Answer:
1a) [tex]m = \frac{60}{ \sqrt{31 - 2n} } [/tex]
b) 8.47 (3 s.f.)
Step-by-step explanation:
If y is inversely proportional to x, then [tex]y = \frac{k}{x} [/tex], where k is a constant.
Since m is inversely proportional to [tex] \sqrt{31 - 2n} [/tex],
[tex]m = \frac{k}{ \sqrt{31 - 2n} } [/tex], where k is a constant.
When n=3,
[tex]m = \frac{k}{ \sqrt{31 - 2(3)} } \\ m = \frac{k}{ \sqrt{31 - 6} } \\ m = \frac{k}{ \sqrt{25} } \\ m = \frac{k}{5} [/tex]
when n=11,
[tex]m = \frac{k}{ \sqrt{31 - 2(11)} } \\ m = \frac{k}{ \sqrt{31 - 22} } \\ m = \frac{k}{ \sqrt{9} } \\ m = \frac{k}{3} [/tex]
Since the sum of the values of m when n=3 and n=11 is 32,
[tex] \frac{k}{3} + \frac{k}{5} = 32 \\ \frac{5k}{15} + \frac{3k}{15} = 32 \\ \frac{8k}{15} = 32 \\ 8k = 32(15) \\ 8k = 480 \\ k = 60[/tex]
a) [tex]m = \frac{60}{ \sqrt{31 - 2n} } [/tex]
b) When m=16,
[tex]16 = \frac{60}{ \sqrt{31 - 2n} } \\ 16( \sqrt{31 - 2n} ) = 60 \\ \sqrt{31 - 2n } = 60 \div 16 \\ \sqrt{31 - 2n} = 3.75 \\ 31 - 2n = 3.75^{2} \\ 31 - 14.0625 = 2n \\ 2n = 16.9375 \\ n = 8.47 \: (3 \: s.f.)[/tex]
