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zhenek [66]
2 years ago
11

Find the volume of the prism.

Mathematics
1 answer:
ExtremeBDS [4]2 years ago
6 0

Answer:

Its A.

Step-by-step explanation:

remember its rectangle 1 + rectange 2.Once i did that i have seen the total volume must be greater then answer B

so it must be a

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VashaNatasha [74]

The total number of coins required to fill all the 64 boxes are \boxed{\bf 18446744073709551615}.

Further explanation:

In a chessboard there are 64 boxes.

The objective is to determine the total number of coins required to fill the 64 boxes in chessboard.

In the question it is given that in the first box there is 1 coin, in the second box there are 2 coins, in the third box there are 8 coins and it continues so on.

A sequence is formed for the number of coins in different boxes.

The sequence formed for the number of coins in different boxes is as follows:

\boxed{1,2,4,8,...}

The above sequence can also be represented as shown below,

\boxed{2^{0},2^{1},2^{2},2^{3},...}

It is observed that the above sequence is a geometric sequence.

A geometric sequence is a sequence in which the common ratio between each successive term and the previous term are equal.

The common ratio (r) for the sequence is calculated as follows:

\begin{aligned}r&=\dfrac{2^{1}}{2^{0}}\\&=2\end{aligned}

The n^{th} term of a geometric sequence is expressed as follows:

\boxed{a_{n}=ar^{n-1}}

In the above equation a is the first term of the sequence and r is the common ratio.

The value of a and r is as follows:

\boxed{\begin{aligned}a&=1\\r&=2\end{aligned}}

Since, the total number of boxes are 64 so, the total number of terms in the sequence is 64.

To obtain the number of coins which are required to fill the 64 boxes we need to find the sum of sequence formed as above.

The sum of n terms of a geometric sequence is calculated as follows:

\boxed{S_{n}=a\left(\dfrac{r^{n}-1}{r-1}\right)}

To obtain the sum of the sequence substitute 64 for n, 1 for a and 2 for r in the above equation.

\begin{aligned}S_{n}&=1\left(\dfrac{2^{64}-1}{2-1}\right)\\&=\dfrac{18446744073709551616-1}{1}\\&=18446744073709551615\end{aligned}

Therefore, the total number of coins required to fill all the 64 boxes are \boxed{\bf 18446744073709551615}.

Learn more:

1. A problem on greatest integer function brainly.com/question/8243712  

2. A problem to find radius and center of circle brainly.com/question/9510228  

3. A problem to determine intercepts of a line brainly.com/question/1332667  

Answer details:  

Grade: High school  

Subject: Mathematics  

Chapter: Sequence

Keywords: Series, sequence, logic, groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule., geometric sequence, common ratio, nth term.

3 0
3 years ago
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jeka94

Answer:

the answer is parallel lines. b is the answer

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