Question

In a video game, two characters follow paths represented by and , respectively. the characters travel at different speeds and could collide with each other. which values of correspond to possible collision points? check all that apply.

Answer 1

The possible collision points of the two paths are given as follows:

• θ = π/6.

• θ = 11π/6.

When do the two paths collide?

Each path is modeled by the equations presented as follows:

• Path 1: $r_1(\theta) = \sqrt{3} + 2\cos{\theta}$

• Path 2: $r_2(\theta) = 4\cos{\theta}$

When the two paths collide, they are at the same position, hence the points are the values of θ that respect the condition given by:

$r_1(\theta) = r_2(\theta)$

Hence the equation to be solved is:

$\sqrt{3} + 2\cos{\theta} = 4\cos{\theta}$

Isolating the cosine variable, we have that:

$2\cos{\theta} = \sqrt{3}$

$\cos{\theta} = \frac{\sqrt{3}}{2}$

Applying the inverse cosine function, the angles are obtained as follows:

$\theta = \cos^{-1}{\left(\frac{\sqrt{3}}{2}\right)}$

Which has two solutions:

• θ = π/6 -> First quadrant.

• θ = 11π/6 -> Fourth quadrant.

Hence the correct options are given by the first option and the last option.

Missing Information

The complete problem is given by the image shown at the end of the answer.

More can be learned about trigonometric equations at https://brainly.com/question/24349828

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Answer 2

Answer:

A and E.

Step-by-step explanation: