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GREYUIT [131]
2 years ago
10

Write an explicit formula for an, the nth term of the sequence 33, 30, 27

Mathematics
1 answer:
lawyer [7]2 years ago
8 0

Answer:

<u>aₙ = aₙ₋₁ - 3</u>

Step-by-step explanation:

Given :

First term : <u>33</u>

Common difference = 30 - 33 = <u>-3</u>

<u />

============================================================

Then the formula will be :

<u>aₙ = aₙ₋₁ - 3</u>

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In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the
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Answer:

1747.9 J

Step-by-step explanation:

The work done to lift a book by a certain height \Delta h is

W=mg\Delta h

where

m = 1.40 kg is the mass of one book

g=9.8 m/s^2 is the acceleration due to gravity

The first shelf is 15.0 cm (0.15 m) from the ground, and it can be filled with 28 books. So, the work done to fill the first shelf is

W_1=28mg\Delta h=28(1.40)(9.8)(0.15)=57.6 J

The 2nd shelf is 38.0 cm above the first one, so its height from the ground is

\Delta h =15.0+38.0 =53.0 cm=0.53 m

It can also contain 28 books, so the work done to fill this shelf is

W_2=28 mg\Delta h=28(1.40)(9.8)(0.53)=203.6 J

The height of the third shelf is

\Delta h =15.0+38.0 +38.0=91.0 cm=0.91 m

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W_3=28 mg\Delta h=28(1.40)(9.8)(0.91)=349.6 J

The height of the 4th shelf is

\Delta h =15.0+38.0 +38.0+38.0=129.0 cm=1.29 m

It can also contain 28 books, so the work done to fill this shelf is

W_4=28 mg\Delta h=28(1.40)(9.8)(1.29)=495.6 J

The height of the 5th shelf is

\Delta h =15.0+38.0 +38.0+38.0+38.0=167.0 cm=1.67 m

It can also contain 28 books, so the work done to fill this shelf is

W_5=28 mg\Delta h=28(1.40)(9.8)(1.67)=641.5 J

Therefore, the total work done is:

W=W_1+W_2+W_3+W_4+W_5=57.6+203.6+349.6+495.6+641.5=1747.9 J

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3 years ago
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