A wall of a building is made from blocks that are each 1 cubic foot. The wall is 6 feet high and 6 feet wide. A window is made b
2 answers:
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Answer:
The proof is derived from the summarily following equations;
∠FBE + ∠EBD = ∠CBA + ∠CBD
∠FBE + ∠EBD = ∠FBD
∠CBA + ∠CBD = ∠ABD
Therefore;
∠ABD ≅ ∠FBD
Step-by-step explanation:
The two column proof is given as follows;
Statement Reason
bisects ∠CBE
Given
Therefore;
∠EBD ≅ ∠CBD Definition of angle bisector
∠FBE ≅ ∠CBA Vertically opposite angles are congruent
Therefore, we have;
∠FBE + ∠EBD = ∠CBA + ∠CBD Transitive property
∠FBE + ∠EBD = ∠FBD Angle addition postulate
∠CBA + ∠CBD = ∠ABD Angle addition postulate
Therefore;
∠ABD ≅ ∠FBD Transitive property.
Consider a circle with radius centered at some point
on the
-axis. This circle has equation
Revolve the region bounded by this circle across the -axis to get a torus. Using the shell method, the volume of the resulting torus is
where .
So the volume is
Substitute
and the integral becomes
Notice that is an odd function, so the integral over
is 0. This leaves us with
Write
so the volume is