Expression 9: "z" Subscript, 2 "p" , Baseline equals 4 pi "r" squared left parenthesis, "y" Subscript, 2 "p" , Baseline , right parenthesis squaredz2p=4πr2y2p2
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Expression 10: "y" Subscript, 3 "s" , Baseline equals StartFraction, 1 Over 81 StartRoot, 3 pi , EndRoot "a" Superscript, 0 , Baseline 3 halves undefined , EndFraction left parenthesis, 27 minus StartFraction, 18 "r" Over "a" Subscript, 0 , Baseline , EndFraction plus StartFraction, 2 "r" squared Over "a" squared , EndFraction , right parenthesis times "e" Superscript, negative StartFraction, "r" Over 3 "a" Subscript, 0 , Baseline , EndFraction , Baseline left brace, "r" greater than 0 , right bracey3s=1813πa32027−18ra0+2r2a20·e−r3a0r>0
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Expression 11: "z" Subscript, 3 "s" , Baseline equals 4 pi "r" squared left parenthesis, "y" Subscript, 3 "s" , Baseline , right parenthesis squaredz3s=4πr2y3s2
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Expression 12: "y" Subscript, 3 "p" , Baseline equals StartFraction, StartRoot, 2 , EndRoot Over 81 StartRoot, pi , EndRoot "a" Superscript, 0 , Baseline 3 halves undefined , EndFraction left parenthesis, 6 minus StartFraction, "r" Over "a" Subscript, 0 , Baseline , EndFraction , right parenthesis times StartFraction, "r" Over "a" Subscript, 0 , Baseline , EndFraction times "e" Superscript, negative StartFraction, "r" Over 3 "a" Subscript, 0 , Baseline , EndFraction , Baseline times cosine "a" left brace, "r" greater than 0 , right bracey3p=281πa3206−ra0·ra0·e−r3a0·cosar>0
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Expression 13: "z" Subscript, 3 "p" , Baseline equals 4 pi "r" squared left parenthesis, "y" Subscript, 3 "p" , Baseline , right parenthesis squaredz3p=4πr2y3p2
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Expression 14: "y" Subscript, 3 "d" , Baseline equals StartFraction, 1 Over 81 StartRoot, 6 pi , EndRoot "a" Superscript, 0 , Baseline 3 halves undefined , EndFraction times StartFraction, "r" Over "a" Subscript, 0 , Baseline , EndFraction squared times "e" Superscript, negative StartFraction, "r" Over 3 "a" Subscript, 0 , Baseline , EndFraction , Baseline times left parenthesis, 3cos squared "a" minus 1 , right parenthesis left brace, "r" greater than 0 , right bracey3d=1816πa320·ra02·e−r3a0·3cos2a−1r>0
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Expression 15: "z" Subscript, 3 "d" , Baseline equals 4 pi "r" squared left parenthesis, "y" Subscript, 3 "d" , Baseline , right parenthesis squaredz3d=4πr2y3d2