If you need part A, draw a person and label them 6 feet tall and a shadow coming off of him that is five feet long and draw a basketball hoop that and label it X feet tall and draw a shadow coming from it that is 8 feet long. To solve, you use proportions 6/5=X/8 solving this you get X=9.6 feet which is the height of the rim. Therefore, the rim does not meet regulation height, since the required height (10 feet) is greater than the actual height (9.6 feet).
Answer:
We have the equation
![c_1\left[\begin{array}{c}0\\0\\0\\1\end{array}\right] +c_2\left[\begin{array}{c}0\\0\\3\\1\end{array}\right] +c_3\left[\begin{array}{c}0\\4\\3\\1\end{array}\right] +c_4\left[\begin{array}{c}8\\4\\3\\1\end{array}\right] =\left[\begin{array}{c}0\\0\\0\\0\end{array}\right]](https://tex.z-dn.net/?f=c_1%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_2%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_3%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C4%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%2Bc_4%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%5C%5C4%5C%5C3%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C0%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Then, the augmented matrix of the system is
![\left[\begin{array}{cccc}0&0&0&8\\0&0&4&4\\0&3&3&3\\1&1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D0%260%260%268%5C%5C0%260%264%264%5C%5C0%263%263%263%5C%5C1%261%261%261%5Cend%7Barray%7D%5Cright%5D)
We exchange rows 1 and 4 and rows 2 and 3 and obtain the matrix:
![\left[\begin{array}{cccc}1&1&1&1\\0&3&3&3\\0&0&4&4\\0&0&0&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%261%261%5C%5C0%263%263%263%5C%5C0%260%264%264%5C%5C0%260%260%268%5Cend%7Barray%7D%5Cright%5D)
This matrix is in echelon form. Then, now we apply backward substitution:
1.
![8c_4=0\\c_4=0](https://tex.z-dn.net/?f=8c_4%3D0%5C%5Cc_4%3D0)
2.
![4c_3+4c_4=0\\4c_3+4*0=0\\c_3=0](https://tex.z-dn.net/?f=4c_3%2B4c_4%3D0%5C%5C4c_3%2B4%2A0%3D0%5C%5Cc_3%3D0)
3.
![3c_2+3c_3+3c_4=0\\3c_2+3*0+3*0=0\\c_2=0](https://tex.z-dn.net/?f=3c_2%2B3c_3%2B3c_4%3D0%5C%5C3c_2%2B3%2A0%2B3%2A0%3D0%5C%5Cc_2%3D0)
4.
![c_1+c_2+c_3+c_4=0\\c_1+0+0+0=0\\c_1=0](https://tex.z-dn.net/?f=c_1%2Bc_2%2Bc_3%2Bc_4%3D0%5C%5Cc_1%2B0%2B0%2B0%3D0%5C%5Cc_1%3D0)
Then the system has unique solution that is
and this imply that the vectors
are linear independent.
<h3>☁️ Learn Math With Me-!</h3>
![\sf\frac{{96}^{84}}{{96}^{82}}=... \\](https://tex.z-dn.net/?f=%5Csf%5Cfrac%7B%7B96%7D%5E%7B84%7D%7D%7B%7B96%7D%5E%7B82%7D%7D%3D...%20%5C%5C%20)
![\sf = {96}^{84} \div {96}^{82}](https://tex.z-dn.net/?f=%20%5Csf%20%3D%20%20%7B96%7D%5E%7B84%7D%20%20%5Cdiv%20%20%7B96%7D%5E%7B82%7D%20)
![\sf = {96}^{84 - 82}](https://tex.z-dn.net/?f=%20%5Csf%20%3D%20%20%7B96%7D%5E%7B84%20-%2082%7D%20)
![\sf = {96}^{2}](https://tex.z-dn.net/?f=%20%5Csf%20%3D%20%20%20%7B96%7D%5E%7B2%7D%20)
![\sf = 96 \times 96](https://tex.z-dn.net/?f=%20%5Csf%20%3D%2096%20%5Ctimes%2096)
![\sf = 9.216](https://tex.z-dn.net/?f=%20%5Csf%20%3D%209.216)
Correct Me If I'm Wrong :)
ANSWER
A) 9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7* 10^3
EXPLANATION
The numbers are given in standard form.
The first criteria we will use to order them is the exponents.
The bigger the exponents the bigger the number.
The second criteria is that, if the exponents of any two numbers are the same, then we use the numbers multiplying the powers of 10 to order.
![9.4 * 10^{-8} \: < \: 9.25 * 10^{-6} \: < \: 2.5 * 10^3 \: < \: 7* 10^3](https://tex.z-dn.net/?f=9.4%20%2A%2010%5E%7B-8%7D%20%20%5C%3A%20%3C%20%20%20%5C%3A%209.25%20%2A%2010%5E%7B-6%7D%20%5C%3A%20%20%3C%20%20%5C%3A%202.5%20%2A%2010%5E3%20%5C%3A%20%20%3C%20%20%5C%3A%207%2A%2010%5E3)
The correct choice is A.