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ANNEXURE D shows photographs of the London Eye, which is a *Ferris wheel: The following information represents features of the Ferris wheel: The structure is 443 feet tall - NSC Mathematical Literacy - Question 4 - 2018 - Paper 2

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ANNEXURE D shows photographs of the London Eye, which is a *Ferris wheel: The following information represents features of the Ferris wheel: The structure is 443 f... show full transcript

Worked Solution & Example Answer:ANNEXURE D shows photographs of the London Eye, which is a *Ferris wheel: The following information represents features of the Ferris wheel: The structure is 443 feet tall - NSC Mathematical Literacy - Question 4 - 2018 - Paper 2

Step 1

4.1.1 Verify the amount spent on tickets

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Answer

To verify the remark, we first calculate the total number of occupants in both capsules:

  • Capsule 24: 18 Adults + 7 Children + 1 Senior = 26
  • Capsule 30: 10 Adults + 1 Child + 5 Seniors = 16

Total occupants = 26 + 16 = 42.

Next, we calculate the ticket prices based on the given categories:

  • Adults: 5 bought tickets online → 5 × £27 = £135
  • Children: 7 Children → 7 × £22 = £154
  • Seniors: 1 Senior → 1 × £25.50 = £25.50
  • For Capsule 30, 10 Adults, 1 Child, and 5 Seniors:
    • Adults: 10 × £27 = £270
    • Child: 1 × £22 = £22
    • Seniors: 5 × £25.50 = £127.50

Total for Capsule 24 = £135 + £154 + £25.50 = £314.50 Total for Capsule 30 = £270 + £22 + £127.50 = £419.50

Total spent = £314.50 + £419.50 = £734.00.

Convert the total to Rand:

Total in Rand = £734 × R16.58 ≈ R12,160.12.

Since R12,160.12 is less than R18,400, the statement by the tourist regarding the amount spent is NOT CORRECT.

Step 2

4.1.2 (a) Calculate (in feet) the circumference of the wheel.

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Answer

To calculate the circumference of the Ferris wheel, use the formula:

Circumference=2×π×radiusCircumference = 2 \times \pi \times radius

Given that radius = 197 feet:

Circumference=2×3.142×197=1237.49 feet (approximately)Circumference = 2 \times 3.142 \times 197 = 1237.49 \text{ feet (approximately)}

Step 3

4.1.2 (b) Hence, calculate the distance (to the nearest metre) on the circumference between any TWO capsules right next to each other.

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Answer

Since there are 32 capsules evenly distributed along the circumference, the distance between two adjacent capsules can be calculated by dividing the circumference by the number of capsules:

Distance=CircumferenceNumber of Capsules=1237.49 feet32≈38.67 feetDistance = \frac{Circumference}{Number \ of \ Capsules} = \frac{1237.49 \text{ feet}}{32} \approx 38.67 \text{ feet}

To convert feet into metres:

  • 1 foot = 0.3048 metres
  • Hence, Distance in Metres = 38.67 × 0.3048 ≈ 11.78 metres.

Rounded to the nearest metre: 12 metres.

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