Respuesta :

[tex]\bf \begin{array}{llllll} \textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\ \textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\ y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x} \\ &&y=\cfrac{{{ k}}}{x} \end{array}\\\\ -------------------------------\\\\ \textit{R is inversely proportional to }\sqrt{F}\implies R=\cfrac{k}{\sqrt{F}} \\\\\\ [/tex]

[tex]\bf \textit{we also know that } \begin{cases} R=32\\ F=16 \end{cases}\implies 32=\cfrac{k}{\sqrt{16}}\implies 32\sqrt{16}=k \\\\\\ 32\cdot 4=k\implies \boxed{128=k}\impliedby \textit{constant of variation} \\\\\\ thus\implies R=\cfrac{128}{\sqrt{F}}\\\\ -------------------------------\\\\ \textit{what's F when R=16?}\implies 16=\cfrac{128}{\sqrt{F}}\implies \sqrt{F}=\cfrac{128}{16} \\\\\\ \sqrt{F}=8\implies F=8^2\implies F=64[/tex]
mreijepatmat
R is inversely proportional to the square root of F.

Let k, be the coefficient of proportionality, then

1)- R = k/√F, Calculate k:
32 =k/√16, Square both sides: 32² = k²/(√16), 1024 =k²/16, k²= 16384, k=√16384 or k = 128

2) Find F if R=16

R = k/√F;  16 = 128/√F; Square both sides; 16² = (128)²/(√F)²

256 = 16384/F ;  F= 16384/256 and F = 64

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