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A corollary to the Schwarz lemma gives when functions are constrained to multiply inputs by values in this set. For 10 points each:
[10h] Name this set that is the image of the function “f-of-x equals e to the i x,” for x in the real numbers.
ANSWER: unit circle [prompt on circle]
[10e] This function of theta equals the length of the vertical side of a right triangle with angle theta and vertices on the origin, horizontal axis, and unit circle. This function equals “opposite over hypotenuse.”
ANSWER: sine [or sin]
[10m] The Schwarz lemma follows from a “principle” named for the modulus with this property. The function “sine-of-theta” has this property only when theta equals pi-over-two plus an integer multiple of two pi.
ANSWER: maximum [accept local maximum; accept word forms in place of “maximum,” like “maxima,” “maximal,” or “maximized”; prompt on answers describing the function being equal to one]
<David Bass, Science - Math&gt; ~22125~ &lt;Editor: David Bass>

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Data

TeamOpponentPart 1Part 2Part 3Total
BeavercreekAlabama Cyber Tech0101020
BloomingtonStevenson A010010
Carl SandburgCarbondale0101020
ChattahoocheeWest Point0101020
Detroit Catholic Central AWinston Churchill B010010
Downingtown STEMDuPage County AT1010020
Fairfield County ATLindbergh0101020
HastingsHunter A010010
Innovation Academy ACanyon Crest0101020
James W. RobinsonMaggie Walker C0101020
Johns Creek ABarrington0101020
Johns Creek BLivingston B010010
LambertHeights0101020
Maggie Walker BSt. Thomas010010
McLean ADetroit Catholic Central C010010
Northmont AGeorgetown Day010010
Northmont BLightridge0101020
OwensboroFreeman010010
Richard Montgomery BGreat Valley010010
Seven LakesMcLean B010010
Strake JesuitBelmont010010
Thomas Jefferson AThomas Jefferson D0101020
William FremdOkemos010010
Winston Churchill ASt. Mark's010010

Summary

TournamentEditionExact Match?HeardPPBEasy %Medium %Hard %
2024 PACE NSC06/08/2024Y2414.58100%42%4%