Let $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$

Multiple Choice

Let $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$ and assume that $z > 0$ If $\frac { d x } { d t } = - 25$ and $\frac { d y } { d t } = - \frac { 50 } { 3 }$ when $x = 200$ and $y = 150 \text {, }$ then $\frac { d z } { d t }$ is

A) -40
B) -30
C) 30
D) 40
E) 50