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sparky16

  • 2 years ago

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

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  1. JamesJ
    • 2 years ago
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    What do you think is a good first step?

  2. sparky16
    • 2 years ago
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    umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]

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

  4. JamesJ
    • 2 years ago
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    *Is

  5. sparky16
    • 2 years ago
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    \[2y ^{-1/2}=10\]

  6. JamesJ
    • 2 years ago
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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

  7. sparky16
    • 2 years ago
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    How did you get 5?

  8. sparky16
    • 2 years ago
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    oh wait never mind. You just divided by 2

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

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

  11. JamesJ
    • 2 years ago
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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.

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

  13. JamesJ
    • 2 years ago
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    yes and hence y = ...

  14. sparky16
    • 2 years ago
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    25?

  15. JamesJ
    • 2 years ago
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    If 1/y = 25, then it can NOT be the case y = 25.

  16. sparky16
    • 2 years ago
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    I'm not sure

  17. JamesJ
    • 2 years ago
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    If 1/x = 2, then x = 1/2. If 1/z = 1/3, then z = 3

  18. JamesJ
    • 2 years ago
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    Hence if 1/y = 25 then y = ...

  19. sparky16
    • 2 years ago
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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

  20. JamesJ
    • 2 years ago
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    Scary. \[ 2 \times \frac{1}{2} = 1 \] Agreed?

  21. JamesJ
    • 2 years ago
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    two times one half equals one, yes?

  22. sparky16
    • 2 years ago
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    yes

  23. JamesJ
    • 2 years ago
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    Suppose now that 2x = 1. What does x equal?

  24. sparky16
    • 2 years ago
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    1/2

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

  26. JamesJ
    • 2 years ago
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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 = ... ?

  27. JamesJ
    • 2 years ago
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    If 1/y = a, then y = 1/a

  28. JamesJ
    • 2 years ago
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    If 1/y = 25, then y = ... ?

  29. sparky16
    • 2 years ago
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    ummm

  30. sparky16
    • 2 years ago
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    I thought I would just times y/1 to both sides

  31. JamesJ
    • 2 years ago
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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 = ...

  32. JamesJ
    • 2 years ago
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    If 1/y = a, then y = 1/a

  33. JamesJ
    • 2 years ago
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    Hence if 1/y = 25, then y = ....

  34. sparky16
    • 2 years ago
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    1/y=25 times by y/1 to both sides... 25y???

  35. JamesJ
    • 2 years ago
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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?

  36. sparky16
    • 2 years ago
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    yes

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

  38. sparky16
    • 2 years ago
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    ok. 25y=1 Oh then divide by 25 so I get 1/25

  39. sparky16
    • 2 years ago
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    thank you!

  40. JamesJ
    • 2 years ago
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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

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