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Loser66

  • one year ago

A total x feet of fencing is to form 3 sides of a level rectangular yard. What is the maximum area of the yard in term of x? A) x^2/9 B) x^2/8 C) x^2/4 D)x^2 E)2x^2 Please, help

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  1. freckles
    • one year ago
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    oops meant to write x

  2. freckles
    • one year ago
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    one sec

  3. freckles
    • one year ago
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    \[2L+W=x \\ A=LW=L(x-2L)\]

  4. freckles
    • one year ago
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    So we want to find A' here

  5. Loser66
    • one year ago
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    yes, then??

  6. freckles
    • one year ago
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    x is a constant I believe \[A=Lx-2L^2 \\ A'=x-4L \\ A'=0 \implies x=4L \\ A=L(x-2L)=L(4L-2L)=L(2L)=2L^2 \\ \] I think you can find A in terms of x now since x=4L

  7. freckles
    • one year ago
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    still processing?

  8. Loser66
    • one year ago
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    Yes. Thanks a lot. I got the right answer. It is not test, just practice exam with the answer sheet. But I want to know logic.

  9. freckles
    • one year ago
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    Why are you doing calculus 1 problems?

  10. Loser66
    • one year ago
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    oh, is it calculus problem??

  11. freckles
    • one year ago
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    Yes it is an optimization problem

  12. Loser66
    • one year ago
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    Question: why do you link to derivative?

  13. freckles
    • one year ago
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    because it say to maximize

  14. Loser66
    • one year ago
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    I assume it is an algebra problem and get no outlet

  15. freckles
    • one year ago
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    usually those in the cal problems I have seen they actually gave a number instead of saying x

  16. Loser66
    • one year ago
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    I am prepare for my GRE test for maths major students. ha!!!

  17. freckles
    • one year ago
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    http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx this example one here is pretty similar

  18. Loser66
    • one year ago
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    My tough one is English, not math.

  19. freckles
    • one year ago
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    except as I said they say 500 feet instead of x feet

  20. Loser66
    • one year ago
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    Any tips for GRE math practice?? I have only 1. :)

  21. freckles
    • one year ago
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    there was a question and I think it was on the gre it was my favorite question to give me a sec and I will remember it

  22. freckles
    • one year ago
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    solve for x+y \[x^2+y^2+2xy+2x+2y=-1 \]

  23. freckles
    • one year ago
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    there was a similar question on the gre or it might have been on another standard test can't remember which standard test

  24. Loser66
    • one year ago
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    hihihi... I have time. I will study carefully before taking the test. But you know, I am old. hahaha..... I am slow!!

  25. freckles
    • one year ago
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    that question isn't too bad did you want me to show you how to do it or did you want to try it first

  26. Loser66
    • one year ago
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    show me, please

  27. freckles
    • one year ago
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    \[x^2+2xy+y^2+2x+2y+1=0 \\ (x+y)^2+2(x+y)+1=0 \\ (x+y+1)^2=0 \\ x+y+1=0 \\ x+y=-1 \]

  28. freckles
    • one year ago
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    I turned it into a quadratic in terms of (x+y)

  29. Loser66
    • one year ago
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    What if we let x+y =t??

  30. Loser66
    • one year ago
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    oh, yea, we met there

  31. freckles
    • one year ago
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    good luck on your gre if i could figure out anything to tell you to help you I will I probably should have studied for it back in the day more than I did

  32. Loser66
    • one year ago
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    Sure. Again, thanks for the help.

  33. freckles
    • one year ago
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    np

  34. Loser66
    • one year ago
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    What is the units digit in standard decimal expansion of the number 7^(25) I don't get what it mean

  35. Loser66
    • one year ago
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    since \(7^{25} = 1.34106862 *10^{21}\) hence the number of digits after decimal point is 8 but it is not one of the options which are 1,3,5,7 or 9

  36. Loser66
    • one year ago
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    @freckles

  37. Loser66
    • one year ago
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    To this problem, if I don't have calculator, how can I find out the answer?

  38. freckles
    • one year ago
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    so you are trying to find out the length of the number 7^(25) ?

  39. Loser66
    • one year ago
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    problem 14 https://www.ets.org/s/gre/pdf/practice_book_math.pdf

  40. freckles
    • one year ago
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    on

  41. freckles
    • one year ago
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    oh*

  42. freckles
    • one year ago
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    the units digit is the ones digit

  43. freckles
    • one year ago
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    answer is 1

  44. Loser66
    • one year ago
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    total??

  45. Loser66
    • one year ago
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    nope, answer is 7

  46. freckles
    • one year ago
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    wait standard notation is not scientific notation is it ?

  47. Loser66
    • one year ago
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    I am not sure.

  48. freckles
    • one year ago
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    there was need to write in scientific notation because standard notation is different from scientific notation

  49. freckles
    • one year ago
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    7^(25) mod 10 will give you number in 1's digit

  50. freckles
    • one year ago
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    or aka units digit

  51. freckles
    • one year ago
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    \[4^2=16 \text{; 16 is standard notation for } 4^2 \\ 4^2=1.6 \times 10 \text{ is sceinfict notation }\]

  52. freckles
    • one year ago
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    I missed the word no in there was need to write in scientific notation there was no need to write in scientific notation*

  53. Loser66
    • one year ago
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    to this http://mathcentral.uregina.ca/QQ/database/QQ.09.06/tyrone1.html they said that the units digit is the last digit of the number in standard form in decimal form, the unit digit of 7^25 is the last one, which is 2, not 7 : (

  54. freckles
    • one year ago
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    \[7^{2} \mod 10=9 \\ 7^4 \mod 10 =9 \cdot 9 \mod 10=81 \mod 10=1 \\ 7^{4(6)+1} \mod 10=(7^4)^6(7) \mod 10=1^6(7) \mod 10 =7 \\ 7^{25} \mod 10=7 \]

  55. freckles
    • one year ago
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    the units digit is the first number it is the one's digit that is what that picture above says also

  56. freckles
    • one year ago
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    for example 61 do you call 1 the first digit because I do and 6 is the last digit 1 is in the one's place (or the units place) 6 is in the ten's palce

  57. freckles
    • one year ago
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    oh I think I see where you are getting confused

  58. freckles
    • one year ago
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    \[7^{25} = 1.34106862 *10^{21} \] you think this equality is exact when it is not

  59. freckles
    • one year ago
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    and even if it was exact you would say the units digit is 0 but it is not the case because this equation is not exact

  60. freckles
    • one year ago
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    like you still need to move that decimal to the right like 21 times

  61. freckles
    • one year ago
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    2 is not in the one's digit

  62. freckles
    • one year ago
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    http://www.wolframalpha.com/input/?i=7%5E25+

  63. freckles
    • one year ago
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    the number where it says result is the number in standard notation

  64. Loser66
    • one year ago
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    oooooooooooooooooh!! got you

  65. freckles
    • one year ago
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    a mod 10 should always give you the units digit of a

  66. Loser66
    • one year ago
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    modular method help me out 7^0 -----1 last digit 7^1 -----7 last digit 7^2 -----9 7^3 -----3 7^4-----1 hence the cycle is 4, 25 = 4*6 +1, hence \(7^25 = 7^24 *7 , but the last digit of 7^24 is 1 then *7 =7

  67. freckles
    • one year ago
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    yah

  68. Loser66
    • one year ago
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    Thanks a ton. :) I do appreciate.

  69. freckles
    • one year ago
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    np

  70. freckles
    • one year ago
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    interesting practice exam I think they have made changes to it seen I last took the gre I feel like that was 8 years ago or something :p

  71. freckles
    • one year ago
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    I don't remember linear algebra or number theory on it

  72. freckles
    • one year ago
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    but maybe there was some

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