 Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2024/paper-1/b2/e/solution

d \overset{z}{ˉ} = c \overset{y}{ˉ}

. Substitute

\overset{y}{ˉ} = d \overset{z}{ˉ} / c

into the juvenile equation and cancel

\overset{z}{ˉ} > 0

\frac{d}{c} = \frac{r}{( b + z ˉ ) ^{2}} .

Thus

\overset{z}{ˉ} = \frac{cr}{d} - b, \overset{y}{ˉ} = \frac{d}{c} (\frac{cr}{d} - b) .

Both coordinates are positive precisely when $cr > d b^{2}$ .

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