Question

Y is inversely proportionl to a^3 when a=2, y=10

Answer 1

y =
`(80)/(a^3)`

Explanation:

Given y is inversely proportional to a³ then the equation relating them is

y =
`(k)/(a^3)` ← k is the constant of variation

To find k use the condition a = 2, y = 10 , then

10 =
`(k)/(2^3)` =
`(k)/(8)` ( multiply both sides by 8 )

80 = k

y =
`(80)/(a^3)` ← equation of variation

Answer 2

Answer:

y = 16/25x³

Explanation:

If y is inversely proportional to a^3, this is expressed as;

y∝1/a³

y = k/a³ where k is the proportionality constant

Given a=2, y=10, then 10 = k/2³

k = 10*2³

k = 80

Substituting k = 80 back into the formula;

y = 80/a³ ............. 1

Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx

If x=4, a=20 then;

20 = 4k

k = 20/4

k = 5

Substituting k = 5 back into the formula;

a = 5x ....... 2

Substitute equation 2 into 1;

y = 80/a³

y = 80/(5x)³

y = 80/125x³

y = 16/25x³

Hence the formula for y in terms of x is y = 16/25x³

Explanation: