Use implicit differentiation to confirm this for the circle x? + y? = r2 by showing that the line tangent to the circle at the point (a, b) is perpendicular to the radius drawn from (0,0) to (a, b).

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c.what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?