if x is directly proportional to 6 more than the cube of y and x is 28 when y is 2, what is the value of y when x is 140?
x=k(y^3+6)
28=k(8+6) or k= 2
140=2y^3+12
y^3=64
y=4
Well, in this situation, we have a direct proportion between x and (6 + y^3). So, let's set up an equation!
If x is directly proportional to (6 + y^3), we can write this proportion as:
x = k(6 + y^3),
where k is the constant of proportionality.
Now, we are given that x equals 28 when y is 2. Let's substitute these values into our equation:
28 = k(6 + 2^3).
Simplifying, we have:
28 = k(6 + 8),
28 = k(14),
k = 28/14,
k = 2.
Now that we have the constant of proportionality (k = 2), we can find y when x is 140.
140 = 2(6 + y^3).
Let's solve for y:
140 = 12 + 2y^3,
128 = 2y^3,
64 = y^3,
y = ∛64,
y = 4.
So, when x is 140, y will be 4.
To find the value of y when x is 140, we can set up a proportional equation based on the given information.
According to the problem, x is directly proportional to 6 more than the cube of y. So we can write the equation as:
x = k(y^3 + 6)
Where k is the constant of proportionality.
We can find the value of k by substituting the values of x and y from one of the given data points. Let's use the first data point: x = 28 and y = 2.
28 = k(2^3 + 6)
28 = k(8 + 6)
28 = k(14)
Divide both sides of the equation by 14:
28/14 = k
So, k = 2.
Now we can substitute the value of k into the equation:
x = 2(y^3 + 6)
To find the value of y when x is 140, we can substitute x = 140 into the equation and solve for y:
140 = 2(y^3 + 6)
Divide both sides of the equation by 2:
70 = y^3 + 6
Subtract 6 from both sides of the equation:
64 = y^3
Taking the cube root of both sides, we get:
y = 4
Therefore, when x is 140, the value of y is 4.
To find the value of y when x is 140, we need to use the information given in the problem and set up a proportion.
We are given that x is directly proportional to 6 more than the cube of y. This can be written as:
x = k(y^3 + 6)
where k is the constant of proportionality.
We are also given that when y is 2, x is 28. Plugging these values into our equation, we get:
28 = k(2^3 + 6)
28 = k(8 + 6)
28 = k(14)
To solve for k, we divide both sides of the equation by 14:
k = 28/14
k = 2
Now, we can substitute the value of k back into our equation:
x = 2(y^3 + 6)
We want to find the value of y when x is 140. Plugging this into the equation, we get:
140 = 2(y^3 + 6)
Divide both sides of the equation by 2:
70 = y^3 + 6
Subtract 6 from both sides of the equation:
64 = y^3
To find the cube root of 64, we can take the cube root of both sides:
∛64 = ∛y^3
4 = y
Therefore, when x is 140, the value of y is 4.