if x is directly proportional to y3 and x=32 when y=2
More information need but have in mind that
X∝y³
X=ky³
32=8k
K=4
Therefore their relationship is x=4y³
Good
To find the constant of proportionality, we can use the formula for direct proportionality, which states that x = k * y^3, where k is the constant of proportionality.
Using the given information, we have x = 32 and y = 2. Plugging these values into the formula, we get 32 = k * 2^3.
Simplifying, we have 32 = k * 8.
To solve for k, we can divide both sides of the equation by 8:
32/8 = k * 8/8
4 = k
Therefore, the constant of proportionality is 4.
To find the relationship between x and y, we are given that x is directly proportional to y^3. This means that x is a multiple of y^3, where the constant of proportionality is the same for all values.
So, we can write the equation as:
x = k * y^3
To find the value of k, we need to use the given information that x = 32 when y = 2. Plugging these values into the equation, we have:
32 = k * 2^3
32 = k * 8
Now, we can solve for k:
k = 32 / 8
k = 4
Therefore, the equation relating x and y is:
x = 4 * y^3