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Find Y when AxY=B, BxY=C, and B is unknown

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  1. Sep 28, 2017 #1
    How do I:
    Find Y when AxY=B, BxY=C, and B is unknown?
    (A and C are known)

    Example: If A=100 and C=169 then Y=1.3 and B=130

    I assume I use log or pow but cannot figure it out.
    Thanks.
     
  2. jcsd
  3. Sep 28, 2017 #2

    Mark44

    Staff: Mentor

    No, logs are not needed.
    Just solve for y in the first equation, then solve for y in the second equation, and equate the two expressions for y. If you know a and b, then you should be able to find c, and from that, you can find y.

    Tips: Algebra equations typically use lower-case letters for variables. Also, don't use x for multiplication, especially in equations that already involve x (which your equations don't). Instead of writing AxY and BxY, just write AY and BY or ay and by.
     
  4. Sep 28, 2017 #3
    Okay... If B=A*Y and B=C/Y then C/Y=A*Y

    Solution One:
    A=(C/Y)/Y = C/(Y*Y) = C*1/(Y*Y) = 1/(Y*Y)*C
    A/C=1/(Y*Y)
    (A/C)/(Y*Y)=1
    (A/C)*1/(Y*Y)=1
    1/(Y*Y)=1/(A/C)
    I'm clueless what happens next

    Solution Two:
    C=(A*Y)*Y = A*(Y*Y) = (Y*Y)*A
    C/A=Y*Y
    sqrt(C/A)=Y

    Test:
    sqrt(169/100)=1.3
    Yeah!! I did it!!

    Thanks Mark for pointing the way.
     
  5. Sep 28, 2017 #4
    PS... sorry about using Caps
     
  6. Sep 28, 2017 #5
    A/C=1/(Y*Y)
    (A/C)*(Y*Y)=1
    (Y*Y)*(A/C)=1
    (Y*Y)=1/(A/C)
    Y=sqrt(1/(A/C))
    I did it again!!
     
  7. Sep 29, 2017 #6

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I moved the thread to our homework section.

    Note that -1.3 is a solution as well.
     
  8. Sep 29, 2017 #7
    mfb, this wasn't homework. LOL

    Mark, my first instinct regarding pow was right:
    I discovered that sqrt(x) is the same as pow(x, 1/2)
    I mention this because last night while I was trying to sleep it came to me.
    I thought... What if I need 2 or 3 or 4 numbers between the 2 I have (e.g. A,1,2,C or A,1,2,3,C or A,1,2,3,4,C etc.)?
    Well, after a while, it clicked with me what the answer is: pow(x, 1/3) or pow(x, 1/4) or pow(x, 1/5) etc.

    Thanks again though, because I wrote about "equate two equations" (a.k.a. "substitution method") in my personal Math Notes.
    Very helpful - I never know when I will need it again.
     
  9. Sep 29, 2017 #8

    Mark44

    Staff: Mentor

    But it's homework-like or could be a problem in a textbook, which means that the place to post it is here in the Homework & Coursework sections.
    pow() is a standard library function in C and C++ and possibly a few other languages. If all you need is the square root, most languages have a library function called sqrt(). However, why are you bringing in programming functions to what is a fairly simple problem in algebra?

    For this problem, neither would have been helpful. In solving for b, the next to last step is ##b^2 = 169 * 100 = 16,900##. If you naively take the square root (or the 1/2 power), you get b = 130, but b = -130 is also a solution of the equation ##b^2 = 16,900##. This means that ##y = \pm 1.3##. That's what @mfb was talking about at the bottom of post #6.
    I have no idea what you're trying to do here.
    You aren't really "equating two equations" -- you're equating two expressions that have the same value. It doesn't make sense to set two equations equal to each other.
     
  10. Sep 29, 2017 #9
    I'm sorry you have gotten frustrated with me.

    As for what I'm doing... Well to do my best at using math words: I'm "interpolating a power series" (sort of).
    And yes, it's computer code - C++ in fact... I create charts - I'm visual.
    Numbers, formulas, "Math", ugh! - I know it's right when I "see" it.
    I wish I understood it more, but I don't - I accept that (I don't let it get me down).
    I've got you, right?

    (we're almost neighbors. I'm up here in Bellingham - hello there. My wife and I are heading down to Bellevue tomorrow to watch a movie - 11yr anniversary)
     
  11. Oct 1, 2017 #10

    Mark44

    Staff: Mentor

    Hello, back. I'm a couple of counties south of you.
     
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