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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

Relevance

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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• 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

• Again, you made several mistakes hence the thumbs down.

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

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