**Answers to quiz 5**

1,2. dM/M^{2} = dm_{1}/m_{1}^{2} + dm_{2}/m_{2}^{2}

dM/M = M/m_{1}·dm_{1}/m_{1} + M/m_{2}·dm_{2}/m_{2}

if m_{1} = 2m, m_{2} = m, then M = (2/3)m and
dM/M = (1/3)dm_{1}/m_{1} + (2/3)dm_{2}/
m_{2}

1: (1/3)2% + (2/3)(−1%) = 0 (M doesn't change)

2: (1/3)(−1%) + (2/3)2% = 1% (M increases by 1%)

3. f = sinh xy, f_{y} = x cosh xy, f_{xy} = cosh xy + xy sinh xy

3. g = cosh xy, g_{y} = x sinh xy, g_{xy} = sinh xy + xy cosh xy

gg_{xy} − ff_{xy} = xy

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