Apply the r-transform to the following characteristic equations of a discrete-data control system 2 3 2 ( .) 1.5 1 0 ( .) 2 0.5 0 i z z ii z z z        (a) determine the equivalent characteristic equations in r. (b) apply routh-hurwitz to determine how many roots of the characteristic equation are in the left half r-plane, in the right half r-plane, and on the imaginary axis. (c) use matlab or labview mathscript to determine the roots of the z and r characteristic equations and confirm your results in part (b). (use "roots" to solve for the root locations.)

The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is

and similarly, the r% of female is

The number of males decreased by this quantity, so now it is

and the number of female increased by this quantity, so now it is

we know that these two new counts are the same number, so we can build and solve the equality

Subtract 20 and add 0.3r from both sides:

Divide both sides by 0.5 to solve for r:

Let's check the answer

The 20% of 30 is , while the 20% of 20 is 4. So, we are stating that which is true because both expressions evaluate to 24.