If anyone can help me to write recursive and explicit definition for this sequence I'm giving extra points!!
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<h3>HCF and LCM Questions</h3>
Responses:
6. (i) 27
(ii) 4 rose stalks, 3 lily stalks, and 2 orchid stalks
7. After 18 minutes
8. (i) May 7th
(ii) Every 12 days
<h3>How can the HCF and LCM be used to find the right responses?</h3>6. The number of stalks of roses = 108
Number of stalks of lilies = 81
Number of stalks of orchids = 54
(i) The largest number of baskets that can be packed is given by the
Highest Common Factor, GCF , or HCF, of 108, 81, and 54, which is
found as follows;
54 = 2 × 27
81 = 3 × 27
108 = 4 × 27
Therefore;
The HCF of 108, 81, and 54 is 27
Which gives;
- The largest number of baskets that can be packed = <u>27</u>
(ii) From the above factors, we have;
- Number of rose stalks per basket = <u>4</u>
- Number of lilies per basket =<u> 3</u>
- Number of orchids per basket =<u> 2</u>
7. Length of the circular path = 1 km. = 1,000 m.
Time Lixin takes to walk one round = 18 minutes = 1,080 seconds
Time Khairul takes to run one round = 360 seconds
Time Devi takes to cycle 2 rounds = 4 minutes
Therefore;
Time Devi takes to complete 1 round = = 2 minutes = 120 seconds
Required:
The time at which the three of them will next meet at the starting point
Solution:
The time at which they meet at the starting point is given as the lowest
common multiple, LCM of 1,080, 360, and 120, which is given as
follows.
1,080 = 360 × 3
1,080 = 120 × 9
1,080 = 1,080 × 1
Therefore;
The LCM of 1,080, 360, and 120 is 1,080
- The time they will next meet at the starting point is after 1,080 seconds which is <u>18 minutes</u>
8. The days off of Nora = Every 4 days
Days off for Amirah = Every 6 days
Nora's last day of = 29 April
Amirah's last day off = 1 May
(i) The next time they will both have the same day off is given as follows;
6·x = 2 + 4·x
2·x = 2
x = 1
Therefore, the next time Amirah has a day off, which is 1 May + 6 days = 7 May, they will both have the same day off.
- They will both have the same day off on May 7
(ii) The number of days that it will take for them to have the same day off is given by the HCF of 4 and 6, which is <u>every 12 days</u>.
Learn more about LCM and HCF here: