If (x+y)"2 is miscopied as x2+y2, find the percentage error in the calculation where x = 5 and y = 7. 23.) By…

Question

If (x+y)"2 is miscopied as x2+y2, find the percentage error in the calculation where x = 5 and y = 7. 23.) By correcting each number to two significant figures, calculate the percentage error arising from this approximate calculation of 632 × 0.0145. Hence correct to 2 decimal places.

ScanSolve AI Tutor · Accepted Answer

HAmda, hapa kuna hatua za kukokotoa asilimia ya kosa kwa swali la 23:

Tafuta thamani halisi.
Kwanza, tunakokotoa thamani halisi ya $632 \times 0.0145$ .
$632 \times 0.0145 = 9.164$
Zungusha kila namba kwa tarakimu mbili muhimu (significant figures).
- Kwa namba 632: Tarakimu ya kwanza muhimu ni 6, na ya pili ni 3. Tarakimu inayofuata ni 2, ambayo ni chini ya 5, kwa hivyo tunazungusha chini. $632 \approx 630$ (kwa tarakimu mbili muhimu).
- Kwa namba 0.0145: Tarakimu ya kwanza muhimu ni 1, na ya pili ni 4. Tarakimu inayofuata ni 5, kwa hivyo tunazungusha juu tarakimu ya pili muhimu. $0.0145 \approx 0.015$ (kwa tarakimu mbili muhimu).
Tafuta thamani iliyokadiriwa.
Sasa tunazidisha namba zilizozungushwa.
$630 \times 0.015 = 9.45$
Kokotoa kosa kamili (absolute error).
Kosa kamili ni tofauti kati ya thamani halisi na thamani iliyokadiriwa.
$\text{Kosa kamili} = |\text{Thamani Halisi} - \text{Thamani Iliyokadiriwa}|$ $\text{Kosa kamili} = |9.164 - 9.45|$ $\text{Kosa kamili} = |-0.286|$ $\text{Kosa kamili} = 0.286$
Kokotoa asilimia ya kosa (percentage error).
Asilimia ya kosa inapatikana kwa kugawanya kosa kamili kwa thamani halisi na kuzidisha kwa 100%.
$\text{Asilimia ya kosa} = \frac{\text{Kosa kamili}}{\text{Thamani Halisi}} \times 100\%$ $\text{Asilimia ya kosa} = \frac{0.286}{9.164} \times 100\%$ $\text{Asilimia ya kosa} \approx 3.1209079\%$
Zungusha asilimia ya kosa kwa sehemu mbili za desimali.
Tarakimu ya tatu baada ya desimali ni 0, kwa hivyo tunazungusha chini.
$\text{Asilimia ya kosa} \approx \boxed{\text{3.12\%}}$

If (x+y)"2 is miscopied as x2+y2, find the percentage error in the calculation where x = 5 and y = 7. 23.) By correcting each number to two significant figures, calculate the percentage error arising from this approximate calculation of 632 * 0.0145. Hence correct to 2 decimal places.

Step-by-step solution

Tafuta thamani halisi.

Zungusha kila namba kwa tarakimu mbili muhimu (significant figures).

Tafuta thamani iliyokadiriwa.

Kokotoa kosa kamili (absolute error).

Kokotoa asilimia ya kosa (percentage error).

Zungusha asilimia ya kosa kwa sehemu mbili za desimali.

Still stuck on this one?

More Mathematics Questions