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Math Help - Simultaneous equation for two unknowns

  1. #1
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    Simultaneous equation for two unknowns

    Hello

    Please could someone rearrange and show the steps for solving simultaneous equations for 2 unknowns, please? The unknowns are r and theta.

    Equation 1 is

    IB = (2r^2 / (17 x 10^3) x Na) (21 - 11sin^2 theta)

    Equation 2 is

    IB* = (r^2 / (5 x 10^3) x Na) (21 - 8sin^2 theta)

    Thank you very much.

    Kind regards,

    A
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  2. #2
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    What is IB, IB* and Na?
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  3. #3
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    IB = 2.841 x 10^-47

    IB* = 5.45 x 10^-47

    NA = 6.022 x 10^23
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  4. #4
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    IB = (2r^2 / (17 x 10^3) x Na) (21 - 11sin^2 theta)

    Equation 2 is

    IB* = (r^2 / (5 x 10^3) x Na) (21 - 8sin^2 theta)

    IB/IB* = 2*5*(21 - 11sin^2 theta)/17(21 - 8sin^2 theta)
    IB17(21 - 8sin^2 theta) = IB*2*5*(21 - 11sin^2 theta)
    Substitute the values of IB and IB* and solve for sinθ and then θ. Using this value of θ, find the value of r.
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  5. #5
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    BRLLIANT- thank you so much, very clear and well-written!
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  6. #6
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    Do you know how to rearrange for theta? So far I have:

    2.841 x 10^-47 x 17 x (21 – 8sin^2θ) = 5.45 x 10^-47 x 2 x 5 x (21 – 11 sin^2θ)

    4.8297 x 10^-46 x (21 – 8sin^2θ) = 5.45 x 10^-46 x (21 – 11 sin^2θ)

    0.88611 x (21 - (8sin^2) x θ) = 21 - (11sin^2) x θ
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  7. #7
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    Quote Originally Posted by alis88 View Post
    Do you know how to rearrange for theta? So far I have:

    2.841 x 10^-47 x 17 x (21 8sin^2θ) = 5.45 x 10^-47 x 2 x 5 x (21 11 sin^2θ)

    4.8297 x 10^-46 x (21 8sin^2θ) = 5.45 x 10^-46 x (21 11 sin^2θ)

    0.88611 x (21 - (8sin^2) x θ) = 21 - (11sin^2) x θ
    11sin^2(θ) - 0.88611*8sin^2(θ) = 21 - 0.88611 x 21
    sin^2θ(11 - 8*0.88611) = 21(1 - 0.88611)
    Now proceed.
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  8. #8
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    I've found theta and it equals 51.

    Please may you help rearrange the equation for r? I am not very good at handling sin^2. Thank you, and sorry for my slowness.
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  9. #9
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    Quote Originally Posted by alis88 View Post
    I've found theta and it equals 51.

    Please may you help rearrange the equation for r? I am not very good at handling sin^2. Thank you, and sorry for my slowness.
    IB = (2r^2 / (17 x 10^3) x Na) [21 - 11sin^2(θ)]
    Substitute the values of IB, Na and sin^2(51) and solve for r.
    Find sin(51) in the calculator and square it.
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  10. #10
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    r = 1.540 x 10^-10

    did you get the same? x
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