Write 16 cookies to 30 brownies as a ratio in simplest form. Use a ":" in your answer.
2 answers:
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Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
Explanation :
Since we have shown in the figure below :
a=70 mi.
b=52 mi.
c=x mi.
So, we use the cosine rule , which states that
So, c = x= 106.03 mi.
Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.
We call:
as the set of <span>the first 51 consecutive odd positive integers, so:
</span>
Where:
<span>and so on.
In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:
3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.
Then, the common difference is 2, thus:
</span>
<span>
Then:
</span>
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:
There is a formula for arithmetic series, namely:
</span>
<span>
Therefore, we need to find:
</span>
Given that, then:
Thus:
Lastly:
</span>
Where:
<span>and so on.
In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:
3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.
Then, the common difference is 2, thus:
</span>
<span>
Then:
</span>
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:
There is a formula for arithmetic series, namely:
</span>
<span>
Therefore, we need to find:
</span>
Given that
Thus:
Lastly:
Answer:
Step-by-step explanation:
The <em>transpose of a matrix </em> is one where you swap the column and row index for every entry of some original matrix
. Let's go through our first matrix row by row and swap the indices to construct this new matrix. Note that entries with the same index for row and column will stay fixed. Here I'll use the notation
and
to refer to the entry in the i-th row and the j-th column of the matrices
and
respectively:
Constructing the matrix from those entries gives us
which is option a. from the list.
Another interesting quality of the transpose is that we can geometrically represent it as a reflection over the line traced out by all of the entries where the row and column index are equal. In this example, reflecting over the line traced from 2 to 1 gives us our transpose. For another example of this, see the attached image!
