Hi,
Hello, I just had a small question about assumptions in mathematical word problems. Suppose you are given a calculus problem (related-rates), "A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?"(Larson Calculus P 153) This is a quoted problem from Larson's Calculus 10th Edition. My question is here: Why do you assume for example that there is no hole from, which air LEAVES? Basically, in general, why do you make unstated assumptions for example, there is no air leaving, or the balloon doesnt explode before the radius is (a) 30 cm etc..? Here is what others say, Others say it is so you could solve the problem, what do you think?
Thanks a lot =)