Question
change y=(x-2)^3 into a volume equation
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GPT 3.5
To change the equation y = (x-2)^3 into a volume equation, we can consider the scenario of rotating the equation around the x-axis.
Let's assume that y represents the height of a cross-sectional shape, and x represents the radius of that shape.
The volume of a solid of revolution can be calculated using the formula V = ∫πy^2 dx.
In this case, the value of y is given as (x-2)^3. Substituting this into the formula, we get:
V = ∫π((x-2)^3)^2 dx
Simplifying:
V = ∫π(x-2)^6 dx
This is the volume equation for the solid of revolution formed by rotating the equation y = (x-2)^3 about the x-axis.
Let's assume that y represents the height of a cross-sectional shape, and x represents the radius of that shape.
The volume of a solid of revolution can be calculated using the formula V = ∫πy^2 dx.
In this case, the value of y is given as (x-2)^3. Substituting this into the formula, we get:
V = ∫π((x-2)^3)^2 dx
Simplifying:
V = ∫π(x-2)^6 dx
This is the volume equation for the solid of revolution formed by rotating the equation y = (x-2)^3 about the x-axis.
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