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8.7E: Mazoezi

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    Mazoezi hufanya kamili

    Zoezi SET A: Kutatua equations Radical

    Katika mazoezi yafuatayo, tatua.

    1. \(\sqrt{5 x-6}=8\)

    2. \(\sqrt{4 x-3}=7\)

    3. \(\sqrt{5 x+1}=-3\)

    4. \(\sqrt{3 y-4}=-2\)

    5. \(\sqrt[3]{2 x}=-2\)

    6. \(\sqrt[3]{4 x-1}=3\)

    7. \(\sqrt{2 m-3}-5=0\)

    8. \(\sqrt{2 n-1}-3=0\)

    9. \(\sqrt{6 v-2}-10=0\)

    10. \(\sqrt{12 u+1}-11=0\)

    11. \(\sqrt{4 m+2}+2=6\)

    12. \(\sqrt{6 n+1}+4=8\)

    13. \(\sqrt{2 u-3}+2=0\)

    14. \(\sqrt{5 v-2}+5=0\)

    15. \(\sqrt{u-3}+3=u\)

    16. \(\sqrt{v-10}+10=v\)

    17. \(\sqrt{r-1}=r-1\)

    18. \(\sqrt{s-8}=s-8\)

    19. \(\sqrt[3]{6 x+4}=4\)

    20. \(\sqrt[3]{11 x+4}=5\)

    21. \(\sqrt[3]{4 x+5}-2=-5\)

    22. \(\sqrt[3]{9 x-1}-1=-5\)

    23. \((6 x+1)^{\frac{1}{2}}-3=4\)

    24. \((3 x-2)^{\frac{1}{2}}+1=6\)

    25. \((8 x+5)^{\frac{1}{3}}+2=-1\)

    26. \((12 x-5)^{\frac{1}{3}}+8=3\)

    27. \((12 x-3)^{\frac{1}{4}}-5=-2\)

    28. \((5 x-4)^{\frac{1}{4}}+7=9\)

    29. \(\sqrt{x+1}-x+1=0\)

    30. \(\sqrt{y+4}-y+2=0\)

    31. \(\sqrt{z+100}-z=-10\)

    32. \(\sqrt{w+25}-w=-5\)

    33. \(3 \sqrt{2 x-3}-20=7\)

    34. \(2 \sqrt{5 x+1}-8=0\)

    35. \(2 \sqrt{8 r+1}-8=2\)

    36. \(3 \sqrt{7 y+1}-10=8\)

    Jibu

    1. \(m=14\)

    3. hakuna ufumbuzi

    5. \(x=-4\)

    7. \(m=14\)

    9. \(v=17\)

    11. \(m=\frac{7}{2}\)

    13. hakuna ufumbuzi

    15. \(u=3, u=4\)

    17. \(r=1, r=2\)

    19. \(x=10\)

    21. \(x=-8\)

    23. \(x=8\)

    25. \(x=-4\)

    27. \(x=7\)

    29. \(x=3\)

    31. \(z=21\)

    33. \(x=42\)

    35. \(r=3\)

    Zoezi SET B: Kutatua equations Radical na Radicals mbili

    Katika mazoezi yafuatayo, tatua.

    37. \(\sqrt{3 u+7}=\sqrt{5 u+1}\)

    38. \(\sqrt{4 v+1}=\sqrt{3 v+3}\)

    39. \(\sqrt{8+2 r}=\sqrt{3 r+10}\)

    40. \(\sqrt{10+2 c}=\sqrt{4 c+16}\)

    41. \(\sqrt[3]{5 x-1}=\sqrt[3]{x+3}\)

    42. \(\sqrt[3]{8 x-5}=\sqrt[3]{3 x+5}\)

    43. \(\sqrt[3]{2 x^{2}+9 x-18}=\sqrt[3]{x^{2}+3 x-2}\)

    44. \(\sqrt[3]{x^{2}-x+18}=\sqrt[3]{2 x^{2}-3 x-6}\)

    45. \(\sqrt{a}+2=\sqrt{a+4}\)

    46. \(\sqrt{r}+6=\sqrt{r+8}\)

    47. \(\sqrt{u}+1=\sqrt{u+4}\)

    48. \(\sqrt{x}+1=\sqrt{x+2}\)

    49. \(\sqrt{a+5}-\sqrt{a}=1\)

    50. \(-2=\sqrt{d-20}-\sqrt{d}\)

    51. \(\sqrt{2 x+1}=1+\sqrt{x}\)

    52. \(\sqrt{3 x+1}=1+\sqrt{2 x-1}\)

    53. \(\sqrt{2 x-1}-\sqrt{x-1}=1\)

    54. \(\sqrt{x+1}-\sqrt{x-2}=1\)

    55. \(\sqrt{x+7}-\sqrt{x-5}=2\)

    56. \(\sqrt{x+5}-\sqrt{x-3}=2\)

    Jibu

    37. \(u=3\)

    39. \(r=-2\)

    41. \(x=1\)

    43. \(x=-8, x=2\)

    45. \(a=0\)

    47. \(u=\frac{9}{4}\)

    49. \(a=4\)

    51. \(x=0\: x=4\)

    53. \(x=1\: x=5\)

    55. \(x=9\)

    Zoezi SET C: Tumia Radicals katika Maombi

    Katika mazoezi yafuatayo, tatua. Round makadirio ya mahali moja decimal.

    1. Landscaping Reed anataka kuwa na mraba bustani njama katika mashamba yake. Ana mbolea ya kutosha kufunika eneo la miguu ya\(75\) mraba. Tumia formula\(s=\sqrt{A}\) ili kupata urefu wa kila upande wa bustani yake. Pindua jibu lako kwa sehemu ya kumi ya karibu ya mguu.
    2. Landscaping Vince anataka kufanya patio mraba katika yadi yake. Ana saruji ya kutosha kusafisha eneo la miguu ya\(130\) mraba. Kutumia formula\(s=\sqrt{A}\) kupata urefu wa kila upande wa patio yake. Pindua jibu lako kwa sehemu ya kumi ya karibu ya mguu.
    3. Gravity A hutegemea glider imeshuka simu yake ya mkononi kutoka urefu wa\(350\) miguu. Tumia formula\(t=\frac{\sqrt{h}}{4}\) ili kupata sekunde ngapi ilichukua kwa simu ya mkononi kufikia chini.
    4. Gravity mfanyakazi wa ujenzi imeshuka nyundo wakati wa kujenga Grand Canyon skywalk,\(4000\) miguu juu ya Mto Colorado. Tumia formula\(t=\frac{\sqrt{h}}{4}\) ili kupata sekunde ngapi ilichukua kwa nyundo kufikia mto.
    5. Uchunguzi wa ajali alama za skid kwa gari lililohusika katika ajali kipimo cha\(216\) miguu. Tumia formula\(s=\sqrt{24d}\) ili kupata kasi ya gari kabla ya breki zilitumiwa. Pindua jibu lako kwa karibu kumi.
    6. Uchunguzi wa ajali Mpelelezi wa ajali alipima alama za skid za moja ya magari yaliyohusika katika ajali. Urefu wa alama za skid ulikuwa\(175\) miguu. Tumia formula\(s=\sqrt{24d}\) ili kupata kasi ya gari kabla ya breki zilitumika. Pindua jibu lako kwa karibu kumi.
    Jibu

    57. \(8.7\)miguu

    59. \(4.7\)sekunde

    61. \(72\)miguu

    Zoezi SET D: Mazoezi ya kuandika
    1. Eleza kwa nini equation ya fomu\(\sqrt{x}+1=0\) haina ufumbuzi.
      1. Tatua equations\(\sqrt{r+4}-r+2=0\).
      2. Eleza kwa nini moja ya “ufumbuzi” ambayo ilipatikana haikuwa kweli ufumbuzi wa equation.
    Jibu

    63. Majibu yatatofautiana.

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali lina nguzo 4 na safu 4. Mstari wa kwanza ni mstari wa kichwa na vichwa vya kichwa â € can â €, â € € confidentlyâ €, â € na baadhi ya usaidi.â €, na â € no â € “Mimi donâ €™ t kupata! â €. Safu ya kwanza ina maneno â € kutatua equationsâ radical €, â € kutatua equations radical na radicals mbili €, na †kutumia radicals katika maombi â €. Nguzo nyingine zimeachwa tupu ili mwanafunzi aweze kuonyesha kiwango chao cha ufahamu.
    Kielelezo 8.6.42

    b Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?