Consider the function f(x, y, z) = x 2−3y 2−z 2 . All parts refer to this function f. a. Find the absolute maximum and absolute minimum values of f(x, y, z) subject to the constraint x 2 + y 2 + z 2 = 9.

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

Either enter an exact answer in terms of \piπ or use 3.143.14 for \piπ and enter your answer as a decimal.

Thomas works for a company that occupies a large campus every workday he orders a cup of coffee on campus and the $1.50 cost is automatically deducted from his paycheck. if thomas visits the coffee shop 13 times what will the net change in his paycheck be