Grade 10 learners had a mean of 9.467. Use mathematical tables to find the logarithm of the mean. Express…

Question

Grade 10 learners had a mean of 9.467. Use mathematical tables to find the logarithm of the mean. Express 0.00000789 as a power of 10. The perpendicular height of a trapezium is 5.6cm. If the lengths of the two parallel sides are 12.2cm and 14.4cm respectively, work out its area.

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Hapa kuna masuluhisho ya maswali yako:

6. Wanafunzi wa Darasa la 10 walikuwa na wastani wa 9.467. Tumia jedwali za hisabati kutafuta logariti ya wastani huo.

Tambua nambari ya kupata logariti.
Nambari ni 9.467.
Tafuta logariti ya 9.467 kwa kutumia jedwali za hisabati (log tables).
- Tabia (characteristic) ni 0, kwa sababu nambari iko kati ya 1 na 10.
- Mantisa (mantissa) inapatikana kwa kutafuta 94 chini ya 6, kisha kuongeza tofauti ya wastani (mean difference) ya 7.
  
  Log ya 9.46 ni 0.9760.
  
  Tofauti ya wastani kwa 7 ni 3.
  
  Mantisa = $0.9760 + 0.0003 = 0.9763$ . Kwa hivyo, logariti ya 9.467 ni:
$\boxed{0.9763}$
7. Eleza 0.00000789 kama nguvu ya 10.
Sogeza desimali ili kupata nambari kati ya 1 na 10.
Tunahitaji kusogeza desimali sehemu 6 kwenda kulia ili kupata 7.89.
Andika nambari katika mfumo wa kisayansi.
Kwa kuwa desimali ilisogezwa kwenda kulia, kiashiria (exponent) kitakuwa hasi.
$0.00000789 = 7.89 \times 10^{-6}$
Nambari kama nguvu ya 10 ni:
$\boxed{7.89 \times 10^{-6}}$
8. Urefu wa pembejeo wa trapezi ni 5.6cm. Ikiwa urefu wa pande mbili sambamba ni 12.2cm na 14.4cm mtawalia, tafuta eneo lake.
Andika fomula ya eneo la trapezi.
Eneo la trapezi $A = \frac{1}{2}(a+b)h$ , ambapo $a$ na $b$ ni urefu wa pande sambamba, na $h$ ni urefu wa pembejeo.
Badilisha thamani zilizopewa kwenye fomula.
$a = 12.2 \text{ cm}$
$b = 14.4 \text{ cm}$
$h = 5.6 \text{ cm}$
$A = \frac{1}{2}(12.2 \text{ cm} + 14.4 \text{ cm})(5.6 \text{ cm})$
Jumlisha urefu wa pande sambamba.
$A = \frac{1}{2}(26.6 \text{ cm})(5.6 \text{ cm})$
Fanya kuzidisha.
$A = 13.3 \text{ cm} \times 5.6 \text{ cm}$ $A = 74.48 \text{ cm}^2$
Eneo la trapezi ni:
$\boxed{74.48 \text{ cm}^2}$

Grade 10 learners had a mean of 9.467. Use mathematical tables to find the logarithm of the mean. Express 0.00000789 as a power of 10. The perpendicular height of a trapezium is 5.6cm. If the lengths of the two parallel sides are 12.2cm and 14.4cm respectively, work out its area.

Answer

Step-by-step solution

Tambua nambari ya kupata logariti.

Tafuta logariti ya 9.467 kwa kutumia jedwali za hisabati (log tables).

Sogeza desimali ili kupata nambari kati ya 1 na 10.

Andika nambari katika mfumo wa kisayansi.

Andika fomula ya eneo la trapezi.

Badilisha thamani zilizopewa kwenye fomula.

Jumlisha urefu wa pande sambamba.

Fanya kuzidisha.

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