Answer:
(a) D = 192/√m
(bi) 96
(bii) 36
Explanation:
(a) The inverse of something is its reciprocal. The inverse of √m is 1/√m, for example.
When things are proportional, they are related by a constant factor. "y is proportional to x" means y=k·x, for example, for some constant k.
So if D is proportional to the inverse of √m, that means ...
D = k·(1/√m) = k/√m
Using the given values for D and m, you can find the value of k.
64 = k/√9 = k/3
Multiplying by 3 gives the value of k.
64 · 3 = k = 192
So, the required relation is ...
D = 192/√m
(b) Fill in the numbers and solve for the unknown.
(i) D = 192/√4 = 192/2 = 96
(ii) 32 = 192/√m
√m = 192/32 = 6 . . . . . . . multiply by (√m)/32
m = 6² = 36 . . . . . . . . . . . square both sides of the equation