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4.1 Übungen

Aus Online Mathematik Brückenkurs 1

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Version vom 09:43, 22. Okt. 2008

Theorie

Übungen

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

Lösung

Lösung 4.1:1

Exrecise 4.1:2

Transform to radians

\displaystyle 45^\circ

\displaystyle 135^\circ

\displaystyle -63^\circ

\displaystyle 270^\circ

Antwort

Antwort 4.1:2

Lösung

Lösung 4.1:2

Übung 4.1:3

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

[Image]

Antwort

Lösung a

Lösung b

Lösung c

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

Lösung a

Lösung b

Lösung c

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

Lösung a

Lösung 4.1:5a

Lösung b

Lösung 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

Lösung a

Lösung b

Lösung c

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

Lösung a

Lösung b

Lösung c

Lösung d

Übung 4.1:8

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

Antwort

Antwort 4.1:8

Lösung

Lösung 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

Lösung

Lösung 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]