42 / 38x
This sentence is just to fill up space.
Answer:
Jo started decelerating at the 10th minute
His average speed for the last 30 minutes of the journey is 4/30 km/minute
Step-by-step explanation:
To get what Jo did at 10 minute, we look at the graph.
At the 10th minute, we can see that we have a sharp turn from the top to the zero position at the 20th minute
so we can say that Jo started deceleration at the 10th minute
For the last 30 minutes of the journey, he travelled a distance of 4km
So, mathematically, his average speed will be;
Distance/ time = 4km/30 minutes = 4/30 km/minute
Answer:
![\boxed{C. \: x = 2}](https://tex.z-dn.net/?f=%20%5Cboxed%7BC.%20%5C%3A%20x%20%3D%202%7D%20)
Step-by-step explanation:
![= > Solve \: for \: x \: over \: the \: integers: \\ 3 |x - 6| = 12 \\ \\ = > Divide \: both \: sides \: by \: 3: \\ |x - 6| = 4 \\ \\ = > Split \: the \: equation \: into \: two \: possible \: cases: \\ x - 6 = 4 \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: x - 6 = -4 \\ \\ = > Add \: 6 \: to \: both \: sides: \\ x = 10 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: x = 2 \\ \\ Answer: x = 10 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: x = 2](https://tex.z-dn.net/?f=%20%20%3D%20%20%3E%20Solve%20%5C%3A%20%20for%20%20%5C%3A%20x%20%20%5C%3A%20over%20%20%5C%3A%20the%20%5C%3A%20%20integers%3A%20%5C%5C%203%20%7Cx%20-%206%7C%20%3D%2012%20%5C%5C%20%20%5C%5C%20%3D%20%20%3E%20Divide%20%20%5C%3A%20both%20%5C%3A%20%20sides%20%5C%3A%20%20by%20%20%5C%3A%203%3A%20%5C%5C%20%7Cx%20-%206%7C%20%20%3D%204%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20Split%20%5C%3A%20%20the%20%5C%3A%20%20equation%20%5C%3A%20%20into%20%20%5C%3A%20two%20%5C%3A%20%20possible%20%20%5C%3A%20cases%3A%20%5C%5C%20x%20-%206%20%3D%204%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20x%20-%206%20%3D%20-4%20%5C%5C%20%20%5C%5C%20%3C%2Fp%3E%3Cp%3E%20%3D%20%20%3E%20Add%20%20%5C%3A%206%20%20%5C%3A%20to%20%5C%3A%20%20both%20%20%5C%3A%20sides%3A%20%5C%5C%20%3C%2Fp%3E%3Cp%3Ex%20%3D%2010%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20or%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20x%20%20%3D%202%20%5C%5C%20%20%5C%5C%20Answer%3A%20x%20%3D%2010%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20or%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20x%20%3D%202)
The half-life of the element is 13 minutes, which means after 13 minutes, any starting amount decays to half. So element X decays with a rate k such that
![\dfrac12 = e^{13k}](https://tex.z-dn.net/?f=%5Cdfrac12%20%3D%20e%5E%7B13k%7D)
Solve for k :
![\ln\left(\dfrac12\right) = \ln\left(e^{13k}\right)](https://tex.z-dn.net/?f=%5Cln%5Cleft%28%5Cdfrac12%5Cright%29%20%3D%20%5Cln%5Cleft%28e%5E%7B13k%7D%5Cright%29)
![-\ln(2) = 13k \ln(e)](https://tex.z-dn.net/?f=-%5Cln%282%29%20%3D%2013k%20%5Cln%28e%29)
![-\ln(2) = 13k](https://tex.z-dn.net/?f=-%5Cln%282%29%20%3D%2013k)
![\implies k = -\dfrac{\ln(2)}{13}](https://tex.z-dn.net/?f=%5Cimplies%20k%20%3D%20-%5Cdfrac%7B%5Cln%282%29%7D%7B13%7D)
Now, we solve for t such that
![36 = 710e^{kt}](https://tex.z-dn.net/?f=36%20%3D%20710e%5E%7Bkt%7D)
![e^{kt} = \dfrac{18}{355}](https://tex.z-dn.net/?f=e%5E%7Bkt%7D%20%3D%20%5Cdfrac%7B18%7D%7B355%7D)
![\ln\left(e^{kt}\right) = \ln\left(\dfrac{18}{355}\right)](https://tex.z-dn.net/?f=%5Cln%5Cleft%28e%5E%7Bkt%7D%5Cright%29%20%3D%20%5Cln%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29)
![kt = \ln\left(\dfrac{18}{355}\right)](https://tex.z-dn.net/?f=kt%20%3D%20%5Cln%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29)
![-\dfrac{\ln(2)}{13} t = \ln\left(\dfrac{18}{355}\right)](https://tex.z-dn.net/?f=-%5Cdfrac%7B%5Cln%282%29%7D%7B13%7D%20t%20%3D%20%5Cln%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29)
![\implies t = -\dfrac{13 \ln\left(\frac{18}{355}\right)}{\ln(2)}](https://tex.z-dn.net/?f=%5Cimplies%20t%20%3D%20-%5Cdfrac%7B13%20%5Cln%5Cleft%28%5Cfrac%7B18%7D%7B355%7D%5Cright%29%7D%7B%5Cln%282%29%7D)
![\implies t = -13 \log_2\left(\dfrac{18}{355}\right) \approx \boxed{55.9}](https://tex.z-dn.net/?f=%5Cimplies%20t%20%3D%20-13%20%5Clog_2%5Cleft%28%5Cdfrac%7B18%7D%7B355%7D%5Cright%29%20%5Capprox%20%5Cboxed%7B55.9%7D)
Absolute value of -3.25 is 3.25, so you will find it between 2.3 and 3.3 (D)