Answer:
10 years until the value of the car is 11000 dollars
Step-by-step explanation:
The value of the car after t years is modeled by the following equation:
![V(t) = V(0)(1-r)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%281-r%29%5E%7Bt%7D)
In which V(0) is the initial value and r is the yearly depreciation ratio, as a decimal.
A new car is purchased for 21100 dollars.
This means that ![V(0) = 21100](https://tex.z-dn.net/?f=V%280%29%20%3D%2021100)
The value of the car depreciates at 6% per year.
This means that
. So
![V(t) = V(0)(1-r)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%20V%280%29%281-r%29%5E%7Bt%7D)
![V(t) = 21000(1-0.06)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%2021000%281-0.06%29%5E%7Bt%7D)
![V(t) = 21000(0.94)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%2021000%280.94%29%5E%7Bt%7D)
To the nearest year, how long will it be until the value of the car is 11000 dollars?
This is t when ![V(t) = 11000](https://tex.z-dn.net/?f=V%28t%29%20%3D%2011000)
![V(t) = 21000(0.94)^{t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%2021000%280.94%29%5E%7Bt%7D)
![11000 = 21000(0.94)^{t}](https://tex.z-dn.net/?f=11000%20%3D%2021000%280.94%29%5E%7Bt%7D)
![(0.94)^{t} = \frac{11000}{21000}](https://tex.z-dn.net/?f=%280.94%29%5E%7Bt%7D%20%3D%20%5Cfrac%7B11000%7D%7B21000%7D)
![(0.94)^{t} = \frac{11}{21}](https://tex.z-dn.net/?f=%280.94%29%5E%7Bt%7D%20%3D%20%5Cfrac%7B11%7D%7B21%7D)
![\log{(0.94)^{t}} = \log{\frac{11}{21}}](https://tex.z-dn.net/?f=%5Clog%7B%280.94%29%5E%7Bt%7D%7D%20%3D%20%5Clog%7B%5Cfrac%7B11%7D%7B21%7D%7D)
![t\log{0.94} = \log{\frac{11}{21}}](https://tex.z-dn.net/?f=t%5Clog%7B0.94%7D%20%3D%20%5Clog%7B%5Cfrac%7B11%7D%7B21%7D%7D)
![t = \frac{\log{\frac{11}{21}}}{\log{0.94}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B%5Cfrac%7B11%7D%7B21%7D%7D%7D%7B%5Clog%7B0.94%7D%7D)
![t = 10.45](https://tex.z-dn.net/?f=t%20%3D%2010.45)
To the nearest year
10 years until the value of the car is 11000 dollars
I dont know but im a material girl with balls
Answer:
a) Exterior Angle Theorem
b) x = 109°
Step-by-step explanation:
For a, you can thank the Exterior Angle Theorem. Since the angles of a triangle equal 180°, we can figure out what the third interior angle's measurement is, then subtract that from 180 to get the exterior angle's measure. Since the two angles labeled (64° and 45°) will make an obtuse angle, then the third interior is an acute angle. Add 64 and 45 to get the exterior angle's measurement of 109 degrees. That would mean the third interior angle's measurement would be 71 degrees. 64 + 45 + 71 = 180, so this is true.
(I had used the HSEAT to explain this.)
Answer:
Step-by-step explanation:
Length = 6m
Breadth =4m
![Area = length\times breadth\\\\A = 6\times 4\\\\A= 24cm^2](https://tex.z-dn.net/?f=Area%20%3D%20length%5Ctimes%20breadth%5C%5C%5C%5CA%20%3D%206%5Ctimes%204%5C%5C%5C%5CA%3D%2024cm%5E2)
Answer: 230.4 feet
Step-by-step explanation:
arc length = circumfrance x fraction of a circle
=
x ![\frac{165}{360}](https://tex.z-dn.net/?f=%5Cfrac%7B165%7D%7B360%7D)
= ![\frac{2*\pi*80*165 }{360}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2A%5Cpi%2A80%2A165%20%7D%7B360%7D)
= 230.4 feet to nearest tenth