Question

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

Answer 1

`w=100-((100-k)^2)/(100)\\\\z={(100)/(\left(1-(k)/(100)\right)^2) -100`

Explanation:

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

`d=\left(1-(k)/(100)\right)c\\a=\left(1-(k)/(100)\right)d\\ \Rightarrow a=\left(1-(k)/(100)\right)^2c...........(1)\\`

`Again \ a=\left(1-(w)/(100)\right)c...........(2)\\`

from equation
`(1)` and
`(2)`

`\left(1-(k)/(100)\right)^2=\left(1-(w)/(100)\right)\\(w)/(100)=1-\left(1-(k)/(100)\right)^2\\w=100-((100-k)^2)/(100)`

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

`c=\left(1+(z)/(100)\right)a.......(3)\\`

from equation
`(1)` and
`(3)`

`a=\left(1-(k)/(100)\right)^2\left(1+(z)/(100)\right)a\\\left(1+(z)/(100)\right)=(1)/(\left(1-(k)/(100)\right)^2)\\(z)/(100)=(1)/(\left(1-(k)/(100)\right)^2)-1\\z=100\left[(1)/(\left(1-(k)/(100)\right)^2)-1\right]`