Solve the following Algebra problems $(4)$

a$.5(x-3{)}^2=80,x$

b$.,D=D_{0}ex{p}^{-\frac{Q_D}{RT}}$

In each situation indicate $(A)$ whether the critical material property needing modification is Strength, Stiffness, Toughness, or Hardness and $($B$)$ if the property needs to be increased or decreased $(6)$

a$.$ A rope you are using to suspend a platform above a pit of fire is stretching too much and the platform is being singed$.$

A$.$

B$.$

b$.$ When a hitch pin is loaded it shears into two pieces.

A$.$

B$.$

c$.$ A rolling ball bearing is leaving track marks on the raceway of the bearing cup

A$.$

B$.$

Bonus

Match the crystal structure with its attributes $(4)$

Weak, Ductile, Malleable

Strong, Moderately ductile, Not Malleable

Weak, Not Ductile, Not Malleable

Not close packed structure

A FCC

B$.$ HCP

C$.$ BCC