Final answer:
To find the expression for the height of the cylinder, rearrange the equation for the volume of the cylinder and solve for h using the formula V = πr²h.
Step-by-step explanation:
In order to find an expression for the height of the cylinder, we need to rearrange the given equation for the volume of the cylinder and solve for h. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, we have the equation y = 2x² - 100x + 288x - 64. To find the expression for h, we set the equation equal to V and solve for h. y = 2x² - 100x + 288x - 64, V = πr²h. Setting y equal to V: 2x² - 100x + 288x - 64 = πr²h. Combining like terms: 2x² + 188x - 64 = πr²h. Now, we have an expression for the height of the cylinder: h = (2x² + 188x - 64) / πr². This is the expression for the height of the cylinder based on the given equation for the volume.