(a) At what rate is the radius of a spherical balloon changing at the time that the radius is 10cm, if air is being pumped in at a rate of 40cm3s¡1?

(b) Find an expression fordy/dx

given that 3xy+ey= 3.

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- Jan 15th 2009, 06:10 PMFazrate of change(a) At what rate is the radius of a spherical balloon changing at the time that the radius is 10
*cm*, if air is being pumped in at a rate of 40*cm*3*s¡*1?

(b) Find an expression for*dy/dx*

given that 3*xy*+*ey*= 3.

- Jan 15th 2009, 06:16 PMMush
1) The volume of a sphere is . We know that the volume and radius are functions of time here, hence, using implicit differentiation:

Hence:

You know what is, and you know what the radius is at our point of interest. So plug them in!

2)

You could take out a factor of y on the LHS, and then move all other terms to the RHS, giving you a nice explicit function to differentiate. Or you could go about it using implicit differentiation!

Then use the quotient rule!

Or

Rearrange and remember to substitute in y again from the fact that . - Jan 15th 2009, 06:22 PMtrythisThanks & noted
Thank you