Amachine is rolling a metal cylinder under pressure. the radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume, v, is 128pi cubic inches. at what rate is the length, h, changing when the radius, r, is 1.5 inches? note: v=pi(r^2)h

hi, as above this is the problem i am doing. there is no answer given to check so i was wondering about a couple of things:

is volume assumed to be a constant in this problem?

is the height change decreasing (negative rate) or increasing (positive rate) in the final answer?

i worked out dh/dt to be 512/135 in./s

The metal wire in an incandescent lightbulb glows when the light is switched on and stops glowing when it is switched off. this simple process iswhich kind of a change? a.a physical changeb. a chemical changec. a nuclear changed. an ionic change

You are a sales representative for a company that makes a new alternate fuel for vehicles. you have prepared a presentation for the environmental engineers to sell your new product. what question do you expect the audience to ask regarding whether the new fuel will cause less damage to the environment? a. do we have to change any parts of the vehicle to use this alternate fuel? b. will the vehicles get better fuel mileage with the alternate fuel? c. how much greenhouse gas does your fuel produce compared with current fuel sources? d. is the alternate fuel more expensive than fossil fuel?

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?