b

a

Jungen

J

M

Mädchen

Intervalle

Abschätzung

a =

b =

a =

b =

gL: -3
gR: 24
gU: -7
gO: 37
a: 0
b: 20
B: (b, 0)
Intervall = Segment((a, 0), (b, 0))
X1 = Point(Intervall)
X2 = Point(Intervall)
X3 = Point(Intervall)
X4 = Point(Intervall)
X5: B
A: (a, 0)
X0: A
x0: x(X0)
x1: x(X1)
x2: x(X2)
x3: x(X3)
x4: x(X4)
x5: x(X5)
g01: x = (x0 + x1) / 2
g12: x = (x1 + x2) / 2
g23: x = (x2 + x3) / 2
g34: x = (x3 + x4) / 2
g45: x = (x4 + x5) / 2
Y01 = Point(g01)
Y12 = Point(g12)
Y23 = Point(g23)
Y34 = Point(g34)
Y45 = Point(g45)
R01 = Polygon({X0, X1, (x1, y(Y01)), (x0, y(Y01))})
R12 = Polygon({X1, X2, (x2, y(Y12)), (x1, y(Y12))})
R23 = Polygon({X2, X3, (x3, y(Y23)), (x2, y(Y23))})
R34 = Polygon({X3, X4, (x4, y(Y34)), (x3, y(Y34))})
R45 = Polygon({X4, X5, (x5, y(Y45)), (x4, y(Y45))})
IAbschaetzung: R01 + R12 + R23 + R34 + R45
c = false
laengeGeburtJ: (46.4 + 54.4) / 2
laengeGeburtM: (45.4 + 52.9) / 2
DatenJ: {(0, 30.0), (1, 16.0), (2, 10.0), (3, 7.5), (4, 6.0), (5, 5.3), (6, 5.0), (7, 5.0), (8, 5.1), (9, 5.5), (10, 6.2), (11, 7.6), (12, 9.0), (13, 8.3), (14, 6.6), (15, 4.9), (16, 3.6), (17, 2.4), (18, 1.6), (19, 0.9), (20, 0)}
fJ = Spline(DatenJ, 3)
DatenM: {(0, 30), (1, 16), (2, 10), (3, 7.5), (4, 6), (5, 5.3), (6, 5), (7, 5), (8, 5.1), (9, 5.6), (10, 7), (11, 8), (12, 7.7), (13, 6.3), (14, 4.6), (15, 3.0), (16, 1.8), (17, 1), (18, 0.5), (19, 0.2), (20, 0)}
fM = Spline(DatenM, 3)
d = true
anzahl = 0 (slider from 0 to 200, step 10)
breite: (b - a) / anzahl
Unterteilungen = Sequence(((i * breite), 0), i, 0, anzahl)
X: B
iX: IndexOf[X, Unterteilungen] - 1
e = true
MitteUnterteilungen = Sequence((((i + 1 / 2) * breite), 0), i, 0, anzahl - 1)
xWerteMitten = Zip(x(P), P, MitteUnterteilungen)
j1(x) = If[0 ≤ x ≤ 6, (-0.0973 * x^(3)) + (1.8312 * x^(2)) - (11.407 * x) + 28.4909]
j2(x) = If[6 ≤ x ≤ 13, (4 * ℯ^((-1 / 2 * (x - 11.6)^(2)))) + 5]
j3(x) = If[13 ≤ x ≤ 18, (0.275762 * x^(2)) - (9.84747 * x) + 87.9133]
j(x) = If[0 < x ≤ 6, j1(x), If[6 < x ≤ 13, j2(x), If[13 < x ≤ 18, j3(x)]]]
J0(x) = (1.9078633670109 * x^(3)) - (15.9078633670109 * x) + 30
J1(x) = (-1.5393168350546 * (x - 1)^(3)) + (5.7235901010328 * (x - 1)^(2)) - (10.1842732659781 * (x - 1)) + 16
J2(x) = (-0.2505960267924 * (x - 2)^(3)) + (1.1056395958689 * (x - 2)^(2)) - (3.3550435690765 * (x - 2)) + 10
J3(x) = (0.0417009422241 * (x - 3)^(3)) + (0.3538515154917 * (x - 3)^(2)) - (1.8955524577159 * (x - 3)) + 7.5
J4(x) = (-0.1162077421042 * (x - 4)^(3)) + (0.4789543421641 * (x - 4)^(2)) - (1.06274660006 * (x - 4)) + 6
J5(x) = (0.0231300261925 * (x - 5)^(3)) + (0.1303311158517 * (x - 5)^(2)) - (0.4534611420442 * (x - 5)) + 5.3
J6(x) = (-0.0763123626657 * (x - 6)^(3)) + (0.1997211944291 * (x - 6)^(2)) - (0.1234088317634 * (x - 6)) + 5
J7(x) = (0.0821194244705 * (x - 7)^(3)) - (0.0292158935681 * (x - 7)^(2)) + (0.0470964690976 * (x - 7)) + 5
J8(x) = (-0.0521653352163 * (x - 8)^(3)) + (0.2171423798434 * (x - 8)^(2)) + (0.2350229553729 * (x - 8)) + 5.1
J9(x) = (0.1265419163948 * (x - 9)^(3)) + (0.0606463741944 * (x - 9)^(2)) + (0.5128117094108 * (x - 9)) + 5.5
J10(x) = (-0.0540023303629 * (x - 10)^(3)) + (0.4402721233789 * (x - 10)^(2)) + (1.0137302069841 * (x - 10)) + 6.2
J11(x) = (-0.6105325949431 * (x - 11)^(3)) + (0.2782651322901 * (x - 11)^(2)) + (1.732267462653 * (x - 11)) + 7.6
J12(x) = (0.3961327101352 * (x - 12)^(3)) - (1.5533326525391 * (x - 12)^(2)) + (0.4571999424039 * (x - 12)) + 9
J13(x) = (0.1260017544022 * (x - 13)^(3)) - (0.3649345221335 * (x - 13)^(2)) - (1.4610672322687 * (x - 13)) + 8.3
J14(x) = (0.0998602722558 * (x - 14)^(3)) + (0.0130707410732 * (x - 14)^(2)) - (1.812931013329 * (x - 14)) + 6.6
J15(x) = (-0.1254428434255 * (x - 15)^(3)) + (0.3126515578406 * (x - 15)^(2)) - (1.4872087144152 * (x - 15)) + 4.9
J16(x) = (0.1019111014461 * (x - 16)^(3)) - (0.0636769724358 * (x - 16)^(2)) - (1.2382341290103 * (x - 16)) + 3.6
J17(x) = (-0.0822015623588 * (x - 17)^(3)) + (0.2420563319024 * (x - 17)^(2)) - (1.0598547695436 * (x - 17)) + 2.4
J18(x) = (0.0268951479892 * (x - 18)^(3)) - (0.004548355174 * (x - 18)^(2)) - (0.8223467928152 * (x - 18)) + 1.5
J19(x) = (-0.0253790295978 * (x - 19)^(3)) + (0.0761370887935 * (x - 19)^(2)) - (0.7507580591957 * (x - 19)) + 0.7
J(x) = If[0 < x ≤ 1, J0(x), If[1 < x ≤ 2, J1(x), If[2 < x ≤ 3, J2(x), If[3 < x ≤ 4, J3(x), If[4 < x ≤ 5, J4(x), If[5 < x ≤ 6, J5(x), If[6 < x ≤ 7, J6(x), If[7 < x ≤ 8, J7(x), If[8 < x ≤ 9, J8(x), If[9 < x ≤ 10, J9(x), If[10 < x ≤ 11, J10(x), If[11 < x ≤ 12, J11(x), If[12 < x ≤ 13, J12(x), If[13 < x ≤ 14, J13(x), If[14 < x ≤ 15, J14(x), If[15 < x ≤ 16, J15(x), If[16 < x ≤ 17, J16(x), If[17 < x ≤ 18, J17(x), If[18 < x ≤ 19, J18(x), If[19 < x ≤ 20, J19(x)]]]]]]]]]]]]]]]]]]]]
SchnittpunkteJ = Zip((xWert, J(xWert)), xWert, xWerteMitten)
yWerteSchnittpunkteJ = Zip(y(P), P, SchnittpunkteJ)
AenderungenJ = Zip((breite * yWert), yWert, yWerteSchnittpunkteJ)
AenderungenKumulativJ = Sequence(Sum[Take[AenderungenJ, 1, i]], i, 1, anzahl)
RechteckeJ = Zip(Polygon[{P + (breite / 2, 0), P + (breite / 2, hoehe), P + (((-breite)) / 2, hoehe), P + (((-breite)) / 2, 0)}], P, MitteUnterteilungen, hoehe, yWerteSchnittpunkteJ)
GesamtaenderungJ = Element(AenderungenKumulativJ, anzahl)
RechteckeJBisX = Sequence(Element[RechteckeJ, i], i, 1, iX)
GesamtaenderungBisX = Element(AenderungenKumulativJ, iX)
gO2: 150
gU2: -20
IntegralpunkteJ = Append((0, 0), Sequence[((i * breite), Element[AenderungenKumulativJ, i]), i, 1, anzahl])
IntegralpunkteJBisX = Sequence(Element[IntegralpunkteJ, i], i, 1, iX + 1)
m1(x) = If[0 ≤ x ≤ 6, (-0.0973 * x^(3)) + (1.8312 * x^(2)) - (11.407 * x) + 28.4909]
m2(x) = If[6 ≤ x ≤ 8.5, (0.0001733 * ℯ^(x)) + 4.92845]
m3(x) = If[8.5 ≤ x ≤ 14, (-0.243877 * x^(2)) + (4.84906 * x) - 17.7548]
m4(x) = If[14 ≤ x ≤ 18, (23 / 160 * (x - 18)^(2))]
m(x) = If[0 < x ≤ 6, m1(x), If[6 < x < 8.5, m2(x), If[8.5 < x ≤ 14, m3(x), If[14 < x ≤ 18, m4(x)]]]]
M0(x) = (1.9078577594376 * x^(3)) - (15.9078577594376 * x) + 30
M1(x) = (-1.5392887971879 * (x - 1)^(3)) + (5.7235732783127 * (x - 1)^(2)) - (10.1842844811248 * (x - 1)) + 16
M2(x) = (-0.2507025706861 * (x - 2)^(3)) + (1.1057068867491 * (x - 2)^(2)) - (3.355004316063 * (x - 2)) + 10
M3(x) = (0.0420990799321 * (x - 3)^(3)) + (0.3535991746909 * (x - 3)^(2)) - (1.895698254623 * (x - 3)) + 7.5
M4(x) = (-0.1176937490423 * (x - 4)^(3)) + (0.4798964144872 * (x - 4)^(2)) - (1.0622026654449 * (x - 4)) + 6
M5(x) = (0.0286759162371 * (x - 5)^(3)) + (0.1268151673603 * (x - 5)^(2)) - (0.4554910835974 * (x - 5)) + 5.3
M6(x) = (-0.0970099159062 * (x - 6)^(3)) + (0.2128429160717 * (x - 6)^(2)) - (0.1158330001655 * (x - 6)) + 5
M7(x) = (0.1593637473876 * (x - 7)^(3)) - (0.0781868316469 * (x - 7)^(2)) + (0.0188230842593 * (x - 7)) + 5
M8(x) = (-0.0404450736443 * (x - 8)^(3)) + (0.3999044105159 * (x - 8)^(2)) + (0.3405406631283 * (x - 8)) + 5.1
M9(x) = (-0.0975834528106 * (x - 9)^(3)) + (0.2785691895831 * (x - 9)^(2)) + (1.0190142632274 * (x - 9)) + 5.8
M10(x) = (-0.2692211151135 * (x - 10)^(3)) - (0.0141811688485 * (x - 10)^(2)) + (1.283402283962 * (x - 10)) + 7
M11(x) = (0.0744679132647 * (x - 11)^(3)) - (0.8218445141891 * (x - 11)^(2)) + (0.4473766009244 * (x - 11)) + 8
M12(x) = (0.1713494620549 * (x - 12)^(3)) - (0.5984407743951 * (x - 12)^(2)) - (0.9729086876598 * (x - 12)) + 7.7
M13(x) = (0.0401342385158 * (x - 13)^(3)) - (0.0843923882305 * (x - 13)^(2)) - (1.6557418502854 * (x - 13)) + 6.3
M14(x) = (0.0681135838818 * (x - 14)^(3)) + (0.036010327317 * (x - 14)^(2)) - (1.7041239111988 * (x - 14)) + 4.6
M15(x) = (-0.0125885740432 * (x - 15)^(3)) + (0.2403510789625 * (x - 15)^(2)) - (1.4277625049193 * (x - 15)) + 3
M16(x) = (-0.0177592877092 * (x - 16)^(3)) + (0.202585356833 * (x - 16)^(2)) - (0.9848260691238 * (x - 16)) + 1.8
M17(x) = (-0.0163742751201 * (x - 17)^(3)) + (0.1493074937054 * (x - 17)^(2)) - (0.6329332185854 * (x - 17)) + 1
M18(x) = (-0.0167436118105 * (x - 18)^(3)) + (0.1001846683452 * (x - 18)^(2)) - (0.3834410565347 * (x - 18)) + 0.5
M19(x) = (-0.0166512776379 * (x - 19)^(3)) + (0.0499538329137 * (x - 19)^(2)) - (0.2333025552758 * (x - 19)) + 0.2
M(x) = If[0 < x ≤ 1, M0(x), If[1 < x ≤ 2, M1(x), If[2 < x ≤ 3, M2(x), If[3 < x ≤ 4, M3(x), If[4 < x ≤ 5, M4(x), If[5 < x ≤ 6, M5(x), If[6 < x ≤ 7, M6(x), If[7 < x ≤ 8, M7(x), If[8 < x ≤ 9, M8(x), If[9 < x ≤ 10, M9(x), If[10 < x ≤ 11, M10(x), If[11 < x ≤ 12, M11(x), If[12 < x ≤ 13, M12(x), If[13 < x ≤ 14, M13(x), If[14 < x ≤ 15, M14(x), If[15 < x ≤ 16, M15(x), If[16 < x ≤ 17, M16(x), If[17 < x ≤ 18, M17(x), If[18 < x ≤ 19, M18(x), If[19 < x ≤ 20, M19(x)]]]]]]]]]]]]]]]]]]]]
SchnittpunkteM = Zip((xWert, M(xWert)), xWert, xWerteMitten)
yWerteSchnittpunkteM = Zip(y(P), P, SchnittpunkteM)
AenderungenM = Zip((breite * yWert), yWert, yWerteSchnittpunkteM)
AenderungenKumulativM = Sequence(Sum[Take[AenderungenM, 1, i]], i, 1, anzahl)
GesamtaenderungM = Element(AenderungenKumulativM, anzahl)
IntegralpunkteM = Append((0, 0), Sequence[((i * breite), Element[AenderungenKumulativM, i]), i, 1, anzahl])
IntegralpunkteMBisX = Sequence(Element[IntegralpunkteM, i], i, 1, iX + 1)
RechteckeM = Zip(Polygon[{P + (breite / 2, 0), P + (breite / 2, hoehe), P + (((-breite)) / 2, hoehe), P + (((-breite)) / 2, 0)}], P, MitteUnterteilungen, hoehe, yWerteSchnittpunkteM)
RechteckeMBisX = Sequence(Element[RechteckeM, i], i, 1, iX)
Text1: "Gesamtzuwachs: " + GesamtaenderungJ + ""
Text2: "Gesamtzuwachs: " + GesamtaenderungM + ""
Text3: "Gesamtzuwachs: " + IAbschaetzung + ""
Text4: "" + (y(Y01)) + ""
Text5: "" + (y(Y12)) + ""
Y = Point(yAxis)
Text6: "" + (y(Y)) + ""
gH(x) = If[0 ≤ x ≤ 20, y(Y)]
Text7: "a = " + a + ""
Text8: "b = " + b + ""
Eingabefeld1 = Textfield(a)
Eingabefeld2 = Textfield(b)
h(t) = If[x0 ≤ t < x1, y(Y01), If[x1 ≤ t < x2, y(Y12), If[x2 ≤ t < x3, y(Y23), If[x3 ≤ t < x4, y(Y34), If[x4 ≤ t ≤ x5, y(Y45)]]]]]
g0: x = x0
g1: x = x1
g2: x = x2
g3: x = x3
g4: x = x4
g5: x = x5
Text9: "" + x0 + ""
Text10: "" + x1 + ""
Text11: "" + x2 + ""
Text12: "" + x3 + ""
Text13: "" + x4 + ""
Text14: "" + x5 + ""
Eingabefeld3 = Textfield(a)
Eingabefeld4 = Textfield(b)