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gavmur [86]
4 years ago
9

The base of a regular pyramid is a hexagon.

Mathematics
1 answer:
Lyrx [107]4 years ago
4 0
If you think about it, a hexagon can be cut into 6 equilateral triangles. Because of this, all you need to do is find the area of one triangle and multiply it by 6. Since the side length of one triangle is 12, we know that is the base. Since the triangles that are created when cutting the equilateral triangle in half are both 30 60 90, the height must be 6(3)^1/3. We can then multiply 12 • 6 radical 3 •1/2 to get 36 radical 3. Multiply this by 6 and get 216 radical 3 units squared.
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amm1812

For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =

Applying double C we have:

\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =

By definition of multiplication of powers of the same base we have to place the same base and add the exponents:\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =

Canceling common terms:

\frac {mn ^ 5} {p ^ 4}

Answer:

Option A

Question 2:

We should simplify the following expression:

\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}

So, we have:

\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =

Simplifying common terms:

\frac {1} {y ^ 2z ^ 2}

Answer:

Option D

Question 3:

We factor the following expressions to rewrite the experience:

<em>r ^ 2 + 7r + 10: </em>We look for two numbers that multiplied give 10 and added 7:

(r + 5) (r + 2)

<em>r ^ 2-5r-50:</em> We look for two numbers that multiplied give -50 and added -5:

(r-10) (r + 5)

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Rewriting the given expression we have:

\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =

We simplify common terms in the numerator and denominator we have:

(r + 2)

Answer:

Option D

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