Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2 at (6, 6, 7) and use it to approximate the number 6.022 + 5.992 + 6.972 . (round your answer to five decimal places.)

Identify an equation in point slope form for the line perpendicular to y=3x+5 that passes through (4,-1)

Two language majors, anna and megan, took exams in two languages. anna scored 85 on both exams. megan scored 74 on the first exam and 85 on the second exam. overall, student scores on the first exam had a mean of 82 and a standard deviation of 4, and the second exam scores had a mean of 71 and a standard deviation of 13. a) to qualify for language honors, a major must maintain at least an 85 average across all language courses taken. so far, which of anna and megan qualify? b) which student's overall performance was better?

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