Brewed coffee is often too hot to drink right away. You can cool it with an ice cube, but this dilutes it. Or you can buy a device that will cool your coffee without dilution - a 300 g aluminum cylinder that you take from your freezer and place in a mug of hot coffee. If the cylinder is cooled to -20 degreees celsius, a typical freezer temperature, and then dropped into a large cup of coffee (essentially water, with a mass of 500 ) at 85 degrees celsius, what is the final temperature of the coffee?

For the below questions, consider a consumer that consumes two goods, x and z with the following utility function. u with bar on top space equals space x to the power of 1 third end exponent z to the power of 2 over 3 end exponent suppose initial values for income and the prices of goods x and z are y equals 90, p subscript x equals space 10, and p subscript z equals 15 respectively, then the price of good x falls to syntax error from line 1 column 89 to line 1 column 100. unexpected '\'.. what is the magnitude of the total effect