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2 years ago

LCM of a2+b2 and a4-b4

Mathematics

1 answer:

Zarrin [17]2 years ago

4 0

Answer:

The LCM is:

$(a^2+b^2)(a+b)(a-b)$

Step-by-step explanation:

Given polynomials are:

$a^2+b^2\\a^4 - b^4$

We can use factorization to find the LCM of the given polynomials.

Taking the second polynomial, using the identity

$a^2 - b^2 = (a+b)(a-b)$

Applying on 2nd polynomial

$(a^2)^2-(b^2)^2\\=(a^2+b^2)(a^2-b^2)\\=(a^2+b^2)(a+b)(a-b)$

We can see that $a^2+b^2$ is common in both polynomials, it will be counted only one time. The LCM of given polynomials is:

$(a^2+b^2)(a+b)(a-b)$

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A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two op

shutvik [7]

Answer:

Step-by-step explanation:

Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form

$4p(y-k)=-(x-h)^2$

The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.

Filling in the equation with a vertex of (0, 0) which is our h and k respectively:

$4(3)(y-0)=-(x-0)^2$ which simplifies to

$12y=-x^2$ and multiplying both sides by -1:

$-12y=x^2$ . This is not standard form, but it matches what your equation is in the choices. So to sum up:

The focus is located at (0, -3) and the first choice is true.

The parabola opens upside down and the second choice is not true.

The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.

We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.

So the fifth choice is not true.

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2 years ago

Read 2 more answers

You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing th

Pachacha [2.7K]

Solving this problem needs the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / √ (a^2 + b^2)

So we are given the equation: y = 2 x + 4

Rewriting this would be: y – 2 x – 4 = 0 -> a = -2, b = 1, c = -4

We are also given the points:

(-4, 11) = (x, y)

Plugging it in the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / √ [(- 2)^2 + (1)^2]

= 15 / √ (5)

= 6.7

So the tree is approximately 6.7 feet away from the zip line.

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2 years ago

Un guardia forestal divisa, desde un punto de observación A, un incendio en la dirección N27° 10’ E. Otro guardia, que se encuen

Inga [223]

Answer:

la distancia del punto de observación A al incendio = 5.5 millas

la distancia del punto de observación B al incendio = 3.8 millas

Step-by-step explanation:

La expresión esquemática de la pregunta se puede ver en la imagen adjunta a continuación :

Del siguiente diagrama;

Usando la sine regla:

$\dfrac{sin \ F}{f} = \dfrac{sin \ A }{a}$