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7.5E: Mazoezi

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    176672

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    Kutatua milinganyo ya busara

    Katika mazoezi yafuatayo, tatua kila equation ya busara.

    1. \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)

    Jibu

    \(a=10\)

    2. \(\dfrac{6}{3}-\dfrac{2}{d}=\dfrac{4}{9}\)

    3. \(\dfrac{4}{5}+\dfrac{1}{4}=\dfrac{2}{v}\)

    Jibu

    \(v=\dfrac{40}{21}\)

    4. \(\dfrac{3}{8}+\dfrac{2}{y}=\dfrac{1}{4}\)

    5. \(1-\dfrac{2}{m}=\dfrac{8}{m^{2}}\)

    Jibu

    \(m=-2,\; m=4\)

    6. \(1+\dfrac{4}{n}=\dfrac{21}{n^{2}}\)

    7. \(1+\dfrac{9}{p}=\dfrac{-20}{p^{2}}\)

    Jibu

    \(p=-5, \; p=-4\)

    8. \(1-\dfrac{7}{q}=\dfrac{-6}{q^{2}}\)

    9. \(\dfrac{5}{3 v-2}=\dfrac{7}{4 v}\)

    Jibu

    \(v=14\)

    10. \(\dfrac{8}{2 w+1}=\dfrac{3}{w}\)

    11. \(\dfrac{3}{x+4}+\dfrac{7}{x-4}=\dfrac{8}{x^{2}-16}\)

    Jibu

    \(x=-\dfrac{4}{5}\)

    12. \(\dfrac{5}{y-9}+\dfrac{1}{y+9}=\dfrac{18}{y^{2}-81}\)

    13. \(\dfrac{8}{z-10}-\dfrac{7}{z+10}=\dfrac{5}{z^{2}-100}\)

    Jibu

    \(z=-145\)

    14. \(\dfrac{9}{a+11}-\dfrac{6}{a-11}=\dfrac{6}{a^{2}-121}\)

    15. \(\dfrac{-10}{q-2}-\dfrac{7}{q+4}=1\)

    Jibu

    \(q=-18, \; q=-1\)

    16. \(\dfrac{2}{s+7}-\dfrac{3}{s-3}=1\)

    17. \(\dfrac{v-10}{v^{2}-5 v+4}=\dfrac{3}{v-1}-\dfrac{6}{v-4}\)

    Jibu

    hakuna suluhisho

    18. \(\dfrac{w+8}{w^{2}-11 w+28}=\dfrac{5}{w-7}+\dfrac{2}{w-4}\)

    19. \(\dfrac{x-10}{x^{2}+8 x+12}=\dfrac{3}{x+2}+\dfrac{4}{x+6}\)

    Jibu

    hakuna suluhisho

    20. \(\dfrac{y-5}{y^{2}-4 y-5}=\dfrac{1}{y+1}+\dfrac{1}{y-5}\)

    21. \(\dfrac{b+3}{3 b}+\dfrac{b}{24}=\dfrac{1}{b}\)

    Jibu

    \(b=-8\)

    22. \(\dfrac{c+3}{12 c}+\dfrac{c}{36}=\dfrac{1}{4 c}\)

    23. \(\dfrac{d}{d+3}=\dfrac{18}{d^{2}-9}+4\)

    Jibu

    \(d=2\)

    24. \(\dfrac{m}{m+5}=\dfrac{50}{m^{2}-25}+6\)

    25. \(\dfrac{n}{n+2}-3=\dfrac{8}{n^{2}-4}\)

    Jibu

    \(m=1\)

    26. \(\dfrac{p}{p+7}-8=\dfrac{98}{p^{2}-49}\)

    27. \(\dfrac{q}{3 q-9}-\dfrac{3}{4 q+12}=\dfrac{7 q^{2}+6 q+63}{24 q^{2}-216}\)

    Jibu

    hakuna suluhisho

    28. \(\dfrac{r}{3 r-15}-\dfrac{1}{4 r+20}=\dfrac{3 r^{2}+17 r+40}{12 r^{2}-300}\)

    29. \(\dfrac{s}{2 s+6}-\dfrac{2}{5 s+5}=\dfrac{5 s^{2}-3 s-7}{10 s^{2}+40 s+30}\)

    Jibu

    \(s=\dfrac{5}{4}\)

    30. \(\dfrac{t}{6 t-12}-\dfrac{5}{2 t+10}=\dfrac{t^{2}-23 t+70}{12 t^{2}+36 t-120}\)

    31. \(\dfrac{2}{x^{2}+2 x-8}-\dfrac{1}{x^{2}+9 x+20}=\dfrac{4}{x^{2}+3 x-10}\)

    Jibu

    \(x=-\dfrac{4}{3}\)

    32. \(\dfrac{5}{x^{2}+4 x+3}+\dfrac{2}{x^{2}+x-6}=\dfrac{3}{x^{2}-x-2}\)

    33. \(\dfrac{3}{x^{2}-5 x-6}+\dfrac{3}{x^{2}-7 x+6}=\dfrac{6}{x^{2}-1}\)

    Jibu

    hakuna suluhisho

    34. \(\dfrac{2}{x^{2}+2 x-3}+\dfrac{3}{x^{2}+4 x+3}=\dfrac{6}{x^{2}-1}\)

    Tatua usawa wa busara unaohusisha Kazi

    35. Kwa kazi ya busara,\(f(x)=\dfrac{x-2}{x^{2}+6 x+8}\):

    1. Pata uwanja wa kazi
    2. Kutatua\(f(x)=5\)
    3. Pata pointi kwenye grafu kwenye thamani hii ya kazi
    Jibu
    1. Kikoa ni namba zote halisi isipokuwa\(x \neq-2\) na\(x \neq-4\)
    2. \(x=-3, x=-\dfrac{14}{5}\)
    3. \((-3,5),\left(-\dfrac{14}{5}, 5\right)\)

    36. Kwa kazi ya busara,\(f(x)=\dfrac{x+1}{x^{2}-2 x-3}\):

    1. Pata uwanja wa kazi
    2. Kutatua\(f(x)=1\)
    3. Pata pointi kwenye grafu kwenye thamani hii ya kazi

    37. Kwa kazi ya busara,\(f(x)=\dfrac{2-x}{x^{2}-7 x+10}\):

    1. Pata uwanja wa kazi
    2. Kutatua\(f(x)=2\)
    3. Pata pointi kwenye grafu kwenye thamani hii ya kazi
    Jibu
    1. Kikoa ni namba zote halisi isipokuwa\(x \neq 2\) na\(x \neq 5\)
    2. \(x=\dfrac{9}{2}\)
    3. \(\left(\dfrac{9}{2}, 2\right)\)

    38. Kwa kazi ya busara,\(f(x)=\dfrac{5-x}{x^{2}+5 x+6}\):

    1. Pata uwanja wa kazi
    2. Kutatua\(f(x)=3\)
    3. Pata pointi kwenye grafu kwenye thamani hii ya kazi

    Tatua Equation ya Mantiki kwa Variable Maalum

    Katika mazoezi yafuatayo, tatua:

    39. \(\dfrac{c}{r}=2 \pi \text { for } r\)

    Jibu

    \(r=\dfrac{C}{2 \pi}\)

    40. \(\dfrac{I}{r}=P \text { for } r\)

    41. \(\dfrac{v+3}{w-1}=\dfrac{1}{2} \text { for } w\)

    Jibu

    \(w=2 v+7\)

    42. \(\dfrac{x+5}{2-y}=\dfrac{4}{3} \text { for } y\)

    43. \(a=\dfrac{b+3}{c-2} \text { for } c\)

    Jibu

    \(c=\dfrac{b+3+2 a}{a}\)

    44. \(m=\dfrac{n}{2-n} \text { for } n\)

    45. \(\dfrac{1}{p}+\dfrac{2}{q}=4 \text { for } p\)

    Jibu

    \(p=\dfrac{q}{4 q-2}\)

    46. \(\dfrac{3}{s}+\dfrac{1}{t}=2 \text { for } s\)

    47. \(\dfrac{2}{v}+\dfrac{1}{5}=\dfrac{3}{w} \text { for } w\)

    Jibu

    \(w=\dfrac{15 v}{10+v}\)

    48. \(\dfrac{6}{x}+\dfrac{2}{3}=\dfrac{1}{y} \text { for } y\)

    49. \(\dfrac{m+3}{n-2}=\dfrac{4}{5} \text { for } n\)

    Jibu

    \(n=\dfrac{5 m+23}{4}\)

    50. \(r=\dfrac{s}{3-t} \text { for } t\)

    51. \(\dfrac{E}{c}=m^{2} \text { for } c\)

    Jibu

    \(c=\dfrac{E}{m^{2}}\)

    52. \(\dfrac{R}{T}=W \text { for } T\)

    53. \(\dfrac{3}{x}-\dfrac{5}{y}=\dfrac{1}{4} \text { for } y\)

    Jibu

    \(y=\dfrac{20 x}{12-x}\)

    54. \(c=\dfrac{2}{a}+\dfrac{b}{5} \text { for } a\)

    Mazoezi ya kuandika

    55. Darasa lako mate ni kuwa na shida katika sehemu hii. Andika hatua unazozitumia kueleza jinsi ya kutatua equation ya busara.

    Jibu

    Majibu yatatofautiana.

    56. Alek anadhani equation\(\dfrac{y}{y+6}=\dfrac{72}{y^{2}-36}+4\) ina ufumbuzi mbili,\(y=-6\) na\(y=4\). Eleza kwa nini Alek ni makosa.