Consider the right triangle in the figure below and determine the value of a, b,c, and d.

Areflection of shape i across the y-axis, followed by a , and then a translation left 6 units and down 4 units confirms congruence between shape i and shape ii. alternatively, a of shape ii about the origin, followed by a reflection across the y-axis, and then a translation right 4 units and up 6 units confirms congruence between shape ii and shape i.

Acone is placed inside a cylinder. the cone has half the radius of the cylinder, but the height of each figure is the same. the cone is tilted at an angle so its peak touches the edge of the cylinder’s base. what is the volume of the space remaining in the cylinder after the cone is placed inside it?

Find the exact value of cos(arcsin( one fourth for full credit, explain your reasoning. (2 points)