Answer
(a) Respectively: $4400$ and $1665$
(b) The blood moves faster when it is closer to the central axis.
(c)\begin{matrix}
r & v(r) \\
0 & 4625 \\
0.1 & 4400 \\
0.2 & 3885 \\
0.3 & 2960 \\
0.4 & 1665 \\
0.5 & 0 \\
\end{matrix}
(d) $-4400$
Work Step by Step
(a) Substitute the values for $r$ into the function and use a calculator to find $v(r)$ in each case.
$$v(0.1) = 18500(0.25 - (0.1)^2)= 4400$$
$$v(0.4) = 18500(0.25 - (0.4)^2)= 1665$$
(b) The velocity increases when $r$ decreases. Therefore, The blood moves faster when it is closer to the central axis, where r = 0.
(c)
Use the values calculated before, calculate $v(0)$, $v(0.2)$, $v(0.3)$ and $v(0.5)$. Then make a table of values.
$$v(0) = 18500(0.25 - (0)^2)= 4625$$
$$v(0.2) = 18500(0.25 - (0.2)^2)= 3885$$
$$v(0.3) = 18500(0.25 - (0.3)^2)= 2960$$
$$v(0.5) = 18500(0.25 - (0.5)^2)= 0$$
\begin{matrix}
r & v(r) \\
0 & 4625 \\
0.1 & 4400 \\
0.2 & 3885 \\
0.3 & 2960 \\
0.4 & 1665 \\
0.5 & 0 \\
\end{matrix}
(d)
$v(0.5) - v(0.1) = 0 - 4400 = -4400$
