2.2 Übungen
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
(Translated links into English) |
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| Zeile 21: | Zeile 21: | ||
|| <math>5x+7=2x-6</math> | || <math>5x+7=2x-6</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:1|Solution a|Lösning 2.2:1a|Solution b|Lösning 2.2:1b|Solution c|Lösning 2.2:1c|Solution d|Lösning 2.2:1d}} |
===Exercise 2.2:2=== | ===Exercise 2.2:2=== | ||
| Zeile 37: | Zeile 37: | ||
|| <math>(x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2</math> | || <math>(x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:2|Solution a|Lösning 2.2:2a|Solution b|Lösning 2.2:2b|Solution c|Lösning 2.2:2c|Solution d|Lösning 2.2:2d}} |
===Exercise 2.2:3=== | ===Exercise 2.2:3=== | ||
| Zeile 55: | Zeile 55: | ||
|| <math>\left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0</math> | || <math>\left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:3|Solution a|Lösning 2.2:3a|Solution b|Lösning 2.2:3b|Solution c|Lösning 2.2:3c|Solution d|Lösning 2.2:3d}} |
===Exercise 2.2:4=== | ===Exercise 2.2:4=== | ||
| Zeile 61: | Zeile 61: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="100%" | Write the equation for the line <math>\,y=2x+3\,</math> in the form <math>\,ax+by=c\,</math> | + | |width="100%" | Write the equation for the line <math>\,y=2x+3\,</math> in the form <math>\,ax+by=c\,</math>. |
|- | |- | ||
|b) | |b) | ||
| - | || Write the equation for the line <math> 3x+4y-5=0</math> in the form <math>\,y=kx+m\,</math> | + | || Write the equation for the line <math> 3x+4y-5=0</math> in the form <math>\,y=kx+m\,</math>. |
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:4|Solution a|Lösning 2.2:4a|Solution b|Lösning 2.2:4b}} |
===Exercise 2.2:5=== | ===Exercise 2.2:5=== | ||
| Zeile 72: | Zeile 72: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="100%" | Determine the equation for the straight line that goes between the points <math>\,(2,3)\,</math> and<math>\,(3,0)\,</math> | + | |width="100%" | Determine the equation for the straight line that goes between the points <math>\,(2,3)\,</math> and<math>\,(3,0)\,</math>. |
|- | |- | ||
|b) | |b) | ||
| - | || Determine the equation for the straight line that has | + | || Determine the equation for the straight line that has slope <math>\,-3\,</math> and goes through the point <math>\,(1,-2)\,</math>. |
|- | |- | ||
|c) | |c) | ||
| - | || Determine the equation for the straight line that goes through the point <math>\,(-1,2)\,</math> and is parallel to the line <math>\,y=3x+1\,</math> | + | || Determine the equation for the straight line that goes through the point <math>\,(-1,2)\,</math> and is parallel to the line <math>\,y=3x+1\,</math>. |
|- | |- | ||
|d) | |d) | ||
| - | ||Determine the equation for the straight line that goes through the point <math>\,(2,4)\,</math> and is perpendicular to the line <math>\,y=2x+5\,</math> | + | ||Determine the equation for the straight line that goes through the point <math>\,(2,4)\,</math> and is perpendicular to the line <math>\,y=2x+5\,</math>. |
|- | |- | ||
|e) | |e) | ||
| - | || Determine the slope, <math>\,k\,</math> for the straight line that cuts the ''x''-axis at the point <math>\,(5,0)\,</math> and ''y''-axis at the point <math>\,(0,-8)\,</math> | + | || Determine the slope, <math>\,k\,</math>, for the straight line that cuts the ''x''-axis at the point <math>\,(5,0)\,</math> and ''y''-axis at the point <math>\,(0,-8)\,</math>. |
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:5|Solution a|Lösning 2.2:5a|Solution b|Lösning 2.2:5b|Solution c|Lösning 2.2:5c|Solution d|Lösning 2.2:5d|Solution e|Lösning 2.2:5e}} |
===Exercise 2.2:6=== | ===Exercise 2.2:6=== | ||
| Zeile 93: | Zeile 93: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| - | |width="50%" | <math>y=3x+5\ </math> | + | |width="50%" | <math>y=3x+5\ </math> and ''x''-axeln |
|b) | |b) | ||
| - | |width="50%" | <math>y=-x+5\ </math> | + | |width="50%" | <math>y=-x+5\ </math> and ''y''-axeln |
|- | |- | ||
|c) | |c) | ||
| - | |width="50%" | <math>4x+5y+6=0\ </math> | + | |width="50%" | <math>4x+5y+6=0\ </math> and ''y''-axeln |
|d) | |d) | ||
| - | || <math>x+y+1=0\ </math> | + | || <math>x+y+1=0\ </math> and <math>\ x=12</math> |
|- | |- | ||
|e) | |e) | ||
| - | || <math>2x+y-1=0\ </math> | + | || <math>2x+y-1=0\ </math> and <math>\ y-2x-2=0</math> |
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:6|Solution a|Lösning 2.2:6a|Solution b|Lösning 2.2:6b|Solution c|Lösning 2.2:6c|Solution d|Lösning 2.2:6d|Solution e|Lösning 2.2:6e}} |
===Exercise 2.2:7=== | ===Exercise 2.2:7=== | ||
| Zeile 118: | Zeile 118: | ||
|width="33%" | <math>f(x)=2</math> | |width="33%" | <math>f(x)=2</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:7|Solution a|Lösning 2.2:7a|Solution b|Lösning 2.2:7b|Solution c|Lösning 2.2:7c}} |
===Exercise 2.2:8=== | ===Exercise 2.2:8=== | ||
<div class="ovning"> | <div class="ovning"> | ||
| - | In the ''xy''-plane, | + | In the ''xy''-plane, fill in all the points whose coordinates <math>\,(x,y)\,</math> satisfy |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
| Zeile 131: | Zeile 131: | ||
|width="33%" | <math>2x+3y \leq 6 </math> | |width="33%" | <math>2x+3y \leq 6 </math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:8|Solution a|Lösning 2.2:8a|Solution b|Lösning 2.2:8b|Solution c|Lösning 2.2:8c}} |
===Exercise 2.2:9=== | ===Exercise 2.2:9=== | ||
| Zeile 146: | Zeile 146: | ||
|| is described by the inequalities <math>\ x+y \geq -2\,</math>, <math>\ 2x-y \leq 2\ </math> and <math>\ 2y-x \leq 2\,</math>. | || is described by the inequalities <math>\ x+y \geq -2\,</math>, <math>\ 2x-y \leq 2\ </math> and <math>\ 2y-x \leq 2\,</math>. | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT: | + | </div>{{#NAVCONTENT:Answer|Svar 2.2:9|Solution a|Lösning 2.2:9a|Solution b|Lösning 2.2:9b|Solution c|Lösning 2.2:9c}} |
Version vom 14:18, 18. Aug. 2008
Exercise 2.2:1
Solve the equations
| a) | \displaystyle x-2=-1 | b) | \displaystyle 2x+1=13 |
| c) | \displaystyle \displaystyle\frac{1}{3}x-1=x | d) | \displaystyle 5x+7=2x-6 |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Exercise 2.2:2
Solve the equations
| a) | \displaystyle \displaystyle\frac{5x}{6}-\displaystyle\frac{x+2}{9}=\displaystyle\frac{1}{2} | b) | \displaystyle \displaystyle\frac{8x+3}{7}-\displaystyle\frac{5x-7}{4}=2 |
| c) | \displaystyle (x+3)^2-(x-5)^2=6x+4 | d) | \displaystyle (x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2 |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 2.2:3
Solve the equations
| a) | \displaystyle \displaystyle\frac{x+3}{x-3}-\displaystyle\frac{x+5}{x-2}=0 |
| b) | \displaystyle \displaystyle\frac{4x}{4x-7}-\displaystyle\frac{1}{2x-3}=1 |
| c) | \displaystyle \left(\displaystyle\frac{1}{x-1}-\frac{1}{x+1}\right)\left(x^2+\frac{1}{2}\right)=\displaystyle\frac{6x-1}{3x-3} |
| d) | \displaystyle \left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0 |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 2.2:4
| a) | Write the equation for the line \displaystyle \,y=2x+3\, in the form \displaystyle \,ax+by=c\,. |
| b) | Write the equation for the line \displaystyle 3x+4y-5=0 in the form \displaystyle \,y=kx+m\,. |
Exercise 2.2:5
| a) | Determine the equation for the straight line that goes between the points \displaystyle \,(2,3)\, and\displaystyle \,(3,0)\,. |
| b) | Determine the equation for the straight line that has slope \displaystyle \,-3\, and goes through the point \displaystyle \,(1,-2)\,. |
| c) | Determine the equation for the straight line that goes through the point \displaystyle \,(-1,2)\, and is parallel to the line \displaystyle \,y=3x+1\,. |
| d) | Determine the equation for the straight line that goes through the point \displaystyle \,(2,4)\, and is perpendicular to the line \displaystyle \,y=2x+5\,. |
| e) | Determine the slope, \displaystyle \,k\,, for the straight line that cuts the x-axis at the point \displaystyle \,(5,0)\, and y-axis at the point \displaystyle \,(0,-8)\,. |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Exercise 2.2:6
Find the points of intersection between the pairs of lines in the following
| a) | \displaystyle y=3x+5\ and x-axeln | b) | \displaystyle y=-x+5\ and y-axeln |
| c) | \displaystyle 4x+5y+6=0\ and y-axeln | d) | \displaystyle x+y+1=0\ and \displaystyle \ x=12 |
| e) | \displaystyle 2x+y-1=0\ and \displaystyle \ y-2x-2=0 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Exercise 2.2:7
Sketch the graph of the functions
| a) | \displaystyle f(x)=3x-2 | b) | \displaystyle f(x)=2-x | c) | \displaystyle f(x)=2 |
Exercise 2.2:8
In the xy-plane, fill in all the points whose coordinates \displaystyle \,(x,y)\, satisfy
| a) | \displaystyle y \geq x | b) | \displaystyle y < 3x -4 | c) | \displaystyle 2x+3y \leq 6 |
Exercise 2.2:9
Calculate the area of the triangle which
| a) | has corners at the points \displaystyle \,(1,4)\,, \displaystyle \,(3,3)\, and \displaystyle \,(1,0)\,. |
| b) | is bordered by the lines \displaystyle \ x=2y\,, \displaystyle \ y=4\ and \displaystyle \ y=10-2x\,. |
| c) | is described by the inequalities \displaystyle \ x+y \geq -2\,, \displaystyle \ 2x-y \leq 2\ and \displaystyle \ 2y-x \leq 2\,. |
