The function f (x , y r) = 5 xy has an absolute maximum value and absolute minimum value subject to the constraint 2*x ^2 + 2*y^2 - 3*xy=49. use lagrange multipliers to find these values.

Imagine that you have two balloons (or, better yet, actually inflate two balloons, if possible). create static electricity around one of the balloons by rubbing it against your hair or your sweater and then bring that balloon close to the other balloon, which has not been charged. try this with at least one other object—and for variety in the discussion, avoid using an object already described by your classmates. then, for your initial post to the discussion, answer the following questions: what happened with the two balloons?

Question part points submissions used suppose that 2 j of work is needed to stretch a spring from its natural length of 26 cm to a length of 36 cm. (a) how much work is needed to stretch the spring from 28 cm to 32 cm? (round your answer to two decimal places.)

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. to get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1.00ºc. note that this calculation is only approximate because ocean warming is not uniform with depth. (answer in ×10^{-3} −3 m)