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.
https://brainly.com/question/21024882
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Answers
Answer:
The interest on the investment is $16,170.93811
Step-by-step explanation:
The rule of the compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex], where
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1 - 4
Answers
Answer:
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5.-702
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
[tex]b.)31\neq -22[/tex]
Step-by-step explanation:
Simplify each equation using PEMDAS:
Parentheses (x)
Exponents x²
Multiplication and Division, left to right × ÷
Addition and Subtraction, left to right - +
It is also important to follow PEMDAS when working within grouping symbols like parentheses.
Also, remember that two negatives make a positive, and when a negative and positive are multiplied, the result is always negative.
[tex](-2)(8+6+-3)\\\\-2*(8+6-3)\\\\-2*(14-3)\\\\-2*11\\\\-22[/tex]
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---------------------------------------------------
b.) [tex](-2)*(8+6)+(-3)\\\\-2*(8+6)-3\\\\-2*14-3\\\\-28-3\\\\-31[/tex]
---------------------------------------------------
c.) [tex](-2)(8)+(-2)(6)+(-2)(-3)\\\\-2*8-2*6-2*-3\\\\-16-2*6-2*-3\\\\-16-12-2*-3\\\\-16-12+6\\\\-28+6\\\\-22[/tex]
---------------------------------------------------
d.) [tex](-2)(8)+(-2)(6+-3)\\\\-2*8-2*(6-3)\\\\-2*8-2*3\\\\-16-2*3\\\\-16-6\\\\-22[/tex]
---------------------------------------------------
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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:
Given,
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Answers
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Step-by-step explanation:
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True.
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Answers
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Answers
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=
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Answers
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Step-by-step explanation:
I am answering blanks left to right and top to bottom.
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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:
A. -5
Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
Step-by-step explanation:
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[tex]h=-16t^2+64t+190[/tex] ...(1)
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Answers
Answer:
−
2
2
=
2
(
−
1
0
)
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−
2
2
=
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−
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Step-by-step explanation:
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Answers
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Answers
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Answers
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