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3 years ago

Simplify 3[2^3 + (4-2)^3 - (6-2)^2]

Mathematics

1 answer:

Ivahew [28]3 years ago

6 0

Answer:

$\boxed{0}$

Step-by-step explanation:

$3(2^3 + (4 - 2)^3 - (6 - 2)^2)$

$= 3(2^3 + 2^3 - 4^2)$

$= 3(2.2^3 - (2^2)^2)$

$= 3(2^4 - 2^4)$

$= 3(0)$

$= 0$

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Graph the hyperbola using the transverse axis, vertices, and co-vertices:

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See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

<h3>How to graph the hyperbola?</h3>

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

<u>Transverse axis</u>

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

<u>The vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

<u>The co-vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola