8.00 $ Because if she spent 4 fourths she would have no money left so multiply 2 times four and you get 8. Your welcome ;)
How many ounces of nuts are needed to what?
Answer:
76.09 pounds
Step-by-step explanation:
From the information given:
![R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)](https://tex.z-dn.net/?f=R_%7Bin%7D%20%3D%20%28%5Cdfrac%7B1%7D%7B2%7D%20%5C%20lb%2Fgal%20%29%20%2A%286%20%5C%20gal%2Fmin%29)
![R_{in} =3 \ lb/min](https://tex.z-dn.net/?f=R_%7Bin%7D%20%3D3%20%5C%20lb%2Fmin)
At a slower of 4 gal/min, the solution gets pumped out;
So,
![R_{out} = \dfrac{4A}{100+(6-4)t }](https://tex.z-dn.net/?f=R_%7Bout%7D%20%3D%20%5Cdfrac%7B4A%7D%7B100%2B%286-4%29t%20%7D)
![R_{out} = \dfrac{2A}{50+t }](https://tex.z-dn.net/?f=R_%7Bout%7D%20%3D%20%5Cdfrac%7B2A%7D%7B50%2Bt%20%7D)
The differential of the equation is:
![\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%2B%20%5Cdfrac%7B2%7D%7B50%2Bt%7DA%3D3%20---%281%29)
For the linear differential equation, the integrating factor is determined as:
![\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|](https://tex.z-dn.net/?f=%5Cint_e%20%5Cdfrac%7B2%7D%7B50%20%2Bt%7Ddt%20%3D%20e%5E%7B2%20In%7C50%2Bt%7C)
![= (50+t)^2](https://tex.z-dn.net/?f=%3D%20%2850%2Bt%29%5E2)
Multiplying
with the above integration factor;
![(50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2](https://tex.z-dn.net/?f=%2850%2Bt%29%5E2%20%5Cdfrac%7BdA%7D%7Bdt%7D%20%2B%202%20%2850%2Bt%29%20A%20%3D%203%2850%20%2Bt%29%5E2)
![\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdt%7D%5B%20%2850%20%2Bt%29%5E2%20A%5D%20%3D%203%2850%2Bt%29%5E2)
![(50+t)^2 A = (50 +t)^3 + c](https://tex.z-dn.net/?f=%2850%2Bt%29%5E2%20A%20%3D%20%2850%20%2Bt%29%5E3%20%2B%20c)
![A = (50 +t) + c (50 +t )^{-2}](https://tex.z-dn.net/?f=A%20%3D%20%2850%20%2Bt%29%20%2B%20c%20%2850%20%2Bt%20%29%5E%7B-2%7D)
By using the given condition:
A(0) = 40
40 = 50 + c (50)⁻²
10 = c(50)⁻²
OR
c = -10 × 2500
c = -25000
A = (50 + t) - 25000(50 + t)⁻²
The number of pounds of salt in the tank after 30 min is:
A(30) = (50+30) - 25000(50 + 30)⁻²
![A(30) = 80 - \dfrac{25000}{6400}](https://tex.z-dn.net/?f=A%2830%29%20%3D%2080%20-%20%5Cdfrac%7B25000%7D%7B6400%7D)
![A(30) = 76.09 \ pounds](https://tex.z-dn.net/?f=A%2830%29%20%3D%2076.09%20%5C%20pounds)
Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.
Answer is Rs 910 hope it helps you