^3 }) ^2 =(\sqrt{p+r})^2[/tex]
[tex]\frac{v^2 }{3^{3 \times 2} }=(\sqrt{p+r})^2[/tex]
[tex]\frac{v^2 }{3^{6} }=p+r[/tex]
Subtract p from both sides.
[tex]\frac{v^2 }{3^{6} }-p=p+r-p[/tex]
[tex]\frac{v^2 }{3^{6} }-p=r[/tex]
Switch sides.
[tex]r=\frac{v^2 }{3^{6} }-p[/tex]
