Suppose you are traveling straight from Los Angeles, California to Albuquerque, New Mexico, stopping overnight in Flagstaff, Ari
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For the cylinder on the left-hand-side,
now, for the triangular prism on the right-hand-side,
notice is really just 2 triangles and 3 rectangles, stacked up to each other at the edges.
the triangles have a base of 4, and a height of 1.5.
the rectangle on the left and the one on the right is a 6x2.5 rectangle.
the rectangle at the bottom, is a 4x6 rectangle.
adding their areas, is the area of the prism,
![\bf \stackrel{two~triangles}{2\left[\cfrac{1}{2}(4)(1.5) \right]}+\stackrel{left-right~rectangles}{2(6\cdot 2.5)}+\stackrel{bottom~rectangle}{4\cdot 6} \\\\\\ 6~~+~~30~~+~~24](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Btwo~triangles%7D%7B2%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%284%29%281.5%29%20%20%5Cright%5D%7D%2B%5Cstackrel%7Bleft-right~rectangles%7D%7B2%286%5Ccdot%202.5%29%7D%2B%5Cstackrel%7Bbottom~rectangle%7D%7B4%5Ccdot%206%7D%0A%5C%5C%5C%5C%5C%5C%0A6~~%2B~~30~~%2B~~24)
now, for the triangular prism on the right-hand-side,
notice is really just 2 triangles and 3 rectangles, stacked up to each other at the edges.
the triangles have a base of 4, and a height of 1.5.
the rectangle on the left and the one on the right is a 6x2.5 rectangle.
the rectangle at the bottom, is a 4x6 rectangle.
adding their areas, is the area of the prism,
If , then
. You replace all x's in the function with -3.
Finish by evaluating the absolute value and then adding that to the 5 that's behind the absolute value.
Can you finish it from there?