Gleichungen aufstellen und lösen
Author: Mag.G.Wengler

Mit dem Button "NEU" werden neue Angaben zusammen gestellt. 
Schreibe die Gleichung auf, die mit den Strecken dargestellt ist.
Kontrolliere dein Ergebnis mit dem Kontrollkästchen "Gleichung".
Löse die Gleichung und gib deinen Wert ein. Viel Erfolg beim Lösen!

NEU

Gleichung

Gleichung

Gleichungen verstehen

Gleichung

x =

x =

x =

Lösung:

Lösung:

Lösung:

Bravo! \;Alles \;richtig!

1. Aufgabe

2.Aufgabe

3.Aufgabe

A_1 = (-0.36662361303823815, -0.5227133679549147)
l_1 = Random(1, 5)
b_1 = Random(1, 5)
a_1 = Random(2, 6)
c_1: l_1 * a_1 + b_1
P_1 = Sequence(A_1 + (k * l_1, 0), k, 0, a_1)
S_1 = Sequence(Segment[Element[P_1, k], Element[P_1, k + 1]], k, 1, Length[P_1] - 1)
B_1: A_1 + (a_1 * l_1, 0)
C_1: B_1 + (b_1, 0)
s_1 = Segment(B_1, C_1)
Text1: "" + b_1 + ""
a = Line(A_1, yAxis)
D_1 = Point(a)
E_1: D_1 + (c_1, 0)
t_1 = Segment(D_1, E_1)
Text2: "" + c_1 + ""
A_2 = Point(a)
a_2 = Random(2, 6)
b_2 = Random(1, 5)
l_2 = Random(4, 7)
c_2: l_2 * a_2 - b_2
P_2 = Sequence(A_2 + (k * l_2, 0), k, 0, a_2)
A = Point(a)
D_2 = Mirror(A_2, A)
S_2 = Sequence(Segment[Element[P_2, k], Element[P_2, k + 1]], k, 1, Length[P_2] - 1)
T_2 = Sequence(Text["x", ((x(Element[P_2, k]) + x(Element[P_2, k + 1])) / 2, (y(Element[P_2, k]) + y(Element[P_2, k + 1])) / 2 + 0.4)], k, 1, Length[P_2] - 1)
T_1 = Sequence(Text["x", ((x(Element[P_1, k]) + x(Element[P_1, k + 1])) / 2, (y(Element[P_1, k]) + y(Element[P_1, k + 1])) / 2 + 0.4)], k, 1, Length[P_1] - 1)
B_2: A + (l_2 * a_2 - b_2, 0)
C_2: A + (l_2 * a_2, 0)
s_2 = Segment(B_2, C_2)
Text3: "" + b_2 + ""
E_2: D_2 + (l_2 * a_2 - b_2, 0)
t_2 = Segment(D_2, E_2)
Text4: "" + c_2 + ""
B = Point(a)
C = Point(a)
b = Segment(B, C)
c = OrthogonalLine(B, a)
d = OrthogonalLine(C, a)
e = OrthogonalLine(C_1, d)
D = Intersect(c, e)
E = Intersect(d, e)
f = Segment(D, E)
F = Point(a)
G = Point(a)
g = Segment(F, G)
h = OrthogonalLine(C_2, d)
i = OrthogonalLine(E_2, d)
j = OrthogonalLine(D_2, g)
k = OrthogonalLine(G, a)
l = OrthogonalLine(F, a)
H = Intersect(h, l)
I = Intersect(h, k)
m = Segment(H, I)
J = Point(i)
K = Intersect(i, k)
n = Segment(J, K)
q = false
Text5: "" + (LaTeX[a_1]) + "·x  + " + (LaTeX[b_1]) + " =" + (LaTeX[c_1]) + ""
s = false
Text7: "" + (LaTeX[a_2]) + "·x - " + (LaTeX[b_2]) + " = " + (LaTeX[c_2]) + ""
A_3 = Point(a)
a_3 = Random(2, 5)
b_3 = Random(1, 3)
l_3 = Random(1, 4)
c_3: a_3 * (l_3 + b_3)
P_3 = Sequence(A_3 + (k * (l_3 + b_3), 0), k, 0, a_3)
Q_3 = Sequence(A_3 + (k * (l_3 + b_3) + l_3, 0), k, 0, a_3 - 1)
S_3 = Sequence(Segment[A_3 + (k * (l_3 + b_3), 0), A_3 + (k * (l_3 + b_3) + l_3, 0)], k, 0, a_3 - 1)
T_3 = Sequence(Text["x", ((x(Element[P_3, k]) + x(Element[Q_3, k])) / 2, (y(Element[P_3, k]) + y(Element[Q_3, k])) / 2 + 0.4)], k, 1, Length[P_3])
S'_3 = Sequence(Segment[A_3 + (k * (l_3 + b_3) + l_3, 0), A_3 + ((k + 1) * (l_3 + b_3), 0)], k, 0, a_3 - 1)
T'_3 = Sequence(Text[b_3, ((x(Element[Q_3, k]) + x(Element[P_3, k + 1])) / 2, (y(Element[Q_3, k]) + y(Element[P_3, k + 1])) / 2 + 0.4)], k, 1, Length[P_3] - 1)
B_3 = Point(a)
C_3: B_3 + (c_3, 0)
d_1 = Segment(B_3, C_3)
L = Point(a)
M = Point(a)
e_1 = Segment(L, M)
f_1 = OrthogonalLine(L, a)
g_1 = OrthogonalLine(C_3, f_1)
h_1 = OrthogonalLine(M, a)
N = Intersect(f_1, g_1)
O = Intersect(g_1, h_1)
j_1 = Segment(N, O)
Text10: "" + c_3 + ""
v = false
Text11: "" + (LaTeX[a_3]) + "·(x + " + (LaTeX[b_3]) + ") = " + (LaTeX[c_3]) + ""
x_1 = 0
x_2 = 0
x_3 = 0
Textfeld1 = Textfield(x_1)
Textfeld2 = Textfield(x_2)
Textfeld3 = Textfield(x_3)
richtig_1: x_1 ≟ l_1
richtig_2: x_2 ≟ l_2
richtig_3: x_3 ≟ l_3