In a video game, two objects move around the screen according to the equations r = 4cos(0) and r= -1 +
2cos(0). Which coordinates represent a possible collision point of the objects?
Answers
Answer:
The correct option is;
[tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]
Step-by-step explanation:
The given parameters are
The equation of motion of one (the first) object is r = 4·cos(θ)
The equation of motion of the other (the second) object is r = -1 + 2·cos(θ)
Equating both equations gives;
4·cos(θ) = -1 + 2·cos(θ)
4·cos(θ) - 2·cos(θ) = -1
2·cos(θ) = -1
cos(θ) = -1/2
θ = Arccos(-1/2) = 120° = 2·π/3
Therefore, the two equations are equal when θ = 2·π/3 for which we have;
r = 4·cos(2π/3) = -2 and r = -1 + 2·cos(2π/3) = -2
∴ r = 4·cos(2π/3) = -1 + 2·cos(2π/3) = -2
The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore [tex]\left ( -2,\dfrac{2 \cdot \pi }{3} \right)[/tex]
Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex])
Given that ,
The first object is moving around the screen r = 4 cos(0)
The second object is moving around the screen r = -1 + 2cos(0)
We have to find ,
The coordinates represent a possible collision point of the objects.
According to the question,
Coordinate represent collision points to object ,
Equating both equations ;
4·cos(θ) = -1 + 2·cos(θ)
4·cos(θ) - 2·cos(θ) = -1
2·cos(θ) = -1
cos(θ) = -[tex]\frac{1}{2}[/tex]
θ = [tex]cos^{-1} (\frac{1}{2} )[/tex] = 120°
[tex]\theta[/tex] = [tex]\frac{-2\pi }{3}[/tex]
Therefore, the two equations are equal when θ = [tex]\frac{2\pi }{3}[/tex]
We have;
r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -2
And r = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex]) =
r = -2
r = 4·cos([tex]\frac{2\pi }{3}[/tex]) = -1 + 2·cos([tex]\frac{2\pi }{3}[/tex])
r = -2
The coordinate that represents a possible collision point of the objects in the form (r, θ) is therefore r = -2 and [tex]\theta = \frac{2\pi }{3}[/tex] .
Hence, The coordinate that represents a possible collision point of the objects in the form (-2, [tex]\frac{2\pi }{3}[/tex]) .
For the more information about Motion of Equation line click the link given below.
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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cuales son las soluciones (o raices) de la ecuacion x^2 + 6x - 16 = 0?
Answers
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Step-by-step explanation:
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Answer:
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Answers
Answer:
Variable x = $2.39 ⇒ price of 1 pound of cashews
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Step-by-step explanation:
Assume that the price of each pound of cashews is $x and the price of each pound of peanuts is $y
∵ The price of 1 pound of cashews = x
∵ The price of 1 pound of peanuts = y
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∴ 5x + 8y = 26.27 ⇒ (1)
∵ 7 pounds of cashews and 4 pounds of peanuts cost $23.89
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∴ The price of 1 pound of cashews is $2.39
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Answers
Answer:
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Step-by-step explanation:
Sum of the middle two numbers is ''182'' for 4 consecutive even number.
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We have to given that;
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Let 4 consecutive even numbers are,
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
please find the complete question in the attached file.
Time= 10 year =38.0%
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Answers
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Answers
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answers
Answer:
[tex]0.17\ \text{yards}[/tex]
Step-by-step explanation:
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Answers
Answer:
x = -65
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer: 1/26 or 0.0384615
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Answers
Answer: Each girl will receive $18.75.
Step-by-step explanation:
Given: Two girls babysat three children for five hours.
Hourly pay for each child = $2.50
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Answers
Answer:
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Step-by-step explanation: