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A steel wire is drawn from an initial diameter $(d_i$) of $10 \: mm$ to a final diameter ($d_f$) of the $7.5 \: mm$. The half cone angle ($\alpha$) of the die is $5^{\circ}$ and the coefficient of friction ($\mu$) between the die and the wire is $0.1$. The average of the initial and final yield stress $[(\sigma_Y)_{avg}]$ is $350 \: MPa$. The equation for drawing stress $\sigma_f$, in (in MPa) is given as: $$\sigma_f=(\sigma_Y)_{avg} \bigg\{ 1+ \frac{1}{\mu \cot \alpha} \bigg\} \bigg[1- \bigg( \frac{d_f}{d_i} \bigg) ^{2 \mu \: \cot \alpha} \bigg]$$ The drawing stress (in MPa) required to carry out this operation is _____ (correct to two decimal places)
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