Question

Y

∝
√
x
If
y
=
45
when
x
=
81
find,
x
when
y
=
100

Answer 1

x = 400 when y = 100

Explanation:

This is a question in relation to direct variation.

y ∝
`√(x)`

y = k
`√(x)`

Given that, y = 45, x = 81. Then;

45 = k
`√(81)`

45 = 9k

k =
`(45)/(9)`

k = 5

Thus the relationship among the variables is;

y = 5
`√(x)`

If y = 100, then;

100 = 5
`√(x)`

`√(x)` =
`(100)/(5)`

`√(x)` = 20

x =
`(20)^(2)`

x = 400

Therefore, x = 400 when y = 100.