Question

It x and y vary inversely, fill in the following blanks:
(i)

x	12	16	...	8	...
y	...	6	4	...	0.25

(ii)

x	16	32	8	128
y	4	...	...	0.25

(iii)

x	9	...	81	243
y	27	9	...	1

Answer 1

$$\begin{gathered} \left(i\right)\mathrm{Since}x\mathrm{and}y\mathrm{vary}\mathrm{inversely},\mathrm{we}\mathrm{have}: \\ xy=k \\ \mathrm{For}x=16\mathrm{and}y=6,\mathrm{we}\mathrm{have}: \\ 16\times 6=k \\ \Rightarrow k=96 \\ \mathrm{For}x=12\mathrm{and}k=96,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 12y=96 \\ \Rightarrow y=\frac{96}{12} \\ =8 \\ \mathrm{For}y=4\mathrm{and}k=96,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 4x=96 \\ \Rightarrow x=\frac{96}{4} \\ =24 \\ \mathrm{For}x=8\mathrm{and}k=96,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 8y=96 \\ \Rightarrow y=\frac{96}{8} \\ =12 \\ \mathrm{For}y=0.25\mathrm{and}k=96,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 0.25x=96 \\ \Rightarrow x=\frac{96}{0.25} \\ =384 \\ \left(\mathrm{ii}\right)\mathrm{Since}x\mathrm{and}y\mathrm{vary}\mathrm{inversely},\mathrm{we}\mathrm{have}: \\ xy=k \\ \mathrm{For}x=16\mathrm{and}y=4,\mathrm{we}\mathrm{have}: \\ 16\times 4=k \\ \Rightarrow k=64 \\ \mathrm{For}x=32\mathrm{and}k=64,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 32y=64 \\ \Rightarrow y=\frac{64}{32} \\ =2 \\ \mathrm{For}x=8\mathrm{and}k=64 \\ xy=k \\ \Rightarrow 8y=64 \\ \Rightarrow y=\frac{64}{8} \\ =8 \\ \left(\mathrm{iii}\right)\mathrm{Since}x\mathrm{and}y\mathrm{vary}\mathrm{inversely},\mathrm{we}\mathrm{have}: \\ xy=k \\ \mathrm{For}x=9\mathrm{and}y=27 \\ 9\times 27=k \\ \Rightarrow k=243 \\ \mathrm{For}y=9\mathrm{and}k=243,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 9x=243 \\ \Rightarrow y=\frac{243}{9} \\ =27 \\ \mathrm{For}x=81\mathrm{and}k=243,\mathrm{we}\mathrm{have}: \\ xy=k \\ \Rightarrow 81y=243 \\ \Rightarrow y=\frac{243}{81} \\ =3 \end{gathered}$$