anonymous one year ago HELP!! Does this make any sense?! http://mhf4u1.pbworks.com/w/page/26838563/Application%20Problem

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1. anonymous

THIS part!!

2. anonymous

i dont understand how they got that :(

3. Loser66

What don't you get?

4. anonymous

how did they get b/w 9-13 necklaces ??

5. Loser66

the intersections between the graphs|dw:1436711669825:dw|

6. anonymous

no but i graphed it and the points were 3 and 19

7. Loser66

|dw:1436711704284:dw|

8. anonymous

yes

9. Loser66

and between 9 and 13, parabola is higher than the line right?

10. Loser66

that is the revenue > the cost, right?

11. Loser66

12. anonymous

isnt the parabola higher at 3-19?!

13. anonymous

PL HELP!!!

14. anonymous

@misssunshinexxoxo

15. misssunshinexxoxo

@jim_thompson5910

16. anonymous

i think it should be "steph should make 3-19 necklaces each week"

17. anonymous

maybe the website is wrong?!??! because it doesnt make sense to me otherwise :(

18. freckles

$25n-n^2>55+3.5n \\ 0>n^2+3.5n-25n+55 \\ n^2-21.5n+55<0 \\ 10n^2-215n+550<0 \\ 2n^2-43n+110<0 \\ \text{ this does give } n \in (3,19)$

19. freckles

oops $n \in [3,19]$

20. freckles

wanted to but brackets there to show to include the endpoints

21. freckles

since actually you have the lower endpoint is approximately n=2.97 and the upper endpoint is 18.53 so you could actually say the answer is [3,19) didn't include the 19 because 18.53 is less than 19 but definitely include the 3 since 3 is more than 2.97

22. freckles

it looks like there was some dyslexia happening there on the website though :p

23. anonymous

omg so i was right?! its b/w 3-19 ?

24. anonymous

not 13-9?

25. freckles

yep the weird thing is they even put the right answer after they said the wrong answer

26. anonymous

yeah thats what got me confused

27. anonymous

thanks a ton though!! :)

28. freckles

np

29. anonymous

@freckles FRECKLES!!! How did you get

30. anonymous

n∈[3,19]

31. anonymous

??

32. freckles

well actually n in [3,19) since 19 is a little greater than the actual left endpoint

33. anonymous

where did you get the points 3,19? from the graph? or did you get that from the 25n-n^2>55+3.5n??

34. freckles

$2n^2-43n+110<0 \\ 2n^2-43n<-110 \\ n^2-\frac{43}{2}n<-55 \\ n^2-\frac{43}{2}n+(\frac{43}{2} \frac{1}{2})^2<-55+(\frac{43}{2} \frac{1}{2})^2 \\ (n-\frac{43}{4})^2<-55+\frac{43^2}{4^2} \\ (n-\frac{43}{4})^2<\frac{-55(16)+43^2}{16} \\ (n-\frac{43}{4})^2<\frac{969}{16} \\ \sqrt{ (n-\frac{43}{4})^2}< \sqrt{\frac{969}{16}} \\ |n-\frac{43}{4}|<\frac{ \sqrt{969}}{4} \\ - \frac{\sqrt{969}}{4}<n-\frac{43}{4}< \frac{\sqrt{969}}{4} \\ \frac{43}{4}-\frac{\sqrt{969}}{4}<n<\frac{\sqrt{969}}{4}+\frac{43}{4}$

35. freckles

36. anonymous

so how'd you get 3 and 19 from all that?!

37. freckles

calculator to approximate both the 43/4-sqrt(969)/4 and 43/4+sqrt(969)/4

38. anonymous

sorry im being so difficult, i just really dont understand :(

39. freckles

$\frac{\sqrt{969}}{4}+\frac{43}{4} \approx 18.5322 \\ \frac{43}{4}-\frac{\sqrt{969}}{4} \approx 2.96781$

40. anonymous

ohhhhhhh alright

41. anonymous

thank you soo so so much omg

42. freckles

$2.96781<n<18.5322$ n can be a whole number only 3 is in that interval but 19 isn't so you can say the inequality is: $3 \le n <19$

43. freckles

or an interval notation [3,19)

44. freckles

in roster notation {3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}

45. freckles

by the way when we say n in [3,19) we should also include where n is a whole number (or you can say integer or whatever )

46. freckles

lol just trying to be really proper with all the math terminology :p

47. anonymous

so is it 3

48. anonymous

** $3\le n \le 19$

49. freckles

well I put $3 \le n < 19$ since 19 isn't actually included

50. freckles

where n is integer of course