27) [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Sub and solve. [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] becomes
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
and
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
and
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
and
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or
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from which
[unparseable or potentially dangerous latex formula].
Thankfully, [unparseable or potentially dangerous latex formula].
38) You know the centers of the balls on the bottom are [unparseable or potentially dangerous latex formula] inches high, and the center of the top ball is [unparseable or potentially dangerous latex formula] inches from the top. Then connect the four centers of the balls into a pyramid with equilateral triangle faces (regular tetrahedron) and side lengths of [unparseable or potentially dangerous latex formula] in. We only want to find the height of this pyramid, then add [unparseable or potentially dangerous latex formula] to it. Let the diagram show the bottom triangle.
- bowling ball prob.png (1.73 KiB) Viewed 1603 times
The foot of the altitude from the top vertex will land at the centroid of the bottom triangle. The altitude and the red line segment are the legs of a right triangle with hypotenuse [unparseable or potentially dangerous latex formula] in. We know the red line segment has length [unparseable or potentially dangerous latex formula] of the whole cevian (centroid property). So, the red segment is length
[unparseable or potentially dangerous latex formula]
so the height is
[unparseable or potentially dangerous latex formula]
final answer [unparseable or potentially dangerous latex formula]