Find the minimum distance between the parabolas $y=x^2+4$ and $x=y^2.$ Hint: Parameterize the first parabola as $r_1(t)=($:$t,t^2+4$:$)$ and the second parabola as $r_2(s)=($:$s^2,s$:$).$ Then minimize the distance function $d(s,t)=||r_1(t)-r_2(s)||.$ Since the function is positive, this is most easily done by minimizing its square. You may need to use Mathematica or your calculator to get the solution.

Find the volume of the region in the first octant bounded by $y=1-x^2,z=1,$ and $z+y=3.$

pls answer these $2$ questions for me$.$ thank you