Follow the comment and topic is mathematical real analysis
prove |x|−|y| ≤|x−y| for any two real numbers x and y. (hint: recall that |a|≤b if and only if −b≤a≤b. so it is enough to show that −|x−y|≤|x|−|y|≤|x−y|. use the triangle inequality to prove the desired inequalities.

The magnitude, m, of an earthquake is defined to be m=log l/s, where i is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and s is the intensity of a “standard” earthquake, which is barely detectable. what is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.

A50% increase followed by 33 1/2% decrease

Adam used 1072.4 gallons of water over the course of 7 days. how much water did adam use, on average, each day?