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AlexFokin [52]
3 years ago
7

Evaluate 1/2a^-4b^2 for a=-2 and b=4 A) 2 B) 1/2 C)3 D)4

Mathematics
1 answer:
shepuryov [24]3 years ago
5 0

Answer:

The answer to your question is: letter B) 1/2

Step-by-step explanation:

Data

a = -2

b = 4

Equation

(1/2)a⁻⁴b²

Substitution

= (1/2)(-2)⁻⁴(4)²

= (1/2) (1 /2⁴)(4)²

= 1/2 (1/16) (16)

= 16 / 32

= 1 / 2

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Write the equation of the ellipse with foci at (-2,2) and (4,2) and major axis of length 10 *
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Answer:

The answer to your question is   \frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1          

Step-by-step explanation:

Data

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Process

1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.

From the graph we conclude that it is a horizontal ellipse.

2.- Determine the foci axis (distance between the foci)

                  2c = 6

                    c = 6/2

                    c = 3

3.- Determine a

                  2a = 10

                    a = 10/2

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4.- Determine b using the Pythagorean theorem

                   a² = b² + c²

-Solve for b

                   b² = a² - c²

                   b² = 5² - 3²

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                   b² = 16

                   b = 4

5.- Find the center (1, 2)  From the graph, it is in the middle of the foci

6.- Find the equation of the ellipse

                      \frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1

                       \frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1                

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