Answer:
ĐÉO OKF
Step-by-step explanation:
Answer:
taco
Step-by-step explanation:
no hablos espanol
Answer:
To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean
Step-by-step explanation:
We know that
<span>An<span> exterior angle</span></span><span> is one that has its vertex at an outer point of the circumference
</span><span>The measure of the external angle is the semidifference of the arcs that it covers
</span>
so
∠NOP=(70-30)/2-----> 20°
the answer is
<span>∠NOP=20</span>°
find the orthogonal projection of v= [19,12,14,-17] onto the subspace W spanned by [ [ -4,-1,-1,3] ,[ 1,-4,4,3] ] proj w (v) = [
12345 [234]
<h2>
Answer:</h2>
Hence, we have:
![proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]](https://tex.z-dn.net/?f=proj_W%28v%29%3D%5B%5Cdfrac%7B464%7D%7B21%7D%2C%5Cdfrac%7B167%7D%7B21%7D%2C%5Cdfrac%7B71%7D%7B21%7D%2C%5Cdfrac%7B-131%7D%7B7%7D%5D)
<h2>
Step-by-step explanation:</h2>
By the orthogonal decomposition theorem we have:
The orthogonal projection of a vector v onto the subspace W=span{w,w'} is given by:
Here we have:
![v=[19,12,14,-17]\\\\w=[-4,-1,-1,3]\\\\w'=[1,-4,4,3]](https://tex.z-dn.net/?f=v%3D%5B19%2C12%2C14%2C-17%5D%5C%5C%5C%5Cw%3D%5B-4%2C-1%2C-1%2C3%5D%5C%5C%5C%5Cw%27%3D%5B1%2C-4%2C4%2C3%5D)
Now,
![v\cdot w=[19,12,14,-17]\cdot [-4,-1,-1,3]\\\\i.e.\\\\v\cdot w=19\times -4+12\times -1+14\times -1+-17\times 3\\\\i.e.\\\\v\cdot w=-76-12-14-51=-153](https://tex.z-dn.net/?f=v%5Ccdot%20w%3D%5B19%2C12%2C14%2C-17%5D%5Ccdot%20%5B-4%2C-1%2C-1%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%3D19%5Ctimes%20-4%2B12%5Ctimes%20-1%2B14%5Ctimes%20-1%2B-17%5Ctimes%203%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%3D-76-12-14-51%3D-153)
![w\cdot w=[-4,-1,-1,3]\cdot [-4,-1,-1,3]\\\\i.e.\\\\w\cdot w=(-4)^2+(-1)^2+(-1)^2+3^2\\\\i.e.\\\\w\cdot w=16+1+1+9\\\\i.e.\\\\w\cdot w=27](https://tex.z-dn.net/?f=w%5Ccdot%20w%3D%5B-4%2C-1%2C-1%2C3%5D%5Ccdot%20%5B-4%2C-1%2C-1%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%5Ccdot%20w%3D%28-4%29%5E2%2B%28-1%29%5E2%2B%28-1%29%5E2%2B3%5E2%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%5Ccdot%20w%3D16%2B1%2B1%2B9%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%5Ccdot%20w%3D27)
and
![v\cdot w'=[19,12,14,-17]\cdot [1,-4,4,3]\\\\i.e.\\\\v\cdot w'=19\times 1+12\times (-4)+14\times 4+(-17)\times 3\\\\i.e.\\\\v\cdot w'=19-48+56-51\\\\i.e.\\\\v\cdot w'=-24](https://tex.z-dn.net/?f=v%5Ccdot%20w%27%3D%5B19%2C12%2C14%2C-17%5D%5Ccdot%20%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%27%3D19%5Ctimes%201%2B12%5Ctimes%20%28-4%29%2B14%5Ctimes%204%2B%28-17%29%5Ctimes%203%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%27%3D19-48%2B56-51%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%27%3D-24)
![w'\cdot w'=[1,-4,4,3]\cdot [1,-4,4,3]\\\\i.e.\\\\w'\cdot w'=(1)^2+(-4)^2+(4)^2+(3)^2\\\\i.e.\\\\w'\cdot w'=1+16+16+9\\\\i.e.\\\\w'\cdot w'=42](https://tex.z-dn.net/?f=w%27%5Ccdot%20w%27%3D%5B1%2C-4%2C4%2C3%5D%5Ccdot%20%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%27%5Ccdot%20w%27%3D%281%29%5E2%2B%28-4%29%5E2%2B%284%29%5E2%2B%283%29%5E2%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%27%5Ccdot%20w%27%3D1%2B16%2B16%2B9%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%27%5Ccdot%20w%27%3D42)
Hence, we have:
![proj_W(v)=(\dfrac{-153}{27})[-4,-1,-1,3]+(\dfrac{-24}{42})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=\dfrac{-17}{3}[-4,-1,-1,3]+(\dfrac{-4}{7})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=[\dfrac{68}{3},\dfrac{17}{3},\dfrac{17}{3},-17]+[\dfrac{-4}{7},\dfrac{16}{7},\dfrac{-16}{7},\dfrac{-12}{7}]\\\\i.e.\\\\proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]](https://tex.z-dn.net/?f=proj_W%28v%29%3D%28%5Cdfrac%7B-153%7D%7B27%7D%29%5B-4%2C-1%2C-1%2C3%5D%2B%28%5Cdfrac%7B-24%7D%7B42%7D%29%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cproj_W%28v%29%3D%5Cdfrac%7B-17%7D%7B3%7D%5B-4%2C-1%2C-1%2C3%5D%2B%28%5Cdfrac%7B-4%7D%7B7%7D%29%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cproj_W%28v%29%3D%5B%5Cdfrac%7B68%7D%7B3%7D%2C%5Cdfrac%7B17%7D%7B3%7D%2C%5Cdfrac%7B17%7D%7B3%7D%2C-17%5D%2B%5B%5Cdfrac%7B-4%7D%7B7%7D%2C%5Cdfrac%7B16%7D%7B7%7D%2C%5Cdfrac%7B-16%7D%7B7%7D%2C%5Cdfrac%7B-12%7D%7B7%7D%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cproj_W%28v%29%3D%5B%5Cdfrac%7B464%7D%7B21%7D%2C%5Cdfrac%7B167%7D%7B21%7D%2C%5Cdfrac%7B71%7D%7B21%7D%2C%5Cdfrac%7B-131%7D%7B7%7D%5D)
