Consider an I$-$beam section with unequal flanges $($Figure $2),$ where $w_1=9\mathrm{.}5$ in$.,h=8$ in$.,w_2=4$ in$.,f=0\mathrm{.}5$ in$.,$ and $w=1$ in$.$ The beam is subjected to a moment so that the internal moment on the section is about the $z-$axis.

Part A $-$ Locate the centroid

Since the widths of the two flanges are not the same, the centroid is not readily apparent. What is the distance $\frac{?}{\text{b}\text{a}\text{r}}(y{)}^{\text{'}}$ from the bottom of the section to the centroid? $($Figure $3)$

Express your answer with appropriate units to three significant figures.

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$\frac{?}{\text{b}\text{a}\text{r}}(y{)}^{\text{'}}=$

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Part B $-$ Calculate the moment of inertia

Once the position of the centroid is known, the moment of inertia can be calculated. What is the moment of inertia of the section for bending around the $z-$axis?

Express your answer to three significant figures and include the appropriate units.

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$I=$