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kobusy [5.1K]
3 years ago
6

you are a restaurant manager and are responsible for ordering ingredients for the restaurant. at supplier one you can purchase 2

0 gallons of milk for $70. at supplier two you can purchase 50 quarts of milk for $33.50 at supplier 3 you can purchase 15 gallons for $48.75 and receive 8 quarts free. what supplier is the best deal
Mathematics
1 answer:
anzhelika [568]3 years ago
8 0
15 gallons is the best because you get 15 gallons for 48.75 and 2gallons for free

exp. 20gal for $70
   50quarts= 12.5 gal for $33.50
    15 plus 2 gal is 17 for 48.75 much cheaper
mark me as brainlest  
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6^{2} ÷ 2*3+4

You use the order of operations with PEMDAS

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6^{2} ⇒  6*6=36

36*3=108

108 ÷ 2=54

54+4=58

Answer: 58 



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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) = [
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<h2>Answer:</h2>

Hence, we have:

proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]

<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:

proj_W(v)=(\dfrac{v\cdot w}{w\cdot w})w+(\dfrac{v\cdot w'}{w'\cdot w'})w'

Here we have:

v=[19,12,14,-17]\\\\w=[-4,-1,-1,3]\\\\w'=[1,-4,4,3]

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

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

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

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

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}]

6 0
3 years ago
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