Answer:
here
Step-by-step explanation:
Method 1 Method 1 of 3: Making Liquid Cleaners
Mix equal parts water and vinegar in a spray bottle. Use distilled white vinegar and, if possible, distilled or filtered water.
Add lemon juice to disinfect surfaces. Mix one part lemon juice, one part white vinegar and two parts water in a spray bottle.
Add dish soap for persistent stains on carpet. ...
Tackle tough stains and grime with undiluted vinegar. ...
Answer:37
Step-by-step explanation:H-12=37
Answer:
1) ![y(t) = \frac{Ce^{4t} +3}{4}](https://tex.z-dn.net/?f=%20y%28t%29%20%3D%20%5Cfrac%7BCe%5E%7B4t%7D%20%2B3%7D%7B4%7D)
2) ![5 = \frac{C e^0 +3}{4}](https://tex.z-dn.net/?f=%205%20%3D%20%5Cfrac%7BC%20e%5E0%20%2B3%7D%7B4%7D)
![20 = C +3](https://tex.z-dn.net/?f=%2020%20%3D%20C%20%2B3)
![C= 20-3=17](https://tex.z-dn.net/?f=%20C%3D%2020-3%3D17)
So then the model would be given by:
![y(t) = \frac{20e^{4t} +3}{4}](https://tex.z-dn.net/?f=%20y%28t%29%20%3D%20%5Cfrac%7B20e%5E%7B4t%7D%20%2B3%7D%7B4%7D)
Step-by-step explanation:
For this case we have the following differential equation:
![y' = \frac{dy}{dt} = 4y-3](https://tex.z-dn.net/?f=%20y%27%20%3D%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%204y-3)
We can do this using algebra:
![\frac{dy}{4y-3} = dt](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7B4y-3%7D%20%3D%20dt)
Part 1
And now we can integrate both sides like this:
![\int \frac{dy}{4y-3} = \int dt](https://tex.z-dn.net/?f=%20%5Cint%20%5Cfrac%7Bdy%7D%7B4y-3%7D%20%3D%20%5Cint%20dt)
We can use the u substituton for the left part
![du = 4 dy](https://tex.z-dn.net/?f=%20du%20%3D%204%20dy)
We can multiply both sides by 4 and we got:
, where ![c=4k](https://tex.z-dn.net/?f=%20c%3D4k)
and after integrate the left part we got:
![ln |u| = 4t+c](https://tex.z-dn.net/?f=%20ln%20%7Cu%7C%20%3D%204t%2Bc)
And if we apply exponential on both sides we got:
![u = e^{4t} e^c](https://tex.z-dn.net/?f=%20u%20%3D%20e%5E%7B4t%7D%20e%5Ec)
Now we can replace u and we got:
where ![C=e^c](https://tex.z-dn.net/?f=C%3De%5Ec)
And then finally we have:
![y(t) = \frac{Ce^{4t} +3}{4}](https://tex.z-dn.net/?f=%20y%28t%29%20%3D%20%5Cfrac%7BCe%5E%7B4t%7D%20%2B3%7D%7B4%7D)
Part 2
For this case we have the initial condition y(0) =5 and if we use it we got:
![5 = \frac{C e^0 +3}{4}](https://tex.z-dn.net/?f=%205%20%3D%20%5Cfrac%7BC%20e%5E0%20%2B3%7D%7B4%7D)
![20 = C +3](https://tex.z-dn.net/?f=%2020%20%3D%20C%20%2B3)
![C= 20-3=17](https://tex.z-dn.net/?f=%20C%3D%2020-3%3D17)
So then the model would be given by:
![y(t) =\frac{17te^{4t} +3}{4}](https://tex.z-dn.net/?f=%20y%28t%29%20%3D%5Cfrac%7B17te%5E%7B4t%7D%20%2B3%7D%7B4%7D)
Answer:
1= 5x and 7x
2= 3x and 2x
Step-by-step explanation:
its hard to explain you just add them or minus them
The answer is 20. Hope it helps.