Answer:
Option A is the answer
Step-by-step explanation:
From the question we are told that
The mean of laborers is 3
The standard deviation is 1
The mean of white collar workers is 7
The standard deviation for white collar workers is 3.16
From this value given we can see that the white collar worker is more dissatisfied than the laborers
Also the from the value of standard deviation of the laborers we see that the deviation from the mean is 1 which means that they are equally dissatisfied
But in the case of white collar workers we see deviation from the mean is very high which implies that the dissatisfaction varies more with white collar workers
Let
and
denote the Laplace transforms of
and
.
Taking the Laplace transform of both sides of both equations, we have
![\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%7D%7Bdt%7D%20%2B%203x%20%2B%20%5Cdfrac%7Bdy%7D%7Bdt%7D%20%3D%201%20%5Cimplies%20%5Cleft%28sX%28s%29%20-%20x%280%29%5Cright%29%20%2B%203X%28s%29%20%2B%20%5Cleft%28sY%28s%29%20-%20y%280%29%5Cright%29%20%3D%20%5Cdfrac1s%20%5C%5C%5C%5C%20%5Cimplies%20%28s%2B3%29%20X%28s%29%20%2B%20s%20Y%28s%29%20%3D%20%5Cdfrac1s)
![\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%7D%7Bdt%7D%20-%20x%20%2B%20%5Cdfrac%7Bdy%7D%7Bdt%7D%20%3D%20e%5Et%20%5Cimplies%20%5Cleft%28sX%28s%29%20-%20x%280%29%5Cright%29%20-%20X%28s%29%20%2B%20%5Cleft%28sY%28s%29%20-%20y%280%29%5Cright%29%20%3D%20%5Cdfrac1%7Bs-1%7D%20%5C%5C%5C%5C%20%5Cimplies%20%28s-1%29%20X%28s%29%20%2B%20s%20Y%28s%29%20%3D%20%5Cdfrac1%7Bs-1%7D)
Eliminating
, we get
![\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)](https://tex.z-dn.net/?f=%5Cleft%28%28s%2B3%29%20X%28s%29%20%2B%20s%20Y%28s%29%5Cright%29%20-%20%5Cleft%28%28s-1%29%20X%28s%29%20%2B%20s%20Y%28s%29%5Cright%29%20%3D%20%5Cdfrac1s%20-%20%5Cdfrac1%7Bs-1%7D%20%5C%5C%5C%5C%20%5Cimplies%20X%28s%29%20%3D%20%5Cdfrac14%20%5Cleft%28%5Cdfrac1s%20-%20%5Cdfrac1%7Bs-1%7D%5Cright%29)
Take the inverse transform of both sides to solve for
.
![\boxed{x(t) = \dfrac14 (1 - e^t)}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%28t%29%20%3D%20%5Cdfrac14%20%281%20-%20e%5Et%29%7D)
Solve for
.
![(s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}](https://tex.z-dn.net/?f=%28s%20-%201%29%20X%28s%29%20%2B%20s%20Y%28s%29%20%3D%20%5Cdfrac1%7Bs-1%7D%20%5Cimplies%20-%5Cdfrac1%7B4s%7D%20%2B%20s%20Y%28s%29%20%3D%20%5Cdfrac1%7Bs-1%7D%20%5C%5C%5C%5C%20%5Cimplies%20s%20Y%28s%29%20%3D%20%5Cdfrac1%7Bs-1%7D%20%2B%20%5Cdfrac1%7B4s%7D%20%5C%5C%5C%5C%20%5Cimplies%20Y%28s%29%20%3D%20%5Cdfrac1%7Bs%28s-1%29%7D%20%2B%20%5Cdfrac1%7B4s%5E2%7D%20%5C%5C%5C%5C%20%5Cimplies%20Y%28s%29%20%3D%20%5Cdfrac1%7Bs-1%7D%20-%20%5Cdfrac1s%20%2B%20%5Cdfrac1%7B4s%5E2%7D)
Taking the inverse transform of both sides, we get
![\boxed{y(t) = e^t - 1 + \dfrac14 t}](https://tex.z-dn.net/?f=%5Cboxed%7By%28t%29%20%3D%20e%5Et%20-%201%20%2B%20%5Cdfrac14%20t%7D)
5.8/100 = x/18,801,310 ==================================>
x = 1,090,475.98
=================================>
18,801,310 + 1,090,475.98 = 19,891,785.98 population at 2014
=============================>
19,891,785.98/53,625 =
about 371 people per square mile in 2014
=================================>
18,801,310/53,625 =
about 351 people per square mile in 2010
=================================>
371 - 351 = 20 people per square mile increase from 2010 to 2014
Answer:
(-2,5)
Step-by-step explanation:
Answer:
y=30
Step-by-step explanation:
y-8=22
Add 8 on both sides
y=30