4.1 Exercises
From Förberedande kurs i matematik 1
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{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ | + | |width="50%" | <math>\displaystyle \frac{1}{4} \textrm{ revolution} </math> |
|b) | |b) | ||
| - | |width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ | + | |width="50%" | <math>\displaystyle \frac{3}{8} \textrm{ revolution}</math> |
|- | |- | ||
|c) | |c) | ||
| - | |width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ | + | |width="50%" | <math>-\displaystyle \frac{2}{3}\textrm{ revolution}</math> |
|d) | |d) | ||
| - | |width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ | + | |width="50%" | <math>\displaystyle \frac{97}{12} \textrm{ revolution} </math> |
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:1|Solution |Lösning 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:2|Solution |Lösning 4.1:2}} |
===Exercise 4.1:3=== | ===Exercise 4.1:3=== | ||
| Line 50: | Line 50: | ||
|width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}} | |width="33%" | {{:4.1 - Figur - Rätvinklig triangel med sidor 8, x och 17}} | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:3|Solution a|Lösning 4.1:3a|Solution b|Lösning 4.1:3b|Solution c|Lösning 4.1:3c}} |
===Exercise 4.1:4=== | ===Exercise 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). | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:4|Solution a|Lösning 4.1:4a|Solution b|Lösning 4.1:4b|Solution c|Lösning 4.1:4c}} |
===Exercise 4.1:5=== | ===Exercise 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). | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:5|Solution a|Lösning 4.1:5a|Solution b|Lösning 4.1:5b}} |
===Exercise 4.1:6=== | ===Exercise 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:6|Solution a|Lösning 4.1:6a|Solution b|Lösning 4.1:6b|Solution c|Lösning 4.1:6c}} |
===Exercise 4.1:7=== | ===Exercise 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> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:7|Solution a|Lösning 4.1:7a|Solution b|Lösning 4.1:7b|Solution c|Lösning 4.1:7c|Solution d|Lösning 4.1:7d}} |
===Exercise 4.1:8=== | ===Exercise 4.1:8=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | How many | + | How many revolutions does a wheel of radius 50 cm make when it rolls 10m? |
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:8|Solution|Lösning 4.1:8}} |
===Exercise 4.1:9=== | ===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? | On a clock, the second hand is 8 cm long. How large an area does it sweep through in 10 seconds? | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:9|Solution|Lösning 4.1:9}} |
===Exercise 4.1:10=== | ===Exercise 4.1:10=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | A washing line of length 5 | + | 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 | + | 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.( | + | 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: | + | </div>{{#NAVCONTENT:Answer|Svar 4.1:10|Solution|Lösning 4.1:10}} |
Revision as of 13:35, 19 August 2008
| Theory | Exercises |
Exercise 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} |
Answer
Loading...
Solution
Exrecise 4.1:2
Transform to radians
| a) | \displaystyle 45^\circ | b) | \displaystyle 135^\circ | c) | \displaystyle -63^\circ | d) | \displaystyle 270^\circ |
Answer
Solution
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 which 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 |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 4.1:8
How many revolutions does a wheel of radius 50 cm make when it rolls 10m?
Answer
Solution
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?
Answer
Solution
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).
Answer
Solution
