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sparky16 Group Title

Solve: 2y^(-1/2)=10

  • one year ago
  • one year ago

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  1. JamesJ Group Title
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    What do you think is a good first step?

    • one year ago
  2. sparky16 Group Title
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    umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]

    • one year ago
  3. JamesJ Group Title
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    If the problem \[ 2y^{-1/2} - 10 \] or \[ (2y)^{-1/2} = 10 \]

    • one year ago
  4. JamesJ Group Title
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    *Is

    • one year ago
  5. sparky16 Group Title
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    \[2y ^{-1/2}=10\]

    • one year ago
  6. JamesJ Group Title
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    Right. So you want y by itself. That is, you want y^1 by itself equal to something. So first step I would use is to at least get y^something by itself first \[ 2y^{-1/2} = 10 \] implies \[ y^{-1/2} = 5 \] Yes? If you're ok with that step, then suggest what to do next. Remember you want y^1 = y = something

    • one year ago
  7. sparky16 Group Title
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    How did you get 5?

    • one year ago
  8. sparky16 Group Title
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    oh wait never mind. You just divided by 2

    • one year ago
  9. JamesJ Group Title
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    C'mon. Look at the expression before hand. I divided both sides by 2.

    • one year ago
  10. sparky16 Group Title
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    then we should turn y^(-1/2) into \[\sqrt{1/y}\] right?

    • one year ago
  11. JamesJ Group Title
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    There are lots of ways to solve the problem. Writing y^(-1/2) that way is one way. Write now the rest of the solution and then I'll show you another way.

    • one year ago
  12. sparky16 Group Title
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    Ok. \[\sqrt{1/y}=5\] I square both sides right? so 1/y =25

    • one year ago
  13. JamesJ Group Title
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    yes and hence y = ...

    • one year ago
  14. sparky16 Group Title
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    25?

    • one year ago
  15. JamesJ Group Title
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    If 1/y = 25, then it can NOT be the case y = 25.

    • one year ago
  16. sparky16 Group Title
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    I'm not sure

    • one year ago
  17. JamesJ Group Title
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    If 1/x = 2, then x = 1/2. If 1/z = 1/3, then z = 3

    • one year ago
  18. JamesJ Group Title
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    Hence if 1/y = 25 then y = ...

    • one year ago
  19. sparky16 Group Title
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    I don't understand how to find y. I kind of forgot how to do the reciprocal thing .Can u explain

    • one year ago
  20. JamesJ Group Title
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    Scary. \[ 2 \times \frac{1}{2} = 1 \] Agreed?

    • one year ago
  21. JamesJ Group Title
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    two times one half equals one, yes?

    • one year ago
  22. sparky16 Group Title
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    yes

    • one year ago
  23. JamesJ Group Title
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    Suppose now that 2x = 1. What does x equal?

    • one year ago
  24. sparky16 Group Title
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    1/2

    • one year ago
  25. sparky16 Group Title
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    but i mean in the form of 1/y=25. I don't understand this one

    • one year ago
  26. JamesJ Group Title
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    Yes 2x = 1 implies x = 1/2. Now take 2x = 1 and divide both sides by x; we have \[ \frac{2x}{x} = \frac{1}{x} \] Hence \[ 2 = \frac{1}{x} \] I.e., x = 1/2 if and only if 1/x = 2. So if 1/y = 25, what does y = ... ?

    • one year ago
  27. JamesJ Group Title
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    If 1/y = a, then y = 1/a

    • one year ago
  28. JamesJ Group Title
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    If 1/y = 25, then y = ... ?

    • one year ago
  29. sparky16 Group Title
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    ummm

    • one year ago
  30. sparky16 Group Title
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    I thought I would just times y/1 to both sides

    • one year ago
  31. JamesJ Group Title
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    well \[ y \times \frac{1}{y} = 1 \] So if 1/y = 25, then \[ y \times 25 = 1 \] i.e., \( 25y = 1 \). Hence y = ...

    • one year ago
  32. JamesJ Group Title
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    If 1/y = a, then y = 1/a

    • one year ago
  33. JamesJ Group Title
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    Hence if 1/y = 25, then y = ....

    • one year ago
  34. sparky16 Group Title
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    1/y=25 times by y/1 to both sides... 25y???

    • one year ago
  35. JamesJ Group Title
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    No. You are not reading what I am writing. \[ \frac{1}{y} \times y = 1 \] Do you agree with that statement?

    • one year ago
  36. sparky16 Group Title
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    yes

    • one year ago
  37. JamesJ Group Title
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    Now suppose 1/y = 25, then \[ 25 \times y = 1 \] That is \[ 25y = 1 \] Agreed so far?

    • one year ago
  38. sparky16 Group Title
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    ok. 25y=1 Oh then divide by 25 so I get 1/25

    • one year ago
  39. sparky16 Group Title
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    thank you!

    • one year ago
  40. JamesJ Group Title
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    Yes y = 1/25 If 1/y = 25, then y = 1/25 In general, if 1/y = a, then y = 1/a if 1/x = 1/b, then x = b

    • one year ago
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