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hosiduy

  • 2 years ago

can anyone help me with this: x = 2sin t; y = 3cos t; z(x,y) = 3x^2 + 2y find: d(dz)/d^2(t)

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  1. mukushla
    • 2 years ago
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    you mean \[\frac{d^2z}{dt^2}\] ?

  2. mukushla
    • 2 years ago
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    @hosiduy

  3. hosiduy
    • 2 years ago
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    yes

  4. mukushla
    • 2 years ago
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    just put x(t) and y(t) in the equation of z and take derivative twice

  5. mukushla
    • 2 years ago
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    then what will u get?

  6. hosiduy
    • 2 years ago
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    i still don't understand clear your way, can you make that more clear?

  7. meera_yadav
    • 2 years ago
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    hiii z(x,y)=3 x^2+2y first substitute the values of x and y in z(x,y), you'll get z(t)=6sin^2t+6cost dz/dt=6(2sint cost -sint) =6(sin2t-sint) {2sint cost =sin2t} d^2z/dt^2 = 6(2cost2t-cost) :) cheers

  8. mukushla
    • 2 years ago
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    \[x=2 \ sint \\ y=3 \ \cos t \\ z(t)=3x^2+2y=3 (2 \ \sin t)^2+2( 3 \ \cos t)=12 \sin^2t+6 \cos t\]

  9. mukushla
    • 2 years ago
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    @hosiduy now take derivative of z(t) twice am i clear now?

  10. hosiduy
    • 2 years ago
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    oh, i understand now, thank all guys :D

  11. mukushla
    • 2 years ago
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    yw

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