Provide an appropriate response.Use the method of Lagrange multipliers to determine the critical points of f(x, y, z) = x2 - 3y2 - z2 + 6 subject to the constraint 5x - 3y + z = 21.
Fill in the blank(s) with the appropriate word(s).
(5, 1, -1)
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Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
A. 24y(y + 4)
B. 
C. 
D. 
Solve.14 - x2 ? 0
A. (-?, -
]
B. (-14, 14)
C. [-
, 
]
D. [
, ?)
Write the expression in the standard form a + bi.(1 + i)3
A. 2 + 2i B. -2 + 2i C. -2 + i D. -2 - 2i
Solve the problem involving related quantities.The president of a certain university makes three times as much money as one of the department heads. If the total of their salaries is $240,000, find each worker's salary.
A. president's salary = $120,000; department head's salary = $60,000 B. president's salary = $18,000; department head's salary = $6000 C. president's salary = $180,000; department head's salary = $60,000 D. president's salary = $60,000; department head's salary = $180,000