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Zuletzt geändert von Holger Engels am 2025/07/16 10:40
Von Version 63.1
bearbeitet von Holger Engels
am 2025/03/31 13:35
Änderungskommentar: Neuen Anhang Freizeitbad.ggb hochladen
Auf Version 67.2
bearbeitet von Holger Engels
am 2025/07/16 10:40
Änderungskommentar: Es gibt keinen Kommentar für diese Version

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Seiteneigenschaften
Inhalt
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8 8  Karl läuft bei {{formula}}x=1,5{{/formula}} durch einen Torbogen der Form {{formula}}f(x)=-\frac{1}{20}x^4 +\frac{2}{5}x^2+\frac{6}{5}{{/formula}} und stößt sich dabei den Kopf an. Wie groß ist Karl mindestens?
9 9  {{/aufgabe}}
10 10  
11 -{{aufgabe id="Freizeitbad" afb="II" kompetenzen="K4,K5,K6" quelle="Frauke Beckstette; Kim Fujan" cc="BY-SA" zeit="6"}}
12 -Die Besucherzahlen eines Freizeitbades können zwischen 10:00 Uhr und 22:00 Uhr näherungsweise durch die Funktion {{formula}}B(t)=-0,3t^3+9,3t^2-56,4t-66\quad t{{/formula}} in h beschrieben werden.
13 - [[image:Freizeitbad.png||width="700"]]
11 +{{aufgabe id="Freizeitbad" afb="II" kompetenzen="K4,K5,K6" quelle="Frauke Beckstette, Kim Fujan" cc="BY-SA" zeit="6"}}
12 +[[image:Freizeitbad.svg||width="400" style="float:right"]]Die Besucherzahlen eines Freizeitbades können zwischen 10:00 Uhr und 22:00 Uhr näherungsweise durch die Funktion {{formula}}B(t)=-0,3t^3+9,3t^2-56,4t-66t{{/formula}} mit //t// in //h// beschrieben werden.
13 +(%class=abc%)
14 14  1. Weise rechnerisch nach, dass sowohl um 10:00 Uhr als auch um 22:00 Uhr keine Besucher im Freizeitbad sind.
15 15  1. Berechne wie viele Besucher 3h vor Badschluss noch im Freizeitbad sind.
16 16  1. Zu welcher Zeit sind die meisten Besucher im Bad und wie viele sind das? (graphische Lösung)
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18 18  1. Beschreibe wie man diesen Zeitraum rechnerisch ermitteln könnte **ohne** ihn explizit zu berechnen.
19 19  {{/aufgabe}}
20 20  
21 -{{aufgabe id="Heißluftballons" afb="II" kompetenzen="K6,K1,K4" quelle="" cc="BY-SA" niveau="g" zeit="7"}}
22 -**Fahrt eines Heißluftballons**
23 -
24 -[[image:Heißluftballon.png||width="480" height="229"]]
25 -
26 -Das Schaubild stellt die Fahrt eines Heißluftballons dar.
21 +{{aufgabe id="Heißluftballon" afb="II" kompetenzen="K6,K1,K4" quelle="Frauke Beckstette, Kim Fujan" cc="BY-SA" niveau="g" zeit="7"}}
22 +[[image:Heißluftballon.svg||width="500" style="float:right"]] Das Schaubild stellt die Fahrt eines Heißluftballons dar.
27 27  Die Geschwindigkeit (in m/min) ist auf der y-Achse in Abhängigkeit der vergangenen Zeit auf der x-Achse (in min) abgetragen.
28 28  
29 29  //Anmerkung: Wenn der Wind sich dreht, kann der Ballon auch rückwärts fahren.//
30 30  
27 +(%class=abc%)
31 31  1. Welche Bedeutung haben die negativen Funktionswerte?
32 32  1. Welche Aussagen kann man über den zur Fahrt gehörenden Funktionsterm treffen?
33 33  1. Wir wollen nun wissen, zu welchen Zeitpunkten der Ballon weder vorwärts noch rückwärts gefahren ist.
34 34  
35 -
36 36  Die folgende Funktion f mit D=[0;60], beschreibt näherungsweise die Geschwindigkeit des Ballons:
37 -{{formula}} f(x)=-0,0029x^4+0,306x^3-10,28x^2+109,1x{{/formula}}
33 +{{formula}}f(x)=-0,0029x^4+0,306x^3-10,28x^2+109,1x{{/formula}}
38 38  {{/aufgabe}}
39 39  
40 40  {{aufgabe id="Die optimale Geschenkschachtel" afb="III" kompetenzen="K2,K4,K5" quelle="Allgemeingut" cc="BY-SA" zeit="15"}}
41 -Für ein Geburtstagsgeschenk möchtest du eine Schachtel mit möglichst großem Volumen basteln.
37 +Für ein Geburtstagsgeschenk möchtest du eine Schachtel mit möglichst großem Volumen basteln.
42 42  Dafür hast du zwei schöne grüne Kartons im DIN A4-Format (einen für die Schachtel und einen für den Deckel) besorgt.
43 43  Erläutere dein Vorgehen und ermittle die Maße, die du für diese ideale Geschenkschachtel erhälst.
44 44  {{/aufgabe}}
45 45  
46 -{{aufgabe id="Kommode im Dachzimmer" afb="III" kompetenzen="K2,K3,K4,K5" quelle="Frauke Beckstette; Kim Fujan" cc="BY-SA" zeit="8"}}
47 -Kay bezieht ein neues Zimmer im Dachgeschoss. Um möglichst viel Stauraum zu schaffen, soll in dem farbig markierten Bereich mit Dachschräge eine möglichst große Kommode aufgestellt werden. Welche Höhe und Tiefe sollte die 2 m breite Kommode dann haben?
48 - [[image:Dachzimmer.png||width="300"]]
42 +{{aufgabe id="Kommode im Dachzimmer" afb="III" kompetenzen="K2,K3,K4,K5" quelle="Frauke Beckstette, Kim Fujan" cc="BY-SA" zeit="8"}}
43 +[[image:Dachzimmer.png||width="300" style="float:right"]]Kay bezieht ein neues Zimmer im Dachgeschoss. Um möglichst viel Stauraum zu schaffen, soll in dem farbig markierten Bereich mit Dachschräge eine möglichst große Kommode aufgestellt werden. Welche Höhe und Tiefe sollte die 2 m breite Kommode dann haben?
49 49  {{/aufgabe}}
50 50  
51 51  {{aufgabe id="Konditorei" afb="III" kompetenzen="K1,K2,K4,K5,K6" quelle="Martina Wagner" cc="BY-SA" zeit="11"}}
Freizeitbad.svg
Author
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1 +XWiki.holgerengels
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Inhalt
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Heißluftballon.ggb
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Heißluftballon.svg
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