Solve the equation for all real solutions. 15r2 – 6r – 3 = -2r

Mathematics

1 answer:

Solnce55 [7]3 years ago

4 0

Answer:

Step-by-step explanation:

hello :

15r² – 6r – 3 = -2r

15r² – 6r – 3 +2r =0

15r²-4r -3 =0

delta =b² -4ac a=15 b=-4 c=-3

delta =(-4)² - 4(15)(-3)=196 = 14²

r1 = (-b - √delta ) /2a = (4-14)/30 = -10/30 = -2/6 = -1/3

r2 = (-b + √delta ) /2a = (4+14)/30 = 18/30 = 3/5

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an ellipse has a center at the origin , a vertex along the major axis at (13,0), and a focus at (12,0). What is the equation of

-BARSIC- [3]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Center = (0, 0)

Vertex = (13, 0)

Focus = (12, 0)

Process

From the data we know that it is a horizontal ellipse.

1.- Calculate "a", the distance from the center to the vertex.

a = 13

2.- Calculate "c", the distance from the center to the focus

c = 12

3.- Calculate b

Use the Pythagorean theorem to find it

a² = b² + c²

-Solve for b

b² = a² - c²

-Substitution

b² = 13² - 12²

-Simplification

b² = 169 - 144

b² = 25

b = 5

4.- Find the equation of the ellipse

$\frac{x^{2} }{13^{2}} + \frac{y^{2}}{5^{2}} = 1$ or $\frac{x^{2} }{169} + \frac{y^{2}}{25} = 1$

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drek231 [11]

Answer:

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