Answer:
32.
Step-by-step explanation:
This is an arithmetic sequence with first term a1 = -6 and common difference 2.
an = a1 + d(n - 1)
a20 = -6 + 2(20-1) = 32
Answer:
![v_{o} \approx 31.247\,mph](https://tex.z-dn.net/?f=v_%7Bo%7D%20%5Capprox%2031.247%5C%2Cmph)
Step-by-step explanation:
The deceleration experimented by the car is the product of kinetic coefficient of friction and gravitational constant:
![a = \mu_{k}\cdot g](https://tex.z-dn.net/?f=a%20%3D%20%5Cmu_%7Bk%7D%5Ccdot%20g)
![a = (1.02)\cdot \left(32.174\,\frac{ft}{s^{2}} \right)](https://tex.z-dn.net/?f=a%20%3D%20%281.02%29%5Ccdot%20%5Cleft%2832.174%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29)
![a = 32.817\,\frac{ft}{s^{2}}](https://tex.z-dn.net/?f=a%20%3D%2032.817%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D)
The initial speed is computed from the following kinematic expression:
![v^{2} = v_{o}^{2} - 2\cdot a \cdot \Delta s](https://tex.z-dn.net/?f=v%5E%7B2%7D%20%3D%20v_%7Bo%7D%5E%7B2%7D%20-%202%5Ccdot%20a%20%5Ccdot%20%5CDelta%20s)
![v_{o} = \sqrt{v^{2}+2\cdot a\cdot \Delta s}](https://tex.z-dn.net/?f=v_%7Bo%7D%20%3D%20%5Csqrt%7Bv%5E%7B2%7D%2B2%5Ccdot%20a%5Ccdot%20%5CDelta%20s%7D)
![v_{o} = \sqrt{\left(0\,\frac{ft}{s} \right)^{2}+2\cdot \left(32.817\,\frac{ft}{s^{2}} \right)\cdot (32\,ft)}](https://tex.z-dn.net/?f=v_%7Bo%7D%20%3D%20%5Csqrt%7B%5Cleft%280%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%2B2%5Ccdot%20%5Cleft%2832.817%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%20%2832%5C%2Cft%29%7D)
![v_{o}\approx 45.829\,\frac{ft}{s}](https://tex.z-dn.net/?f=v_%7Bo%7D%5Capprox%2045.829%5C%2C%5Cfrac%7Bft%7D%7Bs%7D)
![v_{o} \approx 31.247\,mph](https://tex.z-dn.net/?f=v_%7Bo%7D%20%5Capprox%2031.247%5C%2Cmph)
X = -4
Y = 1
1 = -4 + 5
-4 - 5(1) = -9
Answer:
endpoint is (29, -13)
Step-by-step explanation:
Formula for midpoint is ![(\frac{x_{1} + x_{2} }{2} ,\frac{y_{1} + y_{2} }{2} )](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx_%7B1%7D%20%2B%20x_%7B2%7D%20%7D%7B2%7D%20%2C%5Cfrac%7By_%7B1%7D%20%2B%20y_%7B2%7D%20%20%7D%7B2%7D%20%29)
So, let
be the coordinates of the endpoint you are looking for.
and
= (10, -3)
![\frac{7 + y_{2} }{2} = -3](https://tex.z-dn.net/?f=%5Cfrac%7B7%20%2B%20y_%7B2%7D%20%7D%7B2%7D%20%20%3D%20-3)
-9 +
= 20 7 + ![y_{2} = -6](https://tex.z-dn.net/?f=y_%7B2%7D%20%20%3D%20-6)
![y_{2} = -13](https://tex.z-dn.net/?f=y_%7B2%7D%20%20%3D%20-13)
endpoint is (29, -13)
It’s B because it equals -8 when simplified which is a rational number