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Vinvika [58]
3 years ago
7

Bamboo plants grow rapidly. A bamboo plant is 130 inches tall. Tomorrow it will be 143 inches tall, the next day it will be 156

inches tall, and on the next day it will be 169 inches tall. Write a rule to represent the height of the bamboo plant as an arithmetic sequence. How tall will the plant be in 13 days?
Mathematics
2 answers:
IrinaK [193]3 years ago
7 0

The sequence described is 130, 143, 156, 169, ...

To write the general formula/rule of the arithmetic sequence described above, we will use the the general term of arithmetic progressions formula:

T_{n}=a+(n-1)d

Where,

  • a is the first term,
  • d is the common difference (difference in 2 terms)
  • n is the index of the term

Plugging in 130 as a and 143-130=13 as d, we get,

T_{n}=130+(n-1)(13)\\ = 130 + 13n - 13\\=117+13n

We can use this model to write our own rule:

H=117+13x

Where,

  • H is the height of the bamboo plant, in inches
  • x is the day number, starting from x=1 as DAY 1

To find how tall the plant will be on Day 13, we plug in 13 for x in the formula and get,

H=117+13(13)=286 inches.


ANSWER:

<u>Rule:</u> H=117+13x (H is height, in inches, and x is the Day Number)

13 days later, height of plant will be 286 inches.

sasho [114]3 years ago
5 0
Well, (y for bamboo plant, x per day) y=130+13x  just use 13 for x for the second part. (It is 169+130. 299.)
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Answer:

1) Part A)

Liters    Mililiters

  1            1,000

  5           5,000

  8           8,000

 14          14,000

2) Part B)

One way to convert 4.2 liters to milliliters is to <u>   multiply   </u> the number of liters by the number of milliliters in 1 liter. This means there are <u>   4,200   </u>milliliters in 4.2 liters. The cafeteria has the greatest amount of  <u>   orange   </u>juice, the second greatest amount of    <u>     grape     </u> juice, and the least amount of <u>    cranberry     </u>juice.

Explanation:

<u>1) Data:</u>

  • Grape juice: 8,000 mililiters
  • Cranberry juice: 4.2 liter
  • Orange juice: 12,000 mililiters

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<u>2) Part A:</u>

<u>Table:</u>

The table is garbled. This is what the tables could look like:

Liters    Mililiters

  1            1,000

  5           5,000

  8           8,000

 14          14,000

You can see that the table shows a direct relationship between the number of mililiters and the number of liters:

  • 1,000/1 = 1,000
  • 5,000/5 = 1,000
  • 8,000/8 = 1,000
  • 14,000/14 = 1,000
  • number of mililiters / liters = 1,000

<u>3) Part B)</u>

Fill in the blanks to explain how Landon can convert 4.2 liters of cranberry juice to mililiters so he can compare the amounts of the different juices:

i) One way to convert 4.2 liters to milliliters is to <u>   multiply   </u> the number of

liters by the number of milliliters in 1 liter.

  • As demonstrated above there is a direct relationship between the number of mililiters and the number on liters, then you must multiply the number of liters by the proportionality constant to find the number of mililiters.

ii) This means there are <u>   4,200   </u>milliliters in 4.2 liters.

  • That is the product 4.2 × 1,000 = 4,200.

iii) The cafeteria has the greatest amount of  <u>   orange   </u>juice, the second greatest amount of    <u>     grape     </u> juice, and the least amount of <u>    cranberry     </u>juice.

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            ↑                   ↑                   ↑

       orange            grape        cranberry

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