Easy. There is a pattern on the graph. Each baseball card set costs $4. If you add $4 to the $16 (because that is what she will have left after buying 1 baseball card set), you will get $20. So the answer is $20
Answer:
0.01 x 2.40=0.024
Step-by-step explanation:
Answer:
![s = 21\ ft\\\\a = -6\ \frac{ft}{s^2}](https://tex.z-dn.net/?f=s%20%3D%2021%5C%20ft%5C%5C%5C%5Ca%20%3D%20-6%5C%20%5Cfrac%7Bft%7D%7Bs%5E2%7D)
Step-by-step explanation:
To find the changes in the slope of the function s(t) we find its derivative
![\frac{ds(t)}{dt} = 3t^2 - 18t +24\\](https://tex.z-dn.net/?f=%5Cfrac%7Bds%28t%29%7D%7Bdt%7D%20%3D%203t%5E2%20-%2018t%20%2B24%5C%5C)
Now we make ![\frac{ds(t)}{dt} = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bds%28t%29%7D%7Bdt%7D%20%3D%200)
![3t^2 - 18t +24 = 0](https://tex.z-dn.net/?f=3t%5E2%20-%2018t%20%2B24%20%3D%200)
![3t^2 - 18t +24\\\\3(t^2-6t + 8)\\\\3(t-4)(t-2)\\\\t_1 =4\\t_2=2\\](https://tex.z-dn.net/?f=3t%5E2%20-%2018t%20%2B24%5C%5C%5C%5C3%28t%5E2-6t%20%2B%208%29%5C%5C%5C%5C3%28t-4%29%28t-2%29%5C%5C%5C%5Ct_1%20%3D4%5C%5Ct_2%3D2%5C%5C)
The particle changes direction for the first time at t = 2 sec
The position at t = 2 sec is:
![s(t=2) = (2)^3 - 9(2)^2 + 24(2) + 1\\\\\s(2) = 21\ ft](https://tex.z-dn.net/?f=s%28t%3D2%29%20%3D%20%282%29%5E3%20-%209%282%29%5E2%20%2B%2024%282%29%20%2B%201%5C%5C%5C%5C%5Cs%282%29%20%3D%2021%5C%20ft)
The acceleration after t = 2 sec is the second derivative of s(t), evaluated at t = 2:
![\frac{d^2s(t)}{d^2t} = 6t -18\\\\\frac{d^2s(t)}{d^2t}(2) = 6(2) -18\\\\ a = 12-18\\\\a = -6\ \frac{ft}{s^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2s%28t%29%7D%7Bd%5E2t%7D%20%3D%206t%20-18%5C%5C%5C%5C%5Cfrac%7Bd%5E2s%28t%29%7D%7Bd%5E2t%7D%282%29%20%3D%206%282%29%20-18%5C%5C%5C%5C%20a%20%3D%2012-18%5C%5C%5C%5Ca%20%3D%20-6%5C%20%5Cfrac%7Bft%7D%7Bs%5E2%7D)