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Katyanochek1 [597]
3 years ago
12

If you help me just explain it to me

Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

C

Step-by-step explanation:

lets find median 2, 4, 4, 5, 6, 8, 9, 10, 10, 13, 17

now lets find the lower quartile median and upper quartile median

we don't include the median in the count, only use it to divide the data into the two parts,

2, 4, <u>4</u>, 5, 6, 8, 9, 10, 10, 13, 17

so lower quartile median is 4,

2, 4, <u>4</u>, 5, 6, 8, 9, 10, <u>10</u>, 13, 17

while upper quartile median is 10

the box represents the range between the upper quartile median and lower quartile median, thus is should go from 4 to 10 with the middle line, representing the median at 8,

the whiskers represent the whole data range

thus, the answer is C

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In three dimensions, the cross product of two vectors is defined as shown below

\begin{gathered} \vec{A}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \\ \vec{B}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} \\ \Rightarrow\vec{A}\times\vec{B}=\det (\begin{bmatrix}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}) \end{gathered}

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In our case,

\begin{gathered} (\hat{i}+\hat{j})=1\hat{i}+1\hat{j}+0\hat{k} \\ \text{and} \\ (\hat{i}\times\hat{j})=(1,0,0)\times(0,1,0)=(0)\hat{i}+(0)\hat{j}+(1-0)\hat{k}=\hat{k} \\ \Rightarrow(\hat{i}\times\hat{j})=\hat{k} \end{gathered}

Where we used the formula for AxB to calculate ixj.

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\begin{gathered} (\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=(1,1,0)\times(0,0,1) \\ =(1\cdot1-0\cdot0)\hat{i}+(0\cdot0-1\cdot1)\hat{j}+(1\cdot0-0\cdot1)\hat{k} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=1\hat{i}-1\hat{j} \\ \Rightarrow(\hat{i}+\hat{j})\times(\hat{i}\times\hat{j})=\hat{i}-\hat{j} \end{gathered}

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