Question

Write the expression for W in terms of K AND write the expression of Z in terms of K PLZ HELP

Answer 1

Answer:

$w=100-\frac{(100-k)^2}{100}\\\\z={\frac{100}{\left(1-\frac{k}{100}\right)^2} -100$

Step-by-step explanation:

$\underline{w \ in \ terms \ of \ z:}$

$d=\left(1-\frac{k}{100}\right)c\\a=\left(1-\frac{k}{100}\right)d\\ \Rightarrow a=\left(1-\frac{k}{100}\right)^2c...........(1)$

$Again \ a=\left(1-\frac{w}{100}\right)c...........(2)$

from equation $(1)$ and $(2)$

$\left(1-\frac{k}{100}\right)^2=\left(1-\frac{w}{100}\right)\\\frac{w}{100}=1-\left(1-\frac{k}{100}\right)^2\\w=100-\frac{(100-k)^2}{100}$

$\underline{z \ in \ terms \of \ w:}$

$c=\left(1+\frac{z}{100}\right)a.......(3)$

from equation $(1)$ and $(3)$

$a=\left(1-\frac{k}{100}\right)^2\left(1+\frac{z}{100}\right)a\\\left(1+\frac{z}{100}\right)=\frac{1}{\left(1-\frac{k}{100}\right)^2}\\\frac{z}{100}=\frac{1}{\left(1-\frac{k}{100}\right)^2}-1\\z=100\left[\frac{1}{\left(1-\frac{k}{100}\right)^2}-1\right]$