Answer:
If I read it right I believe it's C.
Step-by-step explanation:
Answer:
![\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%3D%20kx%28t%29%5B1000-x%28t%29%5D%2C%24%20%20x%280%29%3D0)
Step-by-step explanation:
Total Number of People on Campus =1000
Let the number of people who have contracted the flu =x(t)
Therefore, the number of people who have not contracted the flu =1000-x(t)
Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.
![\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)]](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%5Cpropto%20x%28t%29%5B1000-x%28t%29%5D)
Introducing the proportional constant k, we obtain:
![\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)]](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%3D%20kx%28t%29%5B1000-x%28t%29%5D)
At t=0, there was no infected on the campus, therefore the initial condition is given:

Therefore, a differential equation for the number of people x(t) who have contracted the flu is:
![\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%28t%29%7D%7Bdt%7D%20%3D%20kx%28t%29%5B1000-x%28t%29%5D%2C%24%20%20x%280%29%3D0)
2 and 4 are both factors of 8, which means any multiple of 8 can be divided by both 2 and 4 since 8 can be. So, Jose and Jamila are both right.
<span><span> y2(q-4)-c(q-4)</span> </span>Final result :<span> (q - 4) • (y2 - c)
</span>
Step by step solution :<span>Step 1 :</span><span>Equation at the end of step 1 :</span><span><span> ((y2) • (q - 4)) - c • (q - 4)
</span><span> Step 2 :</span></span><span>Equation at the end of step 2 :</span><span> y2 • (q - 4) - c • (q - 4)
</span><span>Step 3 :</span>Pulling out like terms :
<span> 3.1 </span> Pull out q-4
After pulling out, we are left with :
(q-4) • (<span> y2</span> * 1 +( c * (-1) ))
Trying to factor as a Difference of Squares :
<span> 3.2 </span> Factoring: <span> y2-c</span>
Theory : A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 <span>- AB + AB </span>- B2 =
<span> A2 - B2</span>
</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.
Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.
Check : <span> y2 </span>is the square of <span> y1 </span>
Check :<span> <span> c1 </span> is not a square !!
</span>Ruling : Binomial can not be factored as the difference of two perfect squares
Final result :<span> (q - 4) • (y2 - c)
</span><span>
</span>
Answer:
22.5 hours
Step-by-step explanation:
191.25 divided by 8.50 hours will get you the total amount of hours she worked