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Markd

  • 2 years ago

using a=-1, b=2, c=-3, d=4 show an expression using only those 4 letters that equals 22, 28 and 29. You can use square roots and exponents.

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  1. theEric
    • 2 years ago
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    Your teacher is maniacal, in that you can't use algebra to just solve or anything.... You could create a program to find the results of many, many combinations. But for now we'll just have to logic it out. Does that sound good? Or are you in a high level class that I'm not understanding?

  2. theEric
    • 2 years ago
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    Can we use addition and subtraction?

  3. Markd
    • 2 years ago
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    You can use addition or subtraction. it 7th grade math

  4. theEric
    • 2 years ago
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    like \[z+z+z-y\]

  5. theEric
    • 2 years ago
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    Okay, that makes this easier!

  6. Markd
    • 2 years ago
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    example: (b^d)-(a+c) = 20

  7. theEric
    • 2 years ago
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    Okay! Well I was going to be cheap, since you can really count with the -1. I mean, that's a. And -a = 1. So -a = 1, -a + -a =2, -a + -a + -a = 3, etc.

  8. theEric
    • 2 years ago
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    That's probably not the purpose of the assignment, though. Huh?

  9. Markd
    • 2 years ago
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    no, you can only use each number one time in each expression.

  10. theEric
    • 2 years ago
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    Oh! Tricky! :) A challenge!

  11. Markd
    • 2 years ago
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    another example -(d-c)^b/a = 14 note ^ means to the power

  12. theEric
    • 2 years ago
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    Understood, thank you!

  13. theEric
    • 2 years ago
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    And numbers are not allowed, right?

  14. Markd
    • 2 years ago
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    we had to come up with an expression for every day of the month of October. I got 28 of the 31 done and these last three have me stumped!

  15. theEric
    • 2 years ago
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    Oh wow!!

  16. Markd
    • 2 years ago
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    you can use the numbers -1, 2, -3 and 4 instead of the letters if you want to. you find the expression and the least I can do is translate it! lol

  17. theEric
    • 2 years ago
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    Haha, okay.

  18. Markd
    • 2 years ago
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    is this something you think you can help me with?

  19. theEric
    • 2 years ago
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    Haha, I'm working on it! Logically, it stinks that you can't use any more than once, but it's great that you can switch the sign of any of them by making them negative.

  20. theEric
    • 2 years ago
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    I need a break from some math homework of my own that's not due for a little while, so I'll work these out with you.

  21. Markd
    • 2 years ago
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    I kind of added the "switch the sign" rule myself. Im not sure that thats allowed but its the only way I could figure out some of them.

  22. theEric
    • 2 years ago
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    I see. This sounds like a tough math assignment.

  23. Markd
    • 2 years ago
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    Are you in high school or college?

  24. theEric
    • 2 years ago
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    25 = (b-c) ^ (d-a), so you can have that in case you're other one involved just making a variable negative. I'm in college. My brain is currently deflated... I was working on homework in a subject called, "Introduction to Mathematical Proofs". The premise of the class is that, if you know some basic math definitions, you can establish true statements. Everything in math is defined, very specifically. Example, even numbers. They have a definition. Pretty much, an even number is a multiple of 2. Then, (I won't bother you with details) and example of a truth you can mathematically prove is that the product of any two even numbers will be even. It's sort of common sense, but the course demands us to be very specific. Algebra makes it easier. Back to the 22, 28, and 29!

  25. Markd
    • 2 years ago
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    Sounds hard! But believe it our not i did understand what you just said!

  26. theEric
    • 2 years ago
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    Sweet! I believe it! The stuff you're working on is hard too!

  27. Markd
    • 2 years ago
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    Are you sure 25 is correct? (2--3)^4--1= 5^5 correct? isnt that 3,125?

  28. Markd
    • 2 years ago
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    am I wrong on my thinking?

  29. theEric
    • 2 years ago
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    Hahaha!! Umm...... Let's go with (2--3) * (4--1)

  30. Markd
    • 2 years ago
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    that works!

  31. theEric
    • 2 years ago
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    Haha, I did say my brain was deflated! Thank you for catching me, and I'm sorry I told you something incorrect!

  32. Markd
    • 2 years ago
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    its OK. your thinking was right

  33. theEric
    • 2 years ago
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    Haha, thank you.

  34. Markd
    • 2 years ago
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    this is kind of like the show "Are you smarter than a 6th grader"

  35. theEric
    • 2 years ago
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    Hahaha!! You are totally right!

  36. theEric
    • 2 years ago
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    Great comparison...

  37. Markd
    • 2 years ago
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    OK, we could use absolute value on 5 of these and I just found answers to 2 two of the ones I had already done without using absolute values. So I have 2 more I can use now. So if it helps you try using absolure values if you need to.

  38. Markd
    • 2 years ago
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    does that make sence?

  39. Markd
    • 2 years ago
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    example: |d|+|c|+|a|*b=16

  40. theEric
    • 2 years ago
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    Alright! Your assignment makes a point that there are a limited amount of absolute values. |a| = -a. Does your assignment want to limit that -a thing too? It's like (-1)a, which is involving another number... Maybe we can change them later, if you want!

  41. Markd
    • 2 years ago
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    of the 31 expression I can only have 5 that use absolute values. I have 2 more absolute values left to use. Keep in mind you can use as many absolute values you want to in each expression.

  42. theEric
    • 2 years ago
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    But then we can use -2 or -4 in multiplication so easily... They'd have to be multiplied by a = -1. Addition is fine. x + (-b) = x - b. Subtraction is also fine. x - (-b) = x + b

  43. Markd
    • 2 years ago
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    yes, I believe thate right. Im not sure I understood that.

  44. theEric
    • 2 years ago
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    Okay! I'm going to go to a store quickly. I'll be back.

  45. Markd
    • 2 years ago
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    ok

  46. theEric
    • 2 years ago
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    Well you weren't sure if we could just use -a, or -c. If we could, then why put a limit on how many absolute values we use? Since we can get the same result with -a as |a|, why put a limit on how many times we can use |a|, but not limit -a. I think -a would not count because you get -a by multiplying -1 and a. Since -1 is a number, it wouldn't be allowed.

  47. Markd
    • 2 years ago
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    i see your point.

  48. theEric
    • 2 years ago
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    -1, 2, -3, 4 Results by multiplying two different variables -2 = 2 * -1 3 = -3 * -1 -4 = 4 * -1 -6 = -3 * 2 8 = 4 * 2 -12 = 4 * -3 Results by using powers, but not absoute value 1 = 2 ^ -1 -1 = -3 ^ -1 1 = 4 ^ -1 16 = 4 ^ 2 81 = 4 ^ -3 Results by using powers, and possiblly absolute value 1 = 1 ^ 2 1 = 1 ^ 3 1 = 1 ^ 4 8 = 2 ^ 3 16 = 2 ^ 4 81 = 3 ^ 4

  49. theEric
    • 2 years ago
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    Haha, I don't know if that is helpful or not. But those are numbers you might recognize that you need. They are the result of taking two variables and doing something to them. I think I overcomplicated it :P

  50. Markd
    • 2 years ago
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    no, i follow you

  51. theEric
    • 2 years ago
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    Haha, alright.

  52. theEric
    • 2 years ago
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    Some of that is wrong, sorry.. I wrote a program to do that for me, so I wrote it wrong. 81 doesn't equal 4^-3

  53. Markd
    • 2 years ago
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    is 2^-1=-1 why wouldn't it be -2? Is that a rule?

  54. theEric
    • 2 years ago
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    Actually, ignore all of that! I made two mistakes: 1. Many of the second set are wrong because I switched.. like\[4^{-1}\neq1\]\[(-1)^4=1\] 2. Some are wrong otherwise, as my program used a program that rounded. I didn't know that it would. Also, I didn't include all possibilities. Here are the powers, if you use two variables and possibly absolute value: 1 = 1 ^ 2 1 = 1 ^ 3 1 = 1 ^ 4 2 = 2 ^ 1 8 = 2 ^ 3 16 = 2 ^ 4 3 = 3 ^ 1 9 = 3 ^ 2 81 = 3 ^ 4 4 = 4 ^ 1 16 = 4 ^ 2 64 = 4 ^ 3

  55. theEric
    • 2 years ago
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    And obviously we won't worry about anything to the first power.... So here I took that out. 1 = 1 ^ 2 1 = 1 ^ 3 1 = 1 ^ 4 8 = 2 ^ 3 16 = 2 ^ 4 9 = 3 ^ 2 81 = 3 ^ 4 16 = 4 ^ 2 64 = 4 ^ 3

  56. theEric
    • 2 years ago
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    Do you really want to know how a negative power works? It's not that hard, but it doesn't give us any extra help here. I will show you, if you want.

  57. Markd
    • 2 years ago
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    no, its OK. I will work off of what you just sent

  58. theEric
    • 2 years ago
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    Okay! I just thought those numbers could help us possibly.

  59. Markd
    • 2 years ago
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    Dont forget we can also use square roots

  60. theEric
    • 2 years ago
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    Right, thanks!

  61. theEric
    • 2 years ago
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    If only we could reuse some..

  62. Markd
    • 2 years ago
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    Would be nice...

  63. theEric
    • 2 years ago
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    \[\sqrt{4^{\left|-3\right|}}=\sqrt{64}=8\]\[\sqrt{\left|-3\right|^4}=\sqrt{81}=9\] More ways to get to 8 and 9, but maybe you already noticed! No use on focusing on what we can't do!

  64. theEric
    • 2 years ago
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    \[8=2*4\]\[9=(-1)(-3)^2=\left|-3\right|^2\]

  65. Markd
    • 2 years ago
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    can you think of anything that equals 20?

  66. theEric
    • 2 years ago
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    With or without absolute value?

  67. Markd
    • 2 years ago
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    (2^4)-(-1+-3) but that dont leave any numbers to use

  68. Markd
    • 2 years ago
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    either way

  69. theEric
    • 2 years ago
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    Right. I run into that problem too.

  70. Markd
    • 2 years ago
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    What state do you live in?

  71. Markd
    • 2 years ago
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    My brain is fried.

  72. theEric
    • 2 years ago
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    Understood. Maybe a break would help. And I hope you're not staying up too late! I don't know what time it would be where you are.

  73. Markd
    • 2 years ago
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    Im in Charlotte North Carolina. Its 11:40 here

  74. theEric
    • 2 years ago
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    Same here, in central Pennsylvania.

  75. theEric
    • 2 years ago
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    I'm not sure how dangerous it is to give town information over the internet. I'd presume it's not so bad. I never have though.

  76. theEric
    • 2 years ago
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    When is this project due?

  77. Markd
    • 2 years ago
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    Thank you so much for your help! It was a nice surprise to get your messages this morning.

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