Question

Please help i need qn1!!

Answer 1

1a)
`m = (60)/( √(31 - 2n) )`

b) 8.47 (3 s.f.)

Explanation:

If y is inversely proportional to x, then
`y = (k)/(x)`, where k is a constant.

Since m is inversely proportional to
`√(31 - 2n)`,

`m = (k)/( √(31 - 2n) )`, where k is a constant.

When n=3,

`m = (k)/( √(31 - 2(3)) ) \\ m = (k)/( √(31 - 6) ) \\ m = (k)/( √(25) ) \\ m = (k)/(5)`

when n=11,

`m = (k)/( √(31 - 2(11)) ) \\ m = (k)/( √(31 - 22) ) \\ m = (k)/( √(9) ) \\ m = (k)/(3)`

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

`(k)/(3) + (k)/(5) = 32 \\ (5k)/(15) + (3k)/(15) = 32 \\ (8k)/(15) = 32 \\ 8k = 32(15) \\ 8k = 480 \\ k = 60`

a)
`m = (60)/( √(31 - 2n) )`

b) When m=16,

`16 = (60)/( √(31 - 2n) ) \\ 16( √(31 - 2n) ) = 60 \\ √(31 - 2n ) = 60 / 16 \\ √(31 - 2n) = 3.75 \\ 31 - 2n = 3.75^(2) \\ 31 - 14.0625 = 2n \\ 2n = 16.9375 \\ n = 8.47 \: (3 \: s.f.)`