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Anettt [7]
3 years ago
7

write a polar equation of a conic with the focus at the origin and the given data.hyperbola, eccentricity 3.5, directrix y

Mathematics
1 answer:
Colt1911 [192]3 years ago
7 0

Complete Question is;

Write a polar equation of a conic with the focus at the origin and the given data. hyperbola, eccentricity 3.5, directrix y =2

Answer:

r = 14/(2 + 7(sinθ))

Step-by-step explanation:

We are given;

Eccentricity;e = 3.5

Directrix; y = 2

This means that d = 2

We are told that the focus is at the origin, so since the directrix is at y = 2,then the part of the hyperbola that is closest to this focus will open downwards and the equation is given by;

r = ed/(1 + e•sinθ)

Plugging in the relevant values, we have;

r = (3.5 × 2)/(1 + 3.5(sinθ))

r = 7/(1 + 3.5(sinθ))

To make every figure a whole number, let's multiply numerator and denominator by 2 to give;

r = 14/(2 + 7(sinθ))

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snow_tiger [21]
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6 0
3 years ago
f(x) = −16x2 + 24x + 16 Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points) Part B: Is the vertex
DerKrebs [107]

Answer:

see below

Step-by-step explanation:

f(x) = −16x^2 + 24x + 16

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0  = −16x^2 + 24x + 16

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Factor

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Using the zero product property

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x = -1/2      x=2

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(-1/2+2) /2 = 1.5/2 =.75

To find the y value substitute into the function

f(.75) = -8(2x +1) (x-2)

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The vertex is at (.75, 25)

We have the zeros, and  the vertex.  We know the graph is symmetrical about the vertex

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Answer:

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