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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Calculus Related Rates Help?

If 6xy+5x=30, find dx/dt when y=4 and dy/dt=8

4 Answers

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  • 2 months ago
    Favorite Answer

    6xy + 5x = 30

    x(6y + 5) = 30

    x = 30 / (6y + 5)

    dx/dy = 180 / (6y + 5)^2

    When y = 4:

    dx/dy = 180/841

    dx/dt = dx/dy * dy/dt

    dx/dt = (180/841) * 8

    dx/dt = 1440/841

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  • 2 months ago

    6xy+5x=30, find dx/dt when y=4 and dy/dt=8

    6 x y + 5 x  =  30

    Differentiate w.r.to t

    => 6 ( y dx/dt + x dy/dt )  +  5  dx/dt  =  30

    => 6 ( 4 * dx/dt  +  x * 8 )  +  5 * dx/dt  =  30  ....... ( 1 )

    Again given that ------  6 x y + 5 x = 30

    When  y  =  4 

    =>  6 (x) (4) + 5 x  =  30

    =>  29 x  =  30   =>   x  =  30/29

    Substituting  x  =  30/29  and  y =  4 in (1)  we get --

    => 6 ( 4 * dx/dt + 30/29 * 8)+ 5 * dx/dt   =  30

     

    => 24 (dx/dt)  +  (1440/29)  +  5 * (dx/dt)   =  30

    =>  ( 29 ) (dx/dt)  =  30 - ( 1440/29 )  =   -  19.655

    => dx/dt  =  - 19.655/29  =  - 1.02258  ........ Answer

    • rotchm
      Lv 7
      2 months agoReport

      Again, you made several mistakes hence the thumbs down. 

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  • 2 months ago

    6xy+5x=30

    6y*dx/dt + 6x*dy/dt + 5dx/dt=0

    (6y+5)dx/dt + 6x*dy/dt=0

    differntiating with respect to x

    dx/dt when y=4 and dy/dt=8

    (6*4+5)dx/dt + 6x*8=0

    29*dx/dt + 48x=0

    dx/dt=-48x/29

    dx/dt=-2x

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  • rotchm
    Lv 7
    2 months ago

    Many ways. Isolate x, say. Then differentiate each side.

    If you follow my lead, you will get the correct answer, contrary to the answers you got from the others. 

    If you were not anon I would detail further. 

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