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lbvjy [14]
3 years ago
11

The base of a rectangular solid is 4ft. long and 3ft. wide. What is the volume of the solid if its diagonal is sqrt of 41 ft.?

Mathematics
1 answer:
geniusboy [140]3 years ago
8 0
The diagonal of the figure forms a right angle triangle with the diagonal of the base and the height of the figure.
Diagonal of base = √(3² + 4²)
= 5ft
Diagonal of solid² = Diagonal of base² + height²
height = √((√41)² + 5²)
height = 8.12 feet
Volume = width x length x height
Volume = 3 x 4 x 8.12
= 97.44 cubic feet
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Answer:

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The chairs in the auditorium illustrates an arithmetic sequence

  • The recursive rule is:  an = an-1 + 8; a1 = 26
  • The explicit rule is:  an = 18 + 8n
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<h3>The recursive rule</h3>

From the question, we have the following sequence:

Seats: 18, 26, 34

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The number of seats on a row is 8 added to the the number of seats on the previous row.

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<h3>The explicit rule</h3>

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

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an = 26 - 8 + 8n

Evaluate the difference

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Hence, the explicit rule is:

an = 18 + 8n

<h3>The number of seats in the row 7</h3>

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

<h3>The sigma notation</h3>

We have the maximum number of rows to be 12.

So, the sigma notation would be:

\sum\limits^{12}_{n=1} {18 + 8n}

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

Read more about arithmetic sequence at:

brainly.com/question/6561461

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