Answer: ![p_{2}(t)=(-8t^{2}+3t-5,7t^{2}+10,8t^{2}+6t+12)](https://tex.z-dn.net/?f=p_%7B2%7D%28t%29%3D%28-8t%5E%7B2%7D%2B3t-5%2C7t%5E%7B2%7D%2B10%2C8t%5E%7B2%7D%2B6t%2B12%29)
Step-by-step explanation: Velocity is the first derivative of position function, so:
![p'_{1}(t)=(-16t+3,14t,16t+6)](https://tex.z-dn.net/?f=p%27_%7B1%7D%28t%29%3D%28-16t%2B3%2C14t%2C16t%2B6%29)
Since in the second scene acceleration is zero, velocity must be constant, which means velocity in the second scene is the same as in the first scene, i.e.,
![p'_{2}(t)=p'_{1}(t)](https://tex.z-dn.net/?f=p%27_%7B2%7D%28t%29%3Dp%27_%7B1%7D%28t%29)
![p'_{2}(t) = (-16t+3,14t,16t+6)](https://tex.z-dn.net/?f=p%27_%7B2%7D%28t%29%20%3D%20%28-16t%2B3%2C14t%2C16t%2B6%29)
To determine position function, integrate it:
![p_{2}(t) = \int\limits {(-16t+3,14t,16t+6)} \, dt](https://tex.z-dn.net/?f=p_%7B2%7D%28t%29%20%3D%20%5Cint%5Climits%20%7B%28-16t%2B3%2C14t%2C16t%2B6%29%7D%20%5C%2C%20dt)
![p_{2}(t) = (-8t^{2}+3t+c_{1},7t^{2}+c_{2},8t^{2}+6t+c_{3})](https://tex.z-dn.net/?f=p_%7B2%7D%28t%29%20%3D%20%28-8t%5E%7B2%7D%2B3t%2Bc_%7B1%7D%2C7t%5E%7B2%7D%2Bc_%7B2%7D%2C8t%5E%7B2%7D%2B6t%2Bc_%7B3%7D%29)
Now, the "initial condition" is that
![p_{2}(0)=p_{1}(1)](https://tex.z-dn.net/?f=p_%7B2%7D%280%29%3Dp_%7B1%7D%281%29)
![p_{2}(0) = (c_{1}c_{2},c_{3})](https://tex.z-dn.net/?f=p_%7B2%7D%280%29%20%3D%20%28c_%7B1%7Dc_%7B2%7D%2Cc_%7B3%7D%29)
![p_{1}(1)=(-8.1^{2}+3.1,7.1^{2}+3,8.1^{2}+6.1-2)](https://tex.z-dn.net/?f=p_%7B1%7D%281%29%3D%28-8.1%5E%7B2%7D%2B3.1%2C7.1%5E%7B2%7D%2B3%2C8.1%5E%7B2%7D%2B6.1-2%29)
![(c_{1},c_{2},c_{3})=(-5,10,12)](https://tex.z-dn.net/?f=%28c_%7B1%7D%2Cc_%7B2%7D%2Cc_%7B3%7D%29%3D%28-5%2C10%2C12%29)
![p_{2}(t)=(-8t^{2}+3t-5,7t^{2}+10,8t^{2}+6t+12)](https://tex.z-dn.net/?f=p_%7B2%7D%28t%29%3D%28-8t%5E%7B2%7D%2B3t-5%2C7t%5E%7B2%7D%2B10%2C8t%5E%7B2%7D%2B6t%2B12%29)
<u>Position function in the second scene is </u>
<u />
1.
![V=\frac{4}{3} \pi 4.5^{3} = \pi* \frac{243}{2} =381.7in^{3}](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B4%7D%7B3%7D%20%20%5Cpi%204.5%5E%7B3%7D%20%3D%20%20%5Cpi%2A%20%20%5Cfrac%7B243%7D%7B2%7D%20%3D381.7in%5E%7B3%7D%20)
2. For the surface area cm² is appropriate because you're finding the area of the surface (in 2nd dimension).
Answer:
KArl should use 3/16 cups of chili powder
Step-by-step explanation:
Given that:
Recipe's requirement : 3/8 cups
Karl wants to use half : 1/2
The given question involves fractions. When the number of cups has to be divided into half, it will be multiplied with 1/2.
So,
Multiplying the chili powder requirement of the recipe to 1/2
![=\frac{3}{8} * \frac{1}{2}\\= \frac{3}{16}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%7D%7B8%7D%20%2A%20%5Cfrac%7B1%7D%7B2%7D%5C%5C%3D%20%5Cfrac%7B3%7D%7B16%7D)
Hence,
KArl should use 3/16 cups of chili powder
Step-by-step explanation:
= 0,4 ÷ 29,5
= (0,4 × 10) ÷ (29,5 × 10)
= 4 ÷ 295
= 4/295
The answer for your question is 6/8. 6 over 8 is the answer .just write 6 over 8