Answer:
x=49
Step-by-step explanation:
2(3x+1)=3(2−x)
Step 1: Simplify both sides of the equation.
2(3x+1)=3(2−x)
(2)(3x)+(2)(1)=(3)(2)+(3)(−x)(Distribute)
6x+2=6+−3x
6x+2=−3x+6
Step 2: Add 3x to both sides.
6x+2+3x=−3x+6+3x
9x+2=6
Step 3: Subtract 2 from both sides.
9x+2−2=6−2
9x=4
Step 4: Divide both sides by 9.
9x9=49
x=49
Answer:
3.48 hours
Step-by-step explanation:
The equation is:
![M(t)=20 e^{-0.86t}](https://tex.z-dn.net/?f=M%28t%29%3D20%20e%5E%7B-0.86t%7D)
Where
M(t) is the amount of medication remaining in mg
t is the time it takes, in hours
The questions asks HOW LONG it will take to make the remaining medication to 1 milligrams (1 mg)??
We have to substitute M(t) with "1" and find the corresponding value of "t". We will use natural log to solve this. Shown below:
![M(t)=20e^{-0.86t}\\1=20e^{-0.86t}\\0.05=e^{-0.86t}\\Ln(0.05)=Ln(e^{-0.86t})\\Ln(0.05)=(-0.86t)Ln(e)\\t=\frac{Ln(0.05)}{-0.86}\\t=3.48](https://tex.z-dn.net/?f=M%28t%29%3D20e%5E%7B-0.86t%7D%5C%5C1%3D20e%5E%7B-0.86t%7D%5C%5C0.05%3De%5E%7B-0.86t%7D%5C%5CLn%280.05%29%3DLn%28e%5E%7B-0.86t%7D%29%5C%5CLn%280.05%29%3D%28-0.86t%29Ln%28e%29%5C%5Ct%3D%5Cfrac%7BLn%280.05%29%7D%7B-0.86%7D%5C%5Ct%3D3.48)
<u>Note: </u> Ln(e) = 1
This means, the amount of time it will take is about 3.48 hours
The efficiency of Franklin: 200/14 ft^2/hr
Scott: 200/10 ft^2/hr
So together: 200 / (200/14 + 200/10) = 5.83 hours