4.1 Übungen

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|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ revolution} </math>
|width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ revolution} </math>
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</div>{{#NAVCONTENT:Answer|Answer 4.1:1|Solution |Solution 4.1:1}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:1|Solution |Solution 4.1:1}}
===Exrecise 4.1:2===
===Exrecise 4.1:2===
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|width="25%" | <math>270^\circ</math>
|width="25%" | <math>270^\circ</math>
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</div>{{#NAVCONTENT:Answer|Answer 4.1:2|Solution |Solution 4.1:2}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:2|Solution |Solution 4.1:2}}
===Übung 4.1:3===
===Übung 4.1:3===
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|width="33%" | {{:4.1 - Bild - Ein rechteckiges Dreieck mit den Seiten 8, x und 17}}
|width="33%" | {{:4.1 - Bild - Ein rechteckiges Dreieck mit den Seiten 8, x und 17}}
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</div>{{#NAVCONTENT:Answer|Answer 4.1:3|Solution a|Solution 4.1:3a|Solution b|Solution 4.1:3b|Solution c|Solution 4.1:3c}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:3|Solution a|Solution 4.1:3a|Solution b|Solution 4.1:3b|Solution c|Solution 4.1:3c}}
===Übung 4.1:4===
===Übung 4.1:4===
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|width="100%" | Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).
|width="100%" | Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).
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</div>{{#NAVCONTENT:Answer|Answer 4.1:4|Solution a|Solution 4.1:4a|Solution b|Solution 4.1:4b|Solution c|Solution 4.1:4c}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:4|Solution a|Solution 4.1:4a|Solution b|Solution 4.1:4b|Solution c|Solution 4.1:4c}}
===Übung 4.1:5===
===Übung 4.1:5===
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|width="100%" | Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).
|width="100%" | Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).
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</div>{{#NAVCONTENT:Answer|Answer 4.1:5|Solution a|Solution 4.1:5a|Solution b|Solution 4.1:5b}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:5|Solution a|Solution 4.1:5a|Solution b|Solution 4.1:5b}}
===Übung 4.1:6===
===Übung 4.1:6===
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|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
|width="50%" | <math>(3x-1)^2+(3y+7)^2=10</math>
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</div>{{#NAVCONTENT:Answer|Answer 4.1:6|Solution a|Solution 4.1:6a|Solution b|Solution 4.1:6b|Solution c|Solution 4.1:6c}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:6|Solution a|Solution 4.1:6a|Solution b|Solution 4.1:6b|Solution c|Solution 4.1:6c}}
===Übung 4.1:7===
===Übung 4.1:7===
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|width="50%" | <math>x^2-2x+y^2+2y=-2</math>
|width="50%" | <math>x^2-2x+y^2+2y=-2</math>
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</div>{{#NAVCONTENT:Answer|Answer 4.1:7|Solution a|Solution 4.1:7a|Solution b|Solution 4.1:7b|Solution c|Solution 4.1:7c|Solution d|Solution 4.1:7d}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:7|Solution a|Solution 4.1:7a|Solution b|Solution 4.1:7b|Solution c|Solution 4.1:7c|Solution d|Solution 4.1:7d}}
===Übung 4.1:8===
===Übung 4.1:8===
<div class="ovning">
<div class="ovning">
How many revolutions does a wheel of radius 50 cm make when it rolls 10m?
How many revolutions does a wheel of radius 50 cm make when it rolls 10m?
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</div>{{#NAVCONTENT:Answer|Answer 4.1:8|Solution|Solution 4.1:8}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:8|Solution|Solution 4.1:8}}
===Übung 4.1:9===
===Übung 4.1:9===
<div class="ovning">
<div class="ovning">
On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?
On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?
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</div>{{#NAVCONTENT:Answer|Answer 4.1:9|Solution|Solution 4.1:9}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:9|Solution|Solution 4.1:9}}
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<center> {{:4.1 - Bild - Eine Waschleine aufgehängt}} </center>
<center> {{:4.1 - Bild - Eine Waschleine aufgehängt}} </center>
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</div>{{#NAVCONTENT:Answer|Answer 4.1:10|Solution|Solution 4.1:10}}
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</div>{{#NAVCONTENT:Antwort|Antwort 4.1:10|Solution|Solution 4.1:10}}

Version vom 09:27, 22. Okt. 2008

 

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Übung 4.1:1

Write in degrees and radians

a) \displaystyle \displaystyle \frac{1}{4} \textrm{ revolution} b) \displaystyle \displaystyle \frac{3}{8} \textrm{ revolution}
c) \displaystyle -\displaystyle \frac{2}{3}\textrm{ revolution} d) \displaystyle \displaystyle \frac{97}{12} \textrm{ revolution}
Antwort
Antwort 4.1:1
Solution
Solution 4.1:1

Exrecise 4.1:2

Transform to radians

a) \displaystyle 45^\circ b) \displaystyle 135^\circ c) \displaystyle -63^\circ d) \displaystyle 270^\circ
Antwort
Antwort 4.1:2
Solution
Solution 4.1:2

Übung 4.1:3

Determine the length of the side marked \displaystyle \,x\,\mbox{.}

a)

[Image]

b)

[Image]

c)

[Image]

Antwort
Antwort 4.1:3
Solution a
Solution 4.1:3a
Solution b
Solution 4.1:3b
Solution c
Solution 4.1:3c

Übung 4.1:4

a) Determine the distance between the points (1,1) and (5,4).
b) Determine the distance between the points(-2,5) and (3,-1).
c) Find the point on the x-axis which lies as far from the point (3,3) as from (5,1).
Antwort
Antwort 4.1:4
Solution a
Solution 4.1:4a
Solution b
Solution 4.1:4b
Solution c
Solution 4.1:4c

Übung 4.1:5

a) Determine the equation of a circle having its centre at (1,2) and radius 2.
b) Determine the equation of a circle having its centre at (2,-1) and which contains the point (-1,1).
Antwort
Antwort 4.1:5
Solution a
Solution 4.1:5a
Solution b
Solution 4.1:5b

Übung 4.1:6

Sketch the following circles

a) \displaystyle x^2+y^2=9 b) \displaystyle (x-1)^2+(y-2)^2=3
c) \displaystyle (3x-1)^2+(3y+7)^2=10
Antwort
Antwort 4.1:6
Solution a
Solution 4.1:6a
Solution b
Solution 4.1:6b
Solution c
Solution 4.1:6c

Übung 4.1:7

Sketch the following circles

a) \displaystyle x^2+2x+y^2-2y=1 b) \displaystyle x^2+y^2+4y=0
c) \displaystyle x^2-2x+y^2+6y=-3 d) \displaystyle x^2-2x+y^2+2y=-2
Antwort
Antwort 4.1:7
Solution a
Solution 4.1:7a
Solution b
Solution 4.1:7b
Solution c
Solution 4.1:7c
Solution d
Solution 4.1:7d

Übung 4.1:8

How many revolutions does a wheel of radius 50 cm make when it rolls 10m?

Antwort
Antwort 4.1:8
Solution
Solution 4.1:8

Übung 4.1:9

On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?

Antwort
Antwort 4.1:9
Solution
Solution 4.1:9


Übung 4.1:10

A washing line of length 5.4 m hangs between two vertical trees that are at a distance of 4.8 m from each other. One end of the line is fixed 0.6 m higher than the other, and a jacket hangs from a hanger 1.2 m from the tree where the line has its lower point of attachment. Determine how far below the lower attachement point the hanger is hanging. (That is, the distance \displaystyle \,x\, in the figure).


[Image]

Antwort
Antwort 4.1:10
Solution
Solution 4.1:10
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/4.1_%C3%9Cbungen“