If depreciation is 7.25% per year, then the common factor is (1-0.0725), or 0.9275.
Thus, the car's value after 5 years will be:
V = $28000(0.9275)^5 = $28000(0.6864) = $19218.86, or (to the nearest dollar) $19218 (answer)
Answer:
(4,3,2)
Step-by-step explanation:
We can solve this via matrices, so the equations given can be written in matrix form as:
![\left[\begin{array}{cccc}3&2&1&20\\1&-4&-1&-10\\2&1&2&15\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D3%262%261%2620%5C%5C1%26-4%26-1%26-10%5C%5C2%261%262%2615%5Cend%7Barray%7D%5Cright%5D)
Now I will shift rows to make my pivot point (top left) a 1 and so:
![\left[\begin{array}{cccc}1&-4&-1&-10\\2&1&2&15\\3&2&1&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-4%26-1%26-10%5C%5C2%261%262%2615%5C%5C3%262%261%2620%5Cend%7Barray%7D%5Cright%5D)
Next I will come up with algorithms that can cancel out numbers where R1 means row 1, R2 means row 2 and R3 means row three therefore,
-2R1+R2=R2 , -3R1+R3=R3
![\left[\begin{array}{cccc}1&-4&-1&-10\\0&9&4&35\\0&14&4&50\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-4%26-1%26-10%5C%5C0%269%264%2635%5C%5C0%2614%264%2650%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc}1&-4&-1&-10\\0&1&\frac{4}{9}&\frac{35}{9}\\0&14&4&50\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-4%26-1%26-10%5C%5C0%261%26%5Cfrac%7B4%7D%7B9%7D%26%5Cfrac%7B35%7D%7B9%7D%5C%5C0%2614%264%2650%5Cend%7Barray%7D%5Cright%5D)
4R2+R1=R1 , -14R2+R3=R3
![\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&-\frac{20}{9}&-\frac{40}{9}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26%5Cfrac%7B7%7D%7B9%7D%26%5Cfrac%7B50%7D%7B9%7D%5C%5C0%261%26%5Cfrac%7B4%7D%7B9%7D%26%5Cfrac%7B35%7D%7B9%7D%5C%5C0%260%26-%5Cfrac%7B20%7D%7B9%7D%26-%5Cfrac%7B40%7D%7B9%7D%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{cccc}1&0&\frac{7}{9}&\frac{50}{9}\\0&1&\frac{4}{9}&\frac{35}{9}\\0&0&1&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26%5Cfrac%7B7%7D%7B9%7D%26%5Cfrac%7B50%7D%7B9%7D%5C%5C0%261%26%5Cfrac%7B4%7D%7B9%7D%26%5Cfrac%7B35%7D%7B9%7D%5C%5C0%260%261%262%5Cend%7Barray%7D%5Cright%5D)
, 
![\left[\begin{array}{cccc}1&0&0&4\\0&1&0&3\\0&0&1&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%264%5C%5C0%261%260%263%5C%5C0%260%261%262%5Cend%7Barray%7D%5Cright%5D)
Therefore the solution to the system of equations are (x,y,z) = (4,3,2)
Note: If answer choices are given, plug them in and see if you get what is "equal to". Meaning plug in 4 for x, 3 for y and 2 for z in the first equation and you should get 20, second equation -10 and third 15.
vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.
Givens
vi = 160 ft/s
vf = 0 (the rocket stops at the maximum height.)
a = - 9.81 m/s
t = ????
Remark
YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.
Equation
a = (vf - vi)/t
Solve
- 32 = (0 - 160)/t Multiply both sides by t
-32 * t = - 160 Divide by -32
t = - 160/-32
t = 5
You will also need to solve for the height to answer part B
t = 5
vi = 160 m/s
a = - 32
d = ???
d = vi*t + 1/2 a t^2
d = 160*5 + 1/2 * - 32 * 5^2
d = 800 - 400
d = 400 feet
Part B
You are at the maximum height. vi is 0 this time because you are starting to descend.
vi = 0
a = 32 m/s^2
d = 400 feet
t = ??
formula
d = vi*t + 1/2 a t^2
400 = 0 + 1/2 * 32 * t^2
400 = 16 * t^2
400/16 = t^2
t^2 = 25
t = 5 sec
The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.
Answer:
Sorry I don't know
Step-by-step explanation:
