y is inversely proportional to the cube of (x-1). y=9.45 when x=3. Find y when x=4
To solve this problem, we can use the formula for inverse variation:
y = k/(x-1)^3
where k is a constant.
Given that y = 9.45 when x = 3, we can substitute these values into the equation to find k:
9.45 = k/(3-1)^3
9.45 = k/2^3
9.45 = k/8
To solve for k, we can multiply both sides of the equation by 8:
9.45 * 8 = k
75.6 = k
Now we have the value of k, which is 75.6. We can substitute this into the equation y = k/(x-1)^3:
y = 75.6/(x-1)^3
To find y when x = 4, we substitute x = 4 into the equation:
y = 75.6/(4-1)^3
y = 75.6/3^3
y = 75.6/27
y ≈ 2.8
Therefore, when x = 4, y ≈ 2.8.
To find the value of y when x=4, we can use the concept of inverse proportionality and the given information. Let's go step-by-step:
1. Start with the inverse proportionality statement: y is inversely proportional to the cube of (x-1).
2. Mathematically, this can be written as y = k/(x-1)^3, where k is the constant of proportionality.
3. We have been given that y = 9.45 when x = 3. So we can plug these values into the equation: 9.45 = k/(3-1)^3.
4. Simplify the equation: 9.45 = k/2^3, which is 9.45 = k/8.
5. Multiply both sides of the equation by 8 to isolate k: 9.45 * 8 = k, which is k = 75.6.
6. Now, using the value of k, we can calculate the value of y when x = 4. Plug the values into the inverse proportionality equation: y = 75.6/(4-1)^3.
7. Simplify the equation: y = 75.6/3^3, which is y = 75.6/27.
8. Calculate the final value of y: y = 2.8.
Therefore, when x = 4, y will be equal to 2.8.