A diagram shows two similar right-angled triangles, riangle ABE and riangle ACD. BE is parallel to CD. AE = 6 m, ED = y m, BE = 5 m, CD = 8 m. AB = x m. Find x and y.

The diagram shows two similar right-angled triangles: $\triangle ABE$ and $\triangle ACD$. This is because BE is parallel to CD (both are perpendicular to AD).

From similar triangles, we have:

Given $AE = 6 \, \text{m}$, $ED = y \, \text{m}$, so $AD = AE + ED = (6+y) \, \text{m}$.
Given $BE = 5 \, \text{m}$ and $CD = 8 \, \text{m}$.
Substitute these values into the ratio:

In the right-angled triangle $\triangle ABE$, $AB$ is the hypotenuse ($x$), $AE$ is $6 \, \text{m}$, and $BE$ is $5 \, \text{m}$.

The values are:

1. a) Compound Interest:

Principal amount $P = 4000 \, \text{F}$
Annual interest rate $r = 6\% = 0.06$
Compounded quarterly, so $n = 4$ times per year
Time $t = 5$ years