A diabetic patient who has had vomiting and diarrhea for the past 3 days is admitted to the hospital with a blood glucose of 748 mg/ml (41.5 mmol/L) and a urinary output of 120 ml in the first hour. The vital signs are blood pressure (BP) 72/62; pulse 128, irregular and thready; respirations 38; and temperature 97° F (36.1° C). The patient is disoriented and lethargic with cold, clammy skin and cyanosis in the hands and feet. The nurse recognizes that the patient is experiencing the: