C3 connected rates of change Watch

The_Blade
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Not sure how to do it

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brianeverit
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(Original post by The_Blade)
Not sure how to do it

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If the side of the cube is x, what is the volume?
You are given dx/dt.
How is dV/dt related to dV/dx and dx/dt?
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The_Blade
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(Original post by brianeverit)
If the side of the cube is x, what is the volume?
You are given dx/dt.
How is dV/dt related to dV/dx and dx/dt?
Do I need the formula for volume to work out a cube and differentiate it? I don't know how to do that

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krisshP
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Dy
(Original post by The_Blade)
Do I need the formula for volume to work out a cube and differentiate it? I don't know how to do that

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dV/dt = dV/dx X dx/dt by chain rule

V=x^3 so dV/dx=3x^2

You try the rest
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The_Blade
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(Original post by krisshP)
Dy


dV/dt = dV/dx X dx/dt by chain rule

V=x^3 so dV/dx=3x^2

You try the rest
I got 48 but book says 72

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krisshP
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(Original post by The_Blade)
I got 48 but book says 72

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dx/dt =-6
V=x^3
dV/dx=3x^2
dV/dt=dV/dx X dx/dt (chain rule used here)
=3x^2 X -6 (remember the cube side is decreasing at a rate of 6cm s^-1)
=-18x^2
When x=2
dV/dt=-18(2)^2
=-18(4)
=-72cm^3 s^-1

So the volume is decreasing at a rate of 72cm^3 s^-1.

I think your mistake was in the signs, so read the question carefully.
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The_Blade
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(Original post by krisshP)
dx/dt =-6
V=x^3
dV/dx=3x^2
dV/dt=dV/dx X dx/dt (chain rule used here)
=3x^2 X -6 (remember the cube side is decreasing at a rate of 6cm s^-1)
=-18x^2
When x=2
dV/dt=-18(2)^2
=-18(4)
=-72cm^3 s^-1

So the volume is decreasing at a rate of 72cm^3 s^-1.

I think your mistake was in the signs, so read the question carefully.
thank you very much

the problem was i differentiated x^3 to 2x^2 lol
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The_Blade
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(Original post by krisshP)
dx/dt =-6
V=x^3
dV/dx=3x^2
dV/dt=dV/dx X dx/dt (chain rule used here)
=3x^2 X -6 (remember the cube side is decreasing at a rate of 6cm s^-1)
=-18x^2
When x=2
dV/dt=-18(2)^2
=-18(4)
=-72cm^3 s^-1

So the volume is decreasing at a rate of 72cm^3 s^-1.

I think your mistake was in the signs, so read the question carefully.
Can you help me with this one. I don't know the formula for dl/dv

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krisshP
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(Original post by The_Blade)
Can you help me with this one. I don't know the formula for dl/dv

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Let side length=x
V=x^3
dV/dt=2

dx/dV is needed as we want rate of change of x (dx), dependent variable, and we can work out easily volume V

dV/dx=3x^2

Spoiler:
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dx/dV=1/(dV/dx)
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The_Blade
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(Original post by krisshP)
Let side length=x
V=x^3
dV/dt=2

dx/dV is needed as we want rate of change of x (dx), dependent variable, and we can work out easily volume V

dV/dx=3x^2

Spoiler:
Show
dx/dV=1/(dV/dx)
Thank you, you wonderful man

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