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Express 0.04024 in standard form. Find the total surface area of the figure. Given the figure below find angle.

Mathematics

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Answer

4.024×10−2\text{4.024} \times 10^{-2}

340 cm2\text{340 cm}^2

55∘55^\circ

Step-by-step solution

10 steps

Hapa kuna masuluhisho ya maswali yako:

1. Express 0.04024 in standard form.

Ili kuandika nambari katika standard form (a×10na \times 10^n), tunahitaji kusogeza desimali ili aa iwe nambari kati ya 1 na 10.

  1. Sogeza desimali hadi baada ya nambari ya kwanza isiyo sifuri.

    Nambari ni 0.04024. Tukisogeza desimali sehemu mbili kwenda kulia, tunapata 4.024.

  2. Tambua exponent ya 10.

    Kwa sababu tulisogeza desimali sehemu mbili kwenda kulia, exponent itakuwa hasi 2.

    0.04024=4.024×10−20.04024 = 4.024 \times 10^{-2}

    Jibu la mwisho:

    4.024×10−2\boxed{\text{4.024} \times 10^{-2}}

    2. Find the total surface area of the figure.
    Kielelezo ni cuboid (mchemraba) chenye urefu (ll), upana (ww), na kimo (hh). Kutoka kwenye picha, vipimo ni l=10l = 10 cm, w=8w = 8 cm, na h=5h = 5 cm.

  3. Andika formula ya total surface area (TSA) ya cuboid.

    TSA=2(lw+lh+wh)TSA = 2(lw + lh + wh)

  4. Badilisha vipimo kwenye formula.

    TSA=2((10 cm×8 cm)+(10 cm×5 cm)+(8 cm×5 cm))TSA = 2((10 \text{ cm} \times 8 \text{ cm}) + (10 \text{ cm} \times 5 \text{ cm}) + (8 \text{ cm} \times 5 \text{ cm}))

  5. Fanya hesabu ndani ya mabano.

    TSA=2(80 cm2+50 cm2+40 cm2)TSA = 2(80 \text{ cm}^2 + 50 \text{ cm}^2 + 40 \text{ cm}^2)

  6. Jumlisha maeneo na kuzidisha kwa 2.

    TSA=2(170 cm2)TSA = 2(170 \text{ cm}^2) TSA=340 cm2TSA = 340 \text{ cm}^2

    Jibu la mwisho:

    340 cm2\boxed{\text{340 cm}^2}

    3. Given the figure below. Find angle x.
    Kielelezo ni pembetatu yenye pembe xx, 2x−60∘2x-60^\circ, na x+20∘x+20^\circ. Jumla ya pembe za ndani za pembetatu ni 180∘180^\circ.

  7. Tengeneza mlinganyo kwa kujumlisha pembe zote na kuziweka sawa na 180∘180^\circ.

    x+(2x−60∘)+(x+20∘)=180∘x + (2x - 60^\circ) + (x + 20^\circ) = 180^\circ

  8. Unganisha vigezo vya xx na nambari.

    (x+2x+x)+(−60∘+20∘)=180∘(x + 2x + x) + (-60^\circ + 20^\circ) = 180^\circ 4x−40∘=180∘4x - 40^\circ = 180^\circ

  9. Ongeza 40∘40^\circ pande zote mbili za mlinganyo.

    4x=180∘+40∘4x = 180^\circ + 40^\circ 4x=220∘4x = 220^\circ

  10. Gawanya kwa 4 ili kupata thamani ya xx.

    x=220∘4x = \frac{220^\circ}{4} x=55∘x = 55^\circ

    Jibu la mwisho:

    55∘\boxed{55^\circ}
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