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cluponka [151]
3 years ago
9

Help me please don’t lie to me

Mathematics
1 answer:
Alinara [238K]3 years ago
8 0

Answer:

1. yes

2. no

Step-by-step explanation:

1. 3x - 4y ≥ 18

3(2) - 4(-3) = 6 + 12 =18

18≥18 this is a solution

2. 4x + y < 0

4(1) + (-4) = 4 - 4 = 0

0 equals 0, 0 cannot be less than 0, they are the same

<h2><u><em>xoxo, </em></u></h2><h2><u><em>your highness...</em></u></h2>
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1. Determinar la ecuación canónica de la parábola con vértice en (-2,4) y foco en (1,4) 2. Determinar el foco y el vértice de la
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Answer:

1. La ecuación de la parábola en forma canónica es x = 1/12 × (y - 4) ² - 2

2. Vértice = (-1, 3), enfoque = (-5/2, 3)

3. y = 12x no es una parábola

4. y = -8x, no es una parábola

Step-by-step explanation:

1. La ecuación estándar de una parábola es y = a · x² + b · x + c

El vértice V es (h, k)

El foco (h + p, k)

Por lo tanto, tenemos en comparación k = 4, h = -2

h + p = 1

p = 1 - h = 1 - (-2) = 3

Lo que da la ecuación como (y - k) ² = 4 · p · (x - h)

Al ingresar los valores de k, h y p, tenemos

(y - 4) ² = 4 × 3 × (x - (-2)) = 12 × (x + 2)

12 · x + 24 = (y - 4) ²

x = 1/12 × (y - 4) ² - 2

La ecuación de la parábola en forma canónica es x = 1/12 × (y - 4) ² - 2

2. Determinar el foco y el vértice de la parábola (y - 3) ² = -6 · (x + 1)

Reescribimos la ecuación en forma de vértice de la siguiente manera;

-6 · x -6 = (y - 3) ²

x = -1 / 6 × (y - 3) ² - 1

La ecuación de una parábola en forma de vértice es x = a · (y - k) ² + h

Con el vértice = (h, k)

Comparando, tenemos, h = -1 yk = 3, el vértice = (-1, 3)

También la ecuación de la parábola en forma cónica es (y - k) ² = 4 · p · (x - h)

Comparando con (y - 3) ² = -6 · (x + 1), tenemos 4p = -6, p = -3/2

El foco está en (h + p, k) que es (-1 + -3/2, 3) = (-5/2, 3)

Vértice = (-1, 3), Enfoque = (-5/2, 3)

3. Para la parábola, y = 12 · x, tenemos;

En comparación con la forma de la ecuación, y = a · x² + b · x + c

b = 12, a = 0, c = 0

Dado que el vértice = (h, k), tenemos;

h = -b / (2 × 0), h = ∞

k = a · h² + b · h + c = ∞

No hay vértice

Foco x valor = Vértice x valor = ∞

No hay foco

Directrix = (k - 1) / (4 · a) = (k - 1) / (4 × 0) = ∞, sin directriz

y = 12x no es una parábola

4. Para y = -8x, tampoco es una parábola como se muestra arriba.

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