Question
y is inversely proportional to the cube of (x-1). y=9.45 when x=3. Find y when x=4
Answers
GPT 3.5
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.
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.