Answer:
a) 2d - 3w = 0
b) d = 18 cm
Step-by-step explanation:
Since, distance (d) varies directly with the weight (w), mathematically it can be expressed as given below:
a)
[tex]d \: \alpha \: w \\ \\ \therefore \: d = kw...(1) \: \\ (k = constant \: of \: proportionality) \\ \\ when \: w = 6 \: g \implies \: d \: = 9 \: cm \\ plugging \: the \: values \: of \: w \: and \: d \: \\ in \: equation \: (1) \\ \\ 9 = k \times 6 \\ \\ k = \frac{9}{6} \\ \\ k = \frac{3}{2} \\ \\ plug \: k = \frac{3}{2} \: in \: equation \: (1) \\ d = \frac{3}{2} w \\ \\ \therefore \: 2d = 3w \\ \\ \huge \red{ \boxed{ 2d - 3w = 0}} \\ this \: is \: the \: required \: equation \\ \\ \\ b) \: when \: w = 12 \: g, \: \: d =? \\ \\ plug \: w = 12 \: in \: 2d - 3w = 0 \\ \\ 2d - 3 \times 12 = 0 \\ \\ 2d - 36 = 0 \\ \\ 2d = 36 \\ \\ d = \frac{36}{2} \\ \\ \huge \orange{ \boxed{d = 18 \: cm}}[/tex]
