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2 years ago

What are the coordinates of the orthocenter of LMN ?

Mathematics

1 answer:

Sauron [17]2 years ago

8 0

Answer:

a (1, 2.5)

Step-by-step explanation:

When talking about the orthocenter, you want to make sure that the point you are looking for is in the exact center. Since coordinate N of the x value is 1, we can safely assume that your top two choices are either a and b. B wouldn't work since it is not at the exact center which makes your answer A.

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

$h = \frac{3 * 9}{\sqrt 3}$

$h = \frac{27}{\sqrt 3}$

To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

$s = 6$

So:

$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

6 0

3 years ago

Read 2 more answers

What is the ans? what is the ans of it

umka21 [38]

We have 20 chances out of 100 which is 20/100=1/5 other known as 1 in 5 chance

The even numbers are 2, 4, 6, .., 100. 50 chances out of 100 which is 50/100=1/2 other know as 1 in 2 chance

6 0

3 years ago

How do I do this explain

xeze [42]

So you would take 3x1+2 that gives you 5 and you would keep the same denominator and so that would give you 5/3 then do the same to the other side which would give you 5/4 then you would times it and that would give you 2 1/12

5 0

3 years ago

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HigherOrder thing name two rays with the same endpoint in the figure below. Do they form an angle? Explain.

Artist 52 [7]

Answer:

where is the figure?

Step-by-step explanation:

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3 years ago

Find the values of the variables in the parallelogram. The diagram is not to scale.

monitta