Answer:
[tex]z=-2t^{\frac{-1}{2}}+-4.75[/tex]
Step-by-step explanation:
Integrate both sides:
[tex]z=\frac{t^{\frac{-3}{2}+1}}{\frac{-3}{2}+1}+C[/tex]
Simplify:
[tex]z=\frac{t^{\frac{-1}{2}}}{\frac{-1}{2}}+C[/tex]
[tex]z=-2t^{\frac{-1}{2}}+C[/tex]
Now to find [tex]C[/tex]. We are going to use [tex]z(64)=-5[/tex].
[tex]-5=-2(64)^{\frac{-1}{2}}+C[/tex]
[tex]-5=-2(\frac{1}{8})+C[/tex]
[tex]-5=\frac{-1}{4}+C[/tex]
Add 1/4 on both sides:
[tex]-4.75=C[/tex]
So the equation is:
[tex]z=-2t^{\frac{-1}{2}}+C[/tex]
