Use the Method of Disks or Washers, or the Method $$y = 4 x ^ { 2 } , y = 8 x - 4 , y = 16 \text {; the } y \text {-axi }$$

question 68

Essay

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
$$y = 4 x ^ { 2 } , y = 8 x - 4 , y = 16 \text {; the } y \text {-axi }$$

Analyze the impact of the Civil War on government structures and concepts, especially with regard to state sovereignty and federal authority.

Explore the role and impact of the Civil War on women, and understand how the war reshaped gender roles and expectations.

Evaluate the efficacy of the Emancipation Proclamation as a moral, legal, and political document.

Understand the reasons behind the Northern victory and the overall costs and consequences of the Civil War.

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