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Y is inversely proportional to the cube of (x-1). y=9.45 when x=3. Find y when x=4

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Answer:

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.

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