Question

Please help i need qn1!!

Answer 1

Answer:

1a) $m = \frac{60}{ \sqrt{31 - 2n} }$

b) 8.47 (3 s.f.)

Step-by-step explanation:

If y is inversely proportional to x, then $y = \frac{k}{x}$, where k is a constant.

Since m is inversely proportional to $\sqrt{31 - 2n}$,

$m = \frac{k}{ \sqrt{31 - 2n} }$, where k is a constant.

When n=3,

$m = \frac{k}{ \sqrt{31 - 2(3)} } \\ m = \frac{k}{ \sqrt{31 - 6} } \\ m = \frac{k}{ \sqrt{25} } \\ m = \frac{k}{5}$

when n=11,

$m = \frac{k}{ \sqrt{31 - 2(11)} } \\ m = \frac{k}{ \sqrt{31 - 22} } \\ m = \frac{k}{ \sqrt{9} } \\ m = \frac{k}{3}$

Since the sum of the values of m when n=3 and n=11 is 32,

$\frac{k}{3} + \frac{k}{5} = 32 \\ \frac{5k}{15} + \frac{3k}{15} = 32 \\ \frac{8k}{15} = 32 \\ 8k = 32(15) \\ 8k = 480 \\ k = 60$

a) $m = \frac{60}{ \sqrt{31 - 2n} }$

b) When m=16,

$16 = \frac{60}{ \sqrt{31 - 2n} } \\ 16( \sqrt{31 - 2n} ) = 60 \\ \sqrt{31 - 2n } = 60 \div 16 \\ \sqrt{31 - 2n} = 3.75 \\ 31 - 2n = 3.75^{2} \\ 31 - 14.0625 = 2n \\ 2n = 16.9375 \\ n = 8.47 \: (3 \: s.f.)$