The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
![t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Substituting:
![\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81-4%282%29%28-18%29%7D%7D%7B2%282%29%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B81%2B144%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm%5Csqrt%5B%5D%7B225%7D%7D%7B4%7D%20%5C%5C%20t%3D%5Cfrac%7B9%5Cpm15%7D%7B4%7D%20%5Cend%7Bgathered%7D)
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
Answer:
A
Step-by-step explanation:
the probability should always be the same unless the event is different.
Did you mean to include an image?
Order of operations
5/8 = 0.625
1/4 = 0.25
0.25*2 = 0.5
0.625-0.5 = 0.125
so the final answer is 0.125
Answer:
F.
Explanation:
The number of quarts of cream Type A is x.
Type A cream has 18% butterfat, so the amount butterfat will be 0.18x
For type B, we know that the total amount of cream will be 90, so if cream type A is x, cream type B is 90 - x.
Type B crem has 24% butterfat, so teh amount in the mixture will be 0.24(90-x)
Then, the mixture will be 90 quarts of crean that is 22% butterfat, so the amount in the mixture will be 0.22(90)
Therefore, the table that represent this data is table F.
So, the answer is F.
