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scZoUnD [109]
3 years ago
11

HCF and LCM questions​

Mathematics
1 answer:
mina [271]3 years ago
7 0
<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 = \frac{4}{2} = 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:

brainly.com/question/20293084

brainly.com/question/14387448

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Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu
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ANSWER

See below

EXPLANATION

Part a)

The given function is

f(x) =  {x}^{5}  -  {x}^{3}  + 6

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b) Using calculus, we find the first derivative of the given function.

f'(x) = 5 {x}^{4} - 3 {x}^{2}

At turning point f'(x)=0.

5 {x}^{4} - 3 {x}^{2}  = 0

This implies that,

{x}^{2} (5 {x}^{2}  - 3) = 0

{x}^{2}  = 0 \: or \: 5 {x}^{2}  - 3 = 0

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We plug this values into the original function to obtain the y-values of the turning points

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f''( -  \frac{ \sqrt{15} }{5} ) \:   <  \: 0

Hence

(   -  \frac{ \sqrt{15} }{5}  , \frac{1}{125} ( 6 \sqrt{15}  + 750))

is a maximum point.

f''( \frac{ \sqrt{15} }{5} ) \:    >  \: 0

Hence

(     \frac{ \sqrt{15} }{5}  , \frac{1}{125} (- 6 \sqrt{15}  + 750))

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f''(0) \: =\: 0

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Answer:

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Putting the values, we get:

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