All the prime numbers between 1 and 30
2 answers:
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Answer: 
Explanation: For a general binomial expansion,
, we know that the powers have to add up to the initial power. This means that the power of x and power of y have to add up to n. This is the binomial theorem.
To further demonstrate this, let's use:
We can easily expand this. Using Pascal's Triangle, we get:
As we progress along the expansion, we can see that in each term, the summation of each power remains constant, namely 4.
It doesn't matter what term the binomials are, because the power summation will never change.
This is why we can say that it is raised to the 12th power, and the binomial is:
(5x - 6y).
Thus, we get:
Explanation: For a general binomial expansion,
To further demonstrate this, let's use:
We can easily expand this. Using Pascal's Triangle, we get:
As we progress along the expansion, we can see that in each term, the summation of each power remains constant, namely 4.
It doesn't matter what term the binomials are, because the power summation will never change.
This is why we can say that it is raised to the 12th power, and the binomial is:
(5x - 6y).
Thus, we get:
Answer:
The volume of the given pyramid is 300 cm³
Step-by-step explanation:
The volume of a pyramid, , is given as follows;
The height of the pyramid = 12 cm
The side length of the square base of the pyramid = 5 cm
The base area of the pyramid polyhedron with square base = 5 cm × 5 cm = 25 cm²
Therefore, by substitution, we have;
The volume of the given pyramid, V = 300 cm³.