Lösungen Mathematik: Unterschied zwischen den Versionen
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| − | == HA vom 02.12.2008== | + | == HA vom 02.12.2008 == |
'''S. 46 / 6 a)''' | '''S. 46 / 6 a)''' | ||
| Zeile 32: | Zeile 32: | ||
d<sup>2</sup> = 15649 m<sup>2</sup> <br /> | d<sup>2</sup> = 15649 m<sup>2</sup> <br /> | ||
=> d = 125,1 m | => d = 125,1 m | ||
| + | |||
| + | |||
| + | == HA vom 05.12.2008 == | ||
| + | |||
| + | '''S. 48 / 18''' | ||
| + | |||
| + | '''f)'''<br /> | ||
| + | P ( x<sub>1</sub> / y<sub>1</sub> ), Q ( x<sub>2</sub> / y<sub>2</sub> )<br /> | ||
| + | d<sup>2</sup> = (x<sub>1</sub> - x<sub>2</sub>)<sup>2</sup> + (y<sub>1</sub> - y<sub>2</sub>)<sup>2</sup> <br /> | ||
| + | |||
| + | '''a)'''<br /> | ||
| + | P ( 2 / 1 ), Q ( 5 / 5 )<br /> | ||
| + | d<sup>2</sup> = (2 - 5)<sup>2</sup> + (1 - 5)<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = (-3)<sup>2</sup> + (-4)<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = 9 + 16 = 25 <br /> | ||
| + | => d = 5 ( cm ) <br /> | ||
| + | |||
| + | '''b)'''<br /> | ||
| + | P ( -3 / 4 ), Q ( 2 / -1 )<br /> | ||
| + | d<sup>2</sup> = (-3 - 2)<sup>2</sup> + (4 - (-1))<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = (-5)<sup>2</sup> + 5<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = 25 + 25 = 50 <br /> | ||
| + | => d = 7,1 ( cm ) <br /> | ||
| + | |||
| + | '''c)'''<br /> | ||
| + | P ( 3 / 0 ), Q ( 0 / -4 )<br /> | ||
| + | d<sup>2</sup> = (3 - 0)<sup>2</sup> + (0 - (-4))<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = 3<sup>2</sup> + 4<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = 9 + 16 = 25 <br /> | ||
| + | => d = 5 ( cm ) <br /> | ||
| + | |||
| + | '''d)'''<br /> | ||
| + | P ( -5 / -4 ), Q ( 4 / 6 )<br /> | ||
| + | d<sup>2</sup> = (-5 - 4)<sup>2</sup> + (-4 - 6)<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = (-9)<sup>2</sup> + (-10)<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = 81 + 100 = 181 <br /> | ||
| + | => d = 13,5 ( cm ) <br /> | ||
| + | |||
| + | '''e)'''<br /> | ||
| + | P ( -3,5 / -1 ), Q ( 0,7 / 4 )<br /> | ||
| + | d<sup>2</sup> = (-3,5 - 0,7)<sup>2</sup> + (-1 - 4)<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = (-4.2)<sup>2</sup> + (-5)<sup>2</sup> <br /> | ||
| + | d<sup>2</sup> = 17,64 + 25 = 42,64 <br /> | ||
| + | => d = 6,5 ( cm ) <br /> | ||
Aktuelle Version vom 7. Dezember 2008, 18:23 Uhr
HA vom 02.12.2008
S. 46 / 6 a)
x2 = (5 cm)2 + (8 cm)2
x2 = 25 cm2 + 64 cm2
x2 = 89 cm2
=> x = 9,43 cm
S. 46 / 6 c)
(15 cm)2 = (1 dm)2 + z2
225 cm2 = 100 cm2 + z2
125 cm2 = z2
=> z = 11,18 cm
S. 47 / 8
Die Diagonale darf maximale 2,40 m groß sein.
(0,60 m)2 + h2 = (2,40 m)2
0,36 m2 + h2 = 5,76 m2
h2 = 5,40 m2
=> h = 2,32 m
S. 47 / 9 a)
A = 71,4 a = 7140 m2 , b = 105 m
A = b * h => h = A / b = 68 m
d2 = h2 + b2
d2 = (68 m)2 + (105 m)2
d2 = 4624 m2 + 11025 m2
d2 = 15649 m2
=> d = 125,1 m
HA vom 05.12.2008
S. 48 / 18
f)
P ( x1 / y1 ), Q ( x2 / y2 )
d2 = (x1 - x2)2 + (y1 - y2)2
a)
P ( 2 / 1 ), Q ( 5 / 5 )
d2 = (2 - 5)2 + (1 - 5)2
d2 = (-3)2 + (-4)2
d2 = 9 + 16 = 25
=> d = 5 ( cm )
b)
P ( -3 / 4 ), Q ( 2 / -1 )
d2 = (-3 - 2)2 + (4 - (-1))2
d2 = (-5)2 + 52
d2 = 25 + 25 = 50
=> d = 7,1 ( cm )
c)
P ( 3 / 0 ), Q ( 0 / -4 )
d2 = (3 - 0)2 + (0 - (-4))2
d2 = 32 + 42
d2 = 9 + 16 = 25
=> d = 5 ( cm )
d)
P ( -5 / -4 ), Q ( 4 / 6 )
d2 = (-5 - 4)2 + (-4 - 6)2
d2 = (-9)2 + (-10)2
d2 = 81 + 100 = 181
=> d = 13,5 ( cm )
e)
P ( -3,5 / -1 ), Q ( 0,7 / 4 )
d2 = (-3,5 - 0,7)2 + (-1 - 4)2
d2 = (-4.2)2 + (-5)2
d2 = 17,64 + 25 = 42,64
=> d = 6,5 ( cm )
