Answer:
7. is 5 - 35n
8. is -6x - 24
9. is 15m - 30
10. is 24p - 28
11. is 5b - 5
12. 5x + 45
RULE:
WHEN MULTIPLYING TWO NEGATIVES YOU WILL GET POSITIVE.
IF ONE IS NEGATIVE AND THE OTHER IS POSITIVE WHEN MULTIPLYING IT WILL BE NEGATIVE.
WHEN MULTIPLYING TWO POSITIVE NUMBERS IT WILL ALWAYS BE POSITIVE
SAME THING IF YOU MULTIPLY A POSITIVE NUMBER WITH A NEGATIVE NUMBER YOU GET A NEGATIVE AS YOUR ANSWER
YOU NEED ONE SIGN OF THE SAME WHEN MULTIPLYING TO BE A POSITIVE AS YOUR ANSWER
YOU NEED ONE SIGN TO BE DIFFERENT FROM THE OTHER WHEN MULTIPLYING TO GET A NEGATIVE AS YOUR ANSWER
Answer:
Differential equation
![\frac{dy}{dt} =ky(1-y)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3Dky%281-y%29)
Solution
![y=\frac{1}{1+4e^{-0.327t}}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B1%2B4e%5E%7B-0.327t%7D%7D)
Value of constant k=0.327 days^(-1)
The rumor reaches 80% at 8.48 days.
Step-by-step explanation:
We know
y(t): proportion of people that heard the rumor
y'(t)=ky(1-y), rate of spread of the rumor
Differential equation
![\frac{dy}{dt} =ky(1-y)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3Dky%281-y%29)
Solving the differential equation
![\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7By%281-y%29%7D%3Dk%5Ccdot%20dt%20%5C%5C%5C%5C%5Cint%20%5Cfrac%7Bdx%7D%7By%281-y%29%7D%20%3Dk%20%5Cint%20dt%20%5C%5C%5C%5C-ln%281-%5Cfrac%7B1%7D%7By%7D%20%29%2BC_0%3Dkt%5C%5C%5C%5C1-%5Cfrac%7B1%7D%7By%7D%20%3DCe%5E%7B-kt%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7By%7D%20%3D1-Ce%5E%7B-kt%7D%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B1-Ce%5E%7B-kt%7D%7D)
Initial conditions:
![y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}](https://tex.z-dn.net/?f=y%280%29%3D0.2%5C%5Cy%283%29%3D0.4%5C%5C%5C%5Cy%280%29%3D0.2%3D%5Cfrac%7B1%7D%7B1-Ce%5E0%7D%5C%5C%5C%5C1-C%3D1%2F0.2%5C%5C%5C%5CC%3D1-1%2F0.2%3D%20-4%5C%5C%5C%5C%5C%5Cy%283%29%3D0.4%3D%5Cfrac%7B1%7D%7B1%2B4e%5E%7B-3k%7D%7D%20%5C%5C%5C%5C1%2B4e%5E%7B-3k%7D%3D1%2F0.4%5C%5C%5C%5Ce%5E%7B-3k%7D%3D%282.5-1%29%2F4%3D0.375%5C%5C%5C%5Ck%3Dln%280.375%29%2F%28-3%29%3D0.327%5C%5C%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B1%2B4e%5E%7B-0.327t%7D%7D)
Value of constant k=0.327 days^(-1)
At what time the rumor reaches 80%?
![y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48](https://tex.z-dn.net/?f=y%28t%29%3D0.8%3D%5Cfrac%7B1%7D%7B1%2B4e%5E%7B-0.327t%7D%7D%20%5C%5C%5C%5C1%2B4e%5E%7B-0.327t%7D%3D1%2F0.8%3D1.25%5C%5C%5C%5Ce%5E%7B-0.327t%7D%3D%281.25-1%29%2F4%3D0.0625%5C%5C%5C%5Ct%3Dln%280.0625%29%2F%28-0.327%29%3D8.48)
The rumor reaches 80% at 8.48 days.
Answer:
D..........
Step-by-step explanation:
rgW
Answer:
Step-by-step explanation:
She gave out three dozen and she had six dozen so she has three dozen left three dozen 3 * 12 she has 36 cookies
24 divide by two is 12
so x is 24