Determine the graph of the polar equation r =6/2-2cos theta (picture provided)

Mathematics

1 answer:

vredina [299]3 years ago

5 0

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

$r=\frac{3}{1-cos(theta)}$

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at x = -3. Choice D fits this criteria

You might be interested in

using the idea of sum and product of roots of quadratic equation how would you determine that width and length of the basketball

marishachu [46]

Answer: By Using Quadratic Formula as Possible and Finding the solution of the Quadratic Equations

Step-by-step explanation: Hope this helped!

6 0

3 years ago

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

zhuklara [117]

Answer:

The translation that maps the vertex of the graph of the function f(x) = x² onto the vertex of the function g(x) = x² - 10x + 2 is 5 units to the right and 23 units down.

Explanation:

1) Vertex form of the function that represents a parabola.

The general form of a quadratic equation is Ax² + Bx + C = 0, where A ≠ 0, and B and C may be any real number. And the graph of such equation is a parabola with a minimum or maximum value at its vertex.

The vertex form of the graph of such function is: A(x - h)² + k

Where, A a a stretching factor (in the case |A| > 1) or compression factor (in the case |A| < 1) factor.

2) Find the vertex of the first function, f(x) = x²

This is the parent function, for which, by simple inspection, you can tell h = 0 and k = 0, i.e. the vertex of f(x) = x² is (0,0).

3) Find teh vertex of the second function, g(x) = x² -10x + 2

The method is transforming the form of the function by completing squares:

Subtract 2 from both sides: g(x) - 2 = x² - 10x

Add the square of half of the coefficient of x (5² = 25) to both sides: g(x) - 2 + 25 = x² - 10x + 25

Simplify the left side and factor the right side: g(x) + 23 = (x - 5)²

Subtract 23 from both sides: g(x) = (x - 5)² - 23

That is the searched vertex form: g(x) = (x - 5)² - 23.

From that, using the rules of translation you can conclude immediately that the function f(x) was translated 5 units horizontally to the right and 23 units vertically downward.

Also, by comparison with the verex form A(x - h)² + k, you can conclude that the vertex of g(x) is (5, -23), and that means that the vertex (0,0) was translated 5 units to the right and 23 units downward.

5 0

3 years ago

A geometric sequence is defined by the general term tn = 4096 8n - 1 , where n ∈N and n ≥ 1. What is the recursive formula of th

zhenek [66]

Hello her is a solution :