Solve each system of equations without graphing.

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

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Find the center, vertices, and foci for the ellipse 25x^2+64y^2=1600

Ronch [10]

Answer:

Step-by-step explanation:

Answer:

Data

Equation 25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

3.- Find a, b and c

a² = 64 a = 8

b² = 25 b = 5

-Calculate c with the Pythagorean theorem

a² = b² + c²

-Solve for c

c² = a² - b²

-Substitution

c² = 8² - 5²

-Simplification

c² = 64 - 25

c² = 39

-Result

c = √13

4.- Find the center

C = (0, 0)

5.- Find the vertices

V1 = (-8, 0) V2 = (8, 0)

6.- Find the foci

F1 = (-√13, 0) F2 = (√13, 0)

4 0

3 years ago

Read 2 more answers

in a cookie jar,1/5 of the cookies are chocolate chip and 1/2 of the rest are peanut butter.What fraction of all the cookies is

Tamiku [17]

If 1/5 are chocolate chip, then 4/5 are not chocolate chip because 1 - 1/5 = 4/5.

Half of 4/5 are peanut butter. Half of 4/5 is 2/5, so 2/5 of the cookies are peanut butter.

3 0

3 years ago

A class of 25 students took a spelling test. Two students scored 100 on each test, nine students scored 95 on each test, ten stu

lawyer [7]

The average score is 90.6

5 0

3 years ago

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Student loan: A student takes out an emergency loan for tuition, books, and supplies. The loan is for $200 with an interest rate

guapka [62]

Answer:

The answer is 120

Step-by-step explanation:

8 0

3 years ago