Question

If y is directly proportional to the square root of x and y=4 when x=1.

a) Find the formula for y in terms of x.
b) Find the value of y given x=36
c)Find the value x given y=36​

Answer 1

If y is directly proportional to the square root of x, we can write:

y = k * sqrt(x)

where k is the constant of proportionality. To find k, we can use the initial condition given:

y = k * sqrt(x)
y = 4 when x = 1

Substituting these values, we get:

4 = k * sqrt(1)
k = 4

So, the formula for y in terms of x is:

y = 4 * sqrt(x)

a) To find the value of y given x = 36, we can substitute:

y = 4 * sqrt(36) = 4 * 6 = 24

Therefore, when x = 36, y = 24.

b) To find the value of x given y = 36, we can solve the formula for x:

y = 4 * sqrt(x)
36 = 4 * sqrt(x)
sqrt(x) = 9
x = 81

Therefore, when y = 36, x = 81.

Answer 2

see explanation

Explanation:

(a)

given y is directly proportional to
`√(x)` , then the equation relating them is

y = k
`√(x)` ← k is the constant of proportion

to find k use the condition y = 4 when x = 1

4 = k
`√(1)` = k

y = 4
`√(x)` ← equation of proportion

(b)

when x = 36 , then

y = 4 ×
`√(36)` = 4 × 6 = 24

(c)

when y = 36 , then

36 = 4
`√(x)` ( divide both sides by 4 )

9 =
`√(x)` ( square both sides to clear the radical )

9² = (
`√(x)` )² , then

81 = x