4.1 Übungen
Aus Online Mathematik Brückenkurs 1
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| - | {{Ej vald flik|[[4.1 Vinklar och cirklar| | + | {{Ej vald flik|[[4.1 Vinklar och cirklar|Theory]]}} |
| - | {{Vald flik|[[4.1 Övningar| | + | {{Vald flik|[[4.1 Övningar|Exercises]]}} |
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| - | === | + | ===Exercise 4.1:1=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Write in degrees and radians | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 23: | Zeile 23: | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:1|Lösning |Lösning 4.1:1}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:1|Lösning |Lösning 4.1:1}} | ||
| - | === | + | ===Exercise [[[[Link title]]]]4.1:2=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Transform to radians | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 38: | Zeile 38: | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:2|Lösning |Lösning 4.1:2}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:2|Lösning |Lösning 4.1:2}} | ||
| - | === | + | ===Exercise 4.1:3=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Determine the length of the side marked <math>\,x\,\mbox{.}</math> | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 52: | Zeile 52: | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:3|Lösning a|Lösning 4.1:3a|Lösning b|Lösning 4.1:3b|Lösning c|Lösning 4.1:3c}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:3|Lösning a|Lösning 4.1:3a|Lösning b|Lösning 4.1:3b|Lösning c|Lösning 4.1:3c}} | ||
| - | === | + | ===Exercise 4.1:4=== |
<div class="ovning"> | <div class="ovning"> | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="100%" | | + | |width="100%" | Determine the distance between the points (1,1) and(5,4). |
|- | |- | ||
|b) | |b) | ||
| - | |width="100%" | | + | |width="100%" | Determine the distance between the points(-2,5) and(3,-1). |
|- | |- | ||
|c) | |c) | ||
| - | |width="100%" | | + | |width="100%" | Find the point on the x-axis which lies as far from the point (3,3) as from (5,1). |
|} | |} | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:4|Lösning a|Lösning 4.1:4a|Lösning b|Lösning 4.1:4b|Lösning c|Lösning 4.1:4c}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:4|Lösning a|Lösning 4.1:4a|Lösning b|Lösning 4.1:4b|Lösning c|Lösning 4.1:4c}} | ||
| - | === | + | ===Exercise 4.1:5=== |
<div class="ovning"> | <div class="ovning"> | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="100%" | | + | |width="100%" | Determine the equation of a circle having its centre at (1,2) and radius 2. |
|- | |- | ||
|b) | |b) | ||
| - | |width="100%" | | + | |width="100%" | Determine the equation of a circle having its centre at (2,-1) and contains the point (-1,1). |
|} | |} | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:5|Lösning a|Lösning 4.1:5a|Lösning b|Lösning 4.1:5b}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:5|Lösning a|Lösning 4.1:5a|Lösning b|Lösning 4.1:5b}} | ||
| - | === | + | ===Exercise 4.1:6=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Sketch the following circles | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 91: | Zeile 91: | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:6|Lösning a|Lösning 4.1:6a|Lösning b|Lösning 4.1:6b|Lösning c|Lösning 4.1:6c}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:6|Lösning a|Lösning 4.1:6a|Lösning b|Lösning 4.1:6b|Lösning c|Lösning 4.1:6c}} | ||
| - | === | + | ===Exercise 4.1:7=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Sketch the following circles | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 107: | Zeile 107: | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:7|Lösning a|Lösning 4.1:7a|Lösning b|Lösning 4.1:7b|Lösning c|Lösning 4.1:7c|Lösning d|Lösning 4.1:7d}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:7|Lösning a|Lösning 4.1:7a|Lösning b|Lösning 4.1:7b|Lösning c|Lösning 4.1:7c|Lösning d|Lösning 4.1:7d}} | ||
| - | === | + | ===Exercise 4.1:8=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | How many resolutions does a wheel of radius 50 cm make when it rolls 10m? | |
</div>{{#NAVCONTENT:Svar|Svar 4.1:8|Lösning|Lösning 4.1:8}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:8|Lösning|Lösning 4.1:8}} | ||
| - | === | + | ===Exercise 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? | |
</div>{{#NAVCONTENT:Svar|Svar 4.1:9|Lösning|Lösning 4.1:9}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:9|Lösning|Lösning 4.1:9}} | ||
| - | === | + | ===Exercise 4.1:10=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | 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 <math>\,x\,</math> in the figure). | ||
<center> {{:4.1 - Figur - Tvättlina med kavaj på galge}} </center> | <center> {{:4.1 - Figur - Tvättlina med kavaj på galge}} </center> | ||
</div>{{#NAVCONTENT:Svar|Svar 4.1:10|Lösning|Lösning 4.1:10}} | </div>{{#NAVCONTENT:Svar|Svar 4.1:10|Lösning|Lösning 4.1:10}} | ||
Version vom 15:03, 3. Aug. 2008
Exercise 4.1:1
Write in degrees and radians
| a) | \displaystyle \displaystyle \frac{1}{4} \textrm{ varv} | b) | \displaystyle \displaystyle \frac{3}{8} \textrm{ varv} |
| c) | \displaystyle -\displaystyle \frac{2}{3}\textrm{ varv} | d) | \displaystyle \displaystyle \frac{97}{12} \textrm{ varv} |
Svar
Laden...
Lösning
Exercise [[Link title]]4.1:2
Transform to radians
| a) | \displaystyle 45^\circ | b) | \displaystyle 135^\circ | c) | \displaystyle -63^\circ | d) | \displaystyle 270^\circ |
Svar
Lösning
Exercise 4.1:3
Determine the length of the side marked \displaystyle \,x\,\mbox{.}
| a) | b) | 4.1 - Figur - Rätvinklig triangel med sidor 12, x och 13 | c) | 4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17 |
Exercise 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). |
Exercise 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 contains the point (-1,1). |
Exercise 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 |
Exercise 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 |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 4.1:8
How many resolutions does a wheel of radius 50 cm make when it rolls 10m?
Svar
Lösning
Exercise 4.1:9
On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds?
Svar
Lösning
Exercise 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).
Svar
Lösning
