Matematik opg 1523 1524 1529 1545

Indholdsfortegnelse

1 Opg 1523
- 1.1 1
- 1.2 2
- 1.3 3
2 Opg 1524
3 Opg 1529
- 3.1 1 Del
- 3.2 2 Del
4 Opg 1545

Opg 1523

Opløsning af vektorer.

1

- $LaTex: 10=-5S+15T$
$LaTex: 6=-5S+13T$
- $LaTex: T=2$
$LaTex: S=4$

2

- $LaTex: -12=4S+72T$
$LaTex: 2=4S+16T$
- $LaTex: T=0,25$
$LaTex: S=-7,5$

3

$LaTex: 4=7S-2T$
- $LaTex: 4=-4S-2T$
- $LaTex: S=-0,36$
- $LaTex: T=-2,72$

Opg 1524

- $LaTex: -9=3S-6T$
$LaTex: 6,5=3S-T$
- $LaTex: T=3,1$
- $LaTex: S=3,2$

Opg 1529

1 Del

$LaTex: \vec a = \left( \begin{array}{l} 12 \\ 5 \\ \end{array} \right) \\ \vec b = \left( \begin{array}{l} 16 \\ k \\ \end{array} \right) \\ k = \left( {16 - 12 + 5} \right) - \left( {\frac{{12}}{5}} \right) \\ k = 6.6 \\$

2 Del

$LaTex: \vec b = t \times \vec a \\ \left( \begin{array}{l} 16 \\ 6.6 \\ \end{array} \right) = t \times \left( \begin{array}{l} 12 \\ 5 \\ \end{array} \right) \\ \frac{{16}}{{12}} = t = \frac{1}{3} \\ \frac{{6.6}}{5} = t = \frac{1}{3} \\$

Opg 1545

Viser koordinaterne beregnet og tegnet med Kig

Viser koordinaterne beregnet og tegnet med Kig

Median A: $LaTex: Mid_{BC} = \left(\frac{3 + 8}{2}; \frac{5 -4 }{2}\right)=(5,5;0,5)$; $LaTex: \vec{Median_A} = {5,5-(-1)\choose 0,5-2}={6,5\choose -1,5}$; $LaTex: |\vec{Median_A}|=\sqrt{6,5^2+(-1,5)^2}=6,67$

Median B: $LaTex: Mid_{AC} = \left(\frac{-1 + 8}{2}; \frac{2 -4 }{2}\right)=(3,5;-1)$; $LaTex: \vec{Median_B} = {3,5-3\choose -1-5}={0,5\choose -6}$; $LaTex: |\vec{Median_B}|=\sqrt{0,5^2+(-6)^2}=6,02$

Median C: $LaTex: Mid_{AB} = \left(\frac{-1+ 3}{2}; \frac{2 +5 }{2}\right)=(1;3,5)$; $LaTex: \vec{Median_C} = {1-8\choose 3,5-(-4)}={-7\choose 7,5}$; $LaTex: |\vec{Median_C}|=\sqrt{(-7)^2+7,5^2}=10,26$

Skæringspunkt

$LaTex: a_{Median_A} = \frac{6,5}{-1,5} = -4\frac{1}{3}$

$LaTex: 2=a_{Median_A}\times -1 + x$

$LaTex: x=-2\frac{1}{3}$

$LaTex: a_{Median_B} = \frac{0,5}{-6} = -0,08\frac{1}{3}$

$LaTex: 5=a_{Median_B}\times 3 + x$

$LaTex: x=5,25$

$LaTex: y=-4\frac{1}{3}\times x - 2\frac{1}{3}$

$LaTex: y=-0,08\frac{1}{3}\times x + 5,25$

$LaTex: x={5,25+2\frac{1}{3}}{-4,25}=-1,784$

$LaTex: x=\frac{5,25+2,333}{0,08333-4,333}=-1,784$

(BUG)

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Kategorier: Matematik Opgaver

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