## Destinyyyy one year ago ..

1. anonymous

2. jim_thompson5910

if you were to fold up the flaps, you'd get something that looks like this |dw:1440726497313:dw|

3. jim_thompson5910

ie an open top box the sides of the bottom of the box are x units long |dw:1440726593269:dw|

4. jim_thompson5910

and the height is 3 units |dw:1440726609264:dw|

5. anonymous

Okay

6. jim_thompson5910

what would the volume expression be?

7. jim_thompson5910

hint: volume of box = length * width * height

8. anonymous

Ummmm.. 3*x*x ???

9. jim_thompson5910

which becomes 3x^2, yes

10. anonymous

Yeah

11. jim_thompson5910

the box must have a volume of 300 cubic inches. This is given in the instructions

12. jim_thompson5910

so 3x^2 = 300 which means x = ??

13. anonymous

x=10

14. jim_thompson5910

correct

15. anonymous

Okay

16. anonymous

Then I plug the 10 into the original problem right? Or no?

17. jim_thompson5910

yeah into the box since that's the answer

18. jim_thompson5910

length = width = x

19. anonymous

Okay

20. anonymous

Finally my last problem number 23...

21. jim_thompson5910

if we look head-on we see this shape |dw:1440727083780:dw|

22. jim_thompson5910

the base is 25-2x |dw:1440727110151:dw|

23. jim_thompson5910

the height is x |dw:1440727145385:dw|

24. jim_thompson5910

what is the area expression of this rectangle? |dw:1440727163012:dw|

25. anonymous

25-2x*x

26. jim_thompson5910

use parenthesis

27. jim_thompson5910

you multiply ALL of 25-2x by x

28. jim_thompson5910

so you'd say (25-2x) * x

29. anonymous

Okay

30. jim_thompson5910

what is (25-2x) * x equivalent to when you distribute?

31. anonymous

-2x^2+25x

32. jim_thompson5910

good

33. jim_thompson5910

the cross sectional area is 43 square inches (given in instructions) so -2x^2 + 25x = 43 solve for x

34. anonymous

I got--- -25+- square root 281 over -4

35. jim_thompson5910

me too, you can simplify that to get $\Large \frac{25\pm\sqrt{281}}{4}$

36. jim_thompson5910

now use a calculator to evaluate those expressions to get the approximate decimal form

37. anonymous

Wait why do you have it as positives??? O.o

38. jim_thompson5910

I divided each piece by -1

39. jim_thompson5910

-25/(-1) = +25 -4/(-1) = +4

40. anonymous

Oh?? So my answer is wrong with the negatives??

41. jim_thompson5910

it really doesn't matter because they want the decimal approximations anyway

42. jim_thompson5910

you have a correct form so don't worry

43. anonymous

Okay

44. anonymous

x= 10.44, 2.05

45. jim_thompson5910

then round each to the nearest tenth

46. anonymous

Um.. 2.1 and 10.4 ?

47. anonymous

Sorry im not good with decimals...

48. jim_thompson5910

you have them both correct

49. anonymous

Okay.. So both are the answer to the depth of the gutter?

50. jim_thompson5910

yes you'll input them both separated by a comma

51. jim_thompson5910

the reason why there are 2 answers is because you can think of the same rectangle in 2 different ways eg: a 6 x 5 rectangle is the same as a 5 x 6 rectangle

52. anonymous

Ohhhh

53. anonymous

Okay. Thank you!! Now I can be done for the night :))

54. jim_thompson5910

you're welcome