Find the center of mass of the lamina bounded by the graphs of the equations 
, 
, 
and
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.
?
A. 
B. ?
C. ?
D. ?
E. ?
Answer: B
Mathematics
src="https://sciemce.com/media/2/ppg__cognero__Section_14.4__media__92f80083-4eb2-4778-a9e2-c09ccd4d51f7.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_98594823db034da3ba8a0aeb6" /> for the density .
?
A.
B. ?
C. ?
D. ?
E. ?
Answer: B
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Find the function with the given derivative whose graph passes through the point P.r'(?) = 4 + sec2 ?, P(
, 0)
A. r(?) = 4? + 
sec3 ?
B. r(?) = 2?2 + tan ? - 3? + 1
C. r(?) = 4? + tan ? - 3? + 1
D. r'(?) = 2?2 + tan ? + 3?
Express the number in scientific notation.0.00007922
A. 7.922 × 10-4 B. 7.922 × 105 C. 7.922 × 104 D. 7.922 × 10-5
Solve the problem.Two pulleys, one with a radius of 19 inches and the other with a radius of 
are connected by a belt. If the larger pulley makes 
per minute, how many revolutions per minute does the smaller pulley make? Round your answer to the nearest tenth.
A. 0.5 rpm B. 8.4 rpm C. 4.8 rpm D. 42.8 rpm
Answer the following:
a. Prove that having n vertices, where n is a positive integer, is an invariant for graph isomorphism. b. Prove that having a vertex of degree 3 is an invariant for graph isomorphism.