Vergelijkingen

Antwoorden bij de opgaven

1. 1. ${\displaystyle 250+\mathrm{0,06}a=\mathrm{0,10}a}$
   2. Beide zijden ${\displaystyle \mathrm{0,06}a}$ aftrekken geeft: ${\displaystyle 250=\mathrm{0,04}a}$.
      Beide zijden delen door 0,04 geeft ${\displaystyle a=250/\mathrm{0,04}=6250}$.
2. GR: Y1=250+0.06X en Y2=0.10X met venster en .
3. 1. ${\displaystyle t=1100/3}$
   2. ${\displaystyle t=220}$
   3. ${\displaystyle t=700/\mathrm{0,57}}$
4. 1. ${\displaystyle t=1100/3}$
   2. ${\displaystyle t=20}$ of ${\displaystyle t=-6\frac{2}{3}}$
   3. ${\displaystyle p=3}$
5. 1. ${\displaystyle x\approx \mathrm{1,379}}$
   2. ${\displaystyle a\approx \mathrm{31,174}}$
6. 1. ${\displaystyle x\approx \mathrm{2,26}}$
   2. ${\displaystyle x\approx \mathrm{7,30}}$
   3. ${\displaystyle l\approx \mathrm{1,13}}$ of ${\displaystyle l\approx \mathrm{8,87}}$
   4. ${\displaystyle p=11}$
7. 1. -
   2. ${\displaystyle (\mathrm{145,68};\mathrm{34,32})}$ en ${\displaystyle (\mathrm{34,32};\mathrm{145,68})}$
   3. ${\displaystyle l\approx \mathrm{145,68}}$ en ${\displaystyle b\approx \mathrm{34,32}}$
8. 1. ${\displaystyle t=\mathrm{37,5}}$
   2. ${\displaystyle t=\pm \sqrt{\mathrm{37,5}}\approx \pm \mathrm{6,12}}$
   3. ${\displaystyle p=16}$
   4. ${\displaystyle x=\pm 4}$
   5. ${\displaystyle x=7}$ of ${\displaystyle x=3}$
   6. ${\displaystyle a=7}$
   7. ${\displaystyle v=\mathrm{0,03}}$
   8. geen oplossingen want ${\displaystyle \sqrt{-4}}$ is geen reëel getal
9. 1. ${\displaystyle x=4}$
   2. ${\displaystyle x=1\vee x\approx \mathrm{1,35}}$
10. 1. -
    2. 140 m³ kost per jaar € 283,- en 160 m³ € 318,-, dus tussen € 283,- en € 318,-.
    3. ${\displaystyle 38+\mathrm{1,75}a=250}$ oplossen ${\displaystyle a\approx \mathrm{121,143}}$ dus maximaal 121 m³.
11. 1. ${\displaystyle p=0}$ geeft ${\displaystyle q=-200}$
       ${\displaystyle q=0}$ geeft ${\displaystyle p=300}$
    2. ${\displaystyle q=0}$ geeft ${\displaystyle W=0}$
       ${\displaystyle W=0}$ geeft ${\displaystyle q=0}$ of ${\displaystyle q=200}$
    3. ${\displaystyle l=0}$ geeft ${\displaystyle k=\pm \sqrt{96}\approx \pm \mathrm{9,80}}$
       ${\displaystyle k=0}$ geeft ${\displaystyle l=8}$ of ${\displaystyle l=-12}$
    4. ${\displaystyle d=0}$ geeft ${\displaystyle a=20}$
       ${\displaystyle a=0}$ geeft geen waarde voor ${\displaystyle d}$
12. 1. ${\displaystyle V=200\pi {(\mathrm{1,5}+\mathrm{0,5}a)}^2-450\pi }$
    2. Y1=200π(1,5+0,5a)^2-450π met en
    3. Ongeveer 23 onderdompelingen
13. 1. ${\displaystyle t=9\frac{1}{6}}$
    2. ${\displaystyle p=11}$
    3. ${\displaystyle x=\pm \sqrt{12}}$
    4. ${\displaystyle g=\pm \sqrt{8\frac{1}{3}}}$
14. ${\displaystyle q\approx \mathrm{21,9}}$ of ${\displaystyle q\approx \mathrm{228,1}}$
15. 1. -
    2. ${\displaystyle 800\pi }$
    3. 59 mm
    4. 122 mm