Answer:
15ft
Step-by-step explanation:
30 divides by 15 to make 2 and 45 divides by 15 to make 3. 5 equal pieces of wire each 15ft
40.7..........................
Answer:
2/7
Step-by-step explanation:
16yr:28yr simplified is:
2:7
then as a fraction it's 2/7
Hope it helps:)
Explanation
The model has the form
![y=ae^{-kt}](https://tex.z-dn.net/?f=y%3Dae%5E%7B-kt%7D)
Where a=initial amount
y= final amount
K= growth rate constant
t= time
When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.
![\begin{gathered} 140=400e^{-7k} \\ e^{-7k}=\frac{140}{400} \\ e^{-7k}=\frac{7}{20} \\ \ln (e^{-7k})=\ln (\frac{7}{20}) \\ -7k=\ln (\frac{7}{20}) \\ k=\frac{\ln(\frac{7}{20})}{-7} \\ \therefore k=\frac{\ln (\frac{20}{7})}{7} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20140%3D400e%5E%7B-7k%7D%20%5C%5C%20e%5E%7B-7k%7D%3D%5Cfrac%7B140%7D%7B400%7D%20%5C%5C%20e%5E%7B-7k%7D%3D%5Cfrac%7B7%7D%7B20%7D%20%5C%5C%20%5Cln%20%28e%5E%7B-7k%7D%29%3D%5Cln%20%28%5Cfrac%7B7%7D%7B20%7D%29%20%5C%5C%20-7k%3D%5Cln%20%28%5Cfrac%7B7%7D%7B20%7D%29%20%5C%5C%20k%3D%5Cfrac%7B%5Cln%28%5Cfrac%7B7%7D%7B20%7D%29%7D%7B-7%7D%20%5C%5C%20%5Ctherefore%20k%3D%5Cfrac%7B%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%7D%7B7%7D%20%5Cend%7Bgathered%7D)
Therefore, the first solution is
![y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}](https://tex.z-dn.net/?f=y%3D400e%5E%7B-%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%5Cfrac%7Bt%7D%7B7%7D%7D)
For part b we have 16 hours.
![\begin{gathered} y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}=400e^{-\ln (\frac{20}{7})\frac{16}{7}} \\ y=36.302\approx36\operatorname{kg}\text{ (To the nearest whole number)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D400e%5E%7B-%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%5Cfrac%7Bt%7D%7B7%7D%7D%3D400e%5E%7B-%5Cln%20%28%5Cfrac%7B20%7D%7B7%7D%29%5Cfrac%7B16%7D%7B7%7D%7D%20%5C%5C%20y%3D36.302%5Capprox36%5Coperatorname%7Bkg%7D%5Ctext%7B%20%28To%20the%20nearest%20whole%20number%29%7D%20%5Cend%7Bgathered%7D)
Thus, the answer is 36kg