anonymous
  • anonymous
The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product. 5(x − 7)2 + 13; The minimum cost to produce the product is $13. 5(x − 7)2 + 13; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is $7. 5(x − 7)2 + 258; The minimum cost to produce the product is $258.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
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anonymous
  • anonymous
@Nnesha
Nnesha
  • Nnesha
Hey, do you know how to `complete the square` ?
anonymous
  • anonymous
Barley

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Nnesha
  • Nnesha
oh alright \[\huge\rm f(x)= 5x^2 − 70x + 258 \] this is our equation where a b ,c values are \[\rm Ax^2+Bx+C=0\] a=leading coefficient b=middle term c=constant term we need to complete the square of (5x^2+70x) \[(5x^2+70x)+258\]
Nnesha
  • Nnesha
first of all take out the common factor from (5x^2+70x) what is common factor(just common number not varaible ) ?
anonymous
  • anonymous
2?
Nnesha
  • Nnesha
nope
Nnesha
  • Nnesha
\[\huge\rm \color{Red}{5}x^2+\color{reD}{70}x\] 5 isn't divisible by 2
anonymous
  • anonymous
Oh, sorry, I mixed that up with something else. So, then what 5?
Nnesha
  • Nnesha
yes right take out the 5 from both terms 5x^2 and 70x\[5(??+??)\]
anonymous
  • anonymous
would you divide 70 by 5?
Nnesha
  • Nnesha
when you take out 5 from 5 what would you get ?
anonymous
  • anonymous
0
Nnesha
  • Nnesha
in other words divide both terms by common factor |dw:1441211901863:dw| what do you get when yo udivide 5 x^2 by 5 and 70x/5 = ? write ur answer in the parentheses
anonymous
  • anonymous
5(x^2 +14)+258?
Nnesha
  • Nnesha
yes right!!
Nnesha
  • Nnesha
wait you forgot x
Nnesha
  • Nnesha
\(\color{blue}{\text{Originally Posted by}}\) @gigirained 5(x^2 +14)+258? \(\color{blue}{\text{End of Quote}}\) 5(x^2 +14x)+258 like this
anonymous
  • anonymous
Oh alright
Nnesha
  • Nnesha
now to complete the square divide b/2 and then take square of (b/2)^2
Nnesha
  • Nnesha
i'll give you an example \[\huge\rm x^2+Bx+C=0\] \[\rm (x +\frac{ b }{ 2})^2 -(\frac{ b }{ 2})^2+C=0\] like this b = middle term
Nnesha
  • Nnesha
what's the middle term in that equation ?
anonymous
  • anonymous
14?
Nnesha
  • Nnesha
yes right divide 14 by 2 then take square root of the result
Nnesha
  • Nnesha
\[\huge\rm 5(x-\frac{ 14 }{ 2 })^2-(\frac{ 14 }{ 2 })^2 +258\]
anonymous
  • anonymous
5(x-7)^2 - 7^2 +258
Nnesha
  • Nnesha
i just noticed it supposed to be negative 14x cux in the original equation 70x is negative
anonymous
  • anonymous
Okay
Nnesha
  • Nnesha
yes right! 7^2 = ?
anonymous
  • anonymous
49
anonymous
  • anonymous
do we do anything with 258?
Nnesha
  • Nnesha
hmm wait
Nnesha
  • Nnesha
ohh yeah we have common factor we have to multiply (b/2)^2 with 5
Nnesha
  • Nnesha
\[\huge\rm \color{Red}{5}(x-7)^2-[(7)^2\times \color{ReD}{5}] +258\]we should multiply (b/2)^2 wth the common factor
anonymous
  • anonymous
would we multiply 7 by 5 for 49 by 5
Nnesha
  • Nnesha
first take square of 7 then multiply by 5
anonymous
  • anonymous
245
Nnesha
  • Nnesha
yes right now combine like terms \[5(x-7)^2\color{Red}{-245+258}\]
anonymous
  • anonymous
5(x-7)^2 + 13
Nnesha
  • Nnesha
then you will get vertex form equation of parabola \[\huge\rm y=a(x-h)^2+k\] where (h,k) is the vertex if a is positive then you wll get minimum point (h,k) if a is negative you will get maximum point (h,k) (h,k) where h represents x-coordinate and k represents y -coordinate cost usually represents by y -coordinate
Nnesha
  • Nnesha
yes right
Nnesha
  • Nnesha
done!
anonymous
  • anonymous
So, i dont know which one, A or B @Nnesha
Nnesha
  • Nnesha
reread my my comment again which coordinate represent cost ?
Nnesha
  • Nnesha
what's the vertex point ?
anonymous
  • anonymous
7
anonymous
  • anonymous
well, the answer i got was b
Nnesha
  • Nnesha
that's one h what is k ?
anonymous
  • anonymous
13
anonymous
  • anonymous
?
Nnesha
  • Nnesha
yes right (h,k) = (7,13) where y -coordinate represent cost
anonymous
  • anonymous
how do i find the y-coordinate
Nnesha
  • Nnesha
(x,y) is same as (h,k) first number is x-coordinate 2nd one is y-coordinate
anonymous
  • anonymous
oh lol never mind
anonymous
  • anonymous
That went right over my head haha
Nnesha
  • Nnesha
in other words k represent cost in this question
anonymous
  • anonymous
Thank you so much!
Nnesha
  • Nnesha
np :)

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