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nika2105 [10]
3 years ago
6

- 100 points -

Mathematics
2 answers:
Molodets [167]3 years ago
8 0

Answer:

B

Step-by-step explanation:

mezya [45]3 years ago
4 0

D) - y = (x + 5)(x - 3)(x + 1).

<h3>EXPLANATION:</h3>

Table in this case would look like this:

Write coefficients of x³, x² ,x and the constant in a row and divisor would be the x value obtained by equation x + 5 = 0.

The sequence of multiplications would be as shown in picture.

x² - 2x - 3

x² - 3x + x - 3

x(x - 3) + 1(x - 3)

(x + 1)(x - 3)(x + 5).

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Wittaler [7]

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Show that the set of points that are twice as far from the origin as they are from (2, 2, 2) is a sphere. Find the center and ra
Viktor [21]

Answer:

This is a sphere with a center  (\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )  and radius \dfrac{4 \sqrt{3}}{3}

Step-by-step explanation:

Given that: (x,y,z)

where;

d₁ is the distance from the origin = \sqrt{x^2+y^2+z^2}

d₂ is the distance from (2,2,2) = \sqrt{(x-2)^2+(y-2)^2+(z-2)^2}

Also;

d₁ = 2d₂

\sqrt{x^2 + y^2 +z^2 } = 2 \sqrt{(x-2)^2 +(y-z)^2+(z-2)^2}

By squaring both sides;

x^2 + y^2 +z^2 = 2^2((x-2)^2 +(y-z)^2+(z-2)^2)

x^2 + y^2 +z^2 = 4(x-2)^2 +4(y-z)^2+4(z-2)^2

x^2 + y^2 +z^2 =4(x^2 -2x -2x +4) + 4(y^2 -2y -2y +4) + 4(z^2 -2z-2z+4)

x^2 + y^2 +z^2 =4x^2 -16x +16 + 4y^2 -16y  +16 + 4z^2 -16z+16

Collect the like terms:

0 = 4x^2 -x^2 -16x +16 + 4y^2 -y^2 -16y +16 +4z^2 -z^2 -16z +16

0 = 3x^2 -16x +16 + 3y^2 -16y +16 +3z^2 -16z +16

Divide both sides by 3

\dfrac{0}{3} = \dfrac{3x^2 -16x +16}{3} + \dfrac{3y^2 -16y +16 }{3} + \dfrac{ +3z^2 -16z +16}{3}

0 = {x^2 - \dfrac{16x}{3} +\dfrac{16}{3} + {y^2 - \dfrac{16y}{3} +\dfrac{16}{3}+{z^2 - \dfrac{16z}{3} +\dfrac{16}{3}

Using the completing the square method;

3(\dfrac{160}{9}) -16 = {x^2 - \dfrac{16x}{3} +\dfrac{160}{9} + {y^2 - \dfrac{16y}{3} +\dfrac{160}{9}+{z^2 - \dfrac{16z}{3} +\dfrac{160}{9}

\dfrac{16}{3}= (x - \dfrac{8}{3})^2+ (y - \dfrac{8}{3})^2+ (z - \dfrac{8}{3})^2

∴

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radius; \sqrt{\dfrac{16}{3}}

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