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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What survival rate in the 10th year would make the average
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Answers
Answer:
The answer is "63%"
Step-by-step explanation:
please find the complete question in the attached file.
Time= 10 year =38.0%
let,
x=rate
[tex]\to 38 = \frac{(36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x)}{10}[/tex]
[tex]\to 38 = \frac{(343 + x )}{10}\\\\\to 380 = (343 + x )\\\\\to 380 - 343 = x \\\\\to x= 37\%[/tex]
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[tex]= 1 - loss\ rate \\\\= 1 - 37\% \\\\= 1 - \frac{37}{100} \\\\= \frac{100-37}{100} \\\\= \frac{63}{100} \\\\=63 \%[/tex]
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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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Mrs. Purple bought 3.5 yards of yellow fabric. She used ⅔ of the fabric to make a chicken costume. Then she used the remaining fabric to make plush banana toys for her seven dogs. How much fabric was used to make each banana?
Answers
Answer:
[tex]0.17\ \text{yards}[/tex]
Step-by-step explanation:
Total length of yellow fabric = 3.5 yards
[tex]\dfrac{2}{3}[/tex] of the yellow fabric was made to make a chicken costume.
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Answers
Answer:
Variable x = $2.39 ⇒ price of 1 pound of cashews
Variable y = $1.79 ⇒ price of 1 pound of peanuts
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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∵ 7 pounds of cashews and 4 pounds of peanuts cost $23.89
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Now we have a system of equations to solve it
→ Multiply equation (2) by -2 to make the coefficients of y equal
in values and different in signs
∵ -2(7x) + -2(4y) = -2(23.89)
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→ Add equations (1) and (3) to eliminate y
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→ Subtract 11.95 from both sides
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→ Divide both sides by 8 to find y
∴ y = 1.79
∴ The price of 1 pound of cashews is $2.39
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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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Answers
Answer:
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Step-by-step explanation:
Given that:
Train to New York city leaves station every 7 minutes
Train to Boston leaves station every 6 minutes
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Answer:
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Answers
Answer:
The height of the kite is approximately 278.6 feet
Step-by-step explanation:
The length of Jason's Kite string, l = 325 feet
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Answer:
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Answer:
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Then place dots at:
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(2,1)
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(6, -7)
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Answers
Answer:
91
Step-by-step explanation:
Sum of the middle two numbers is ''182'' for 4 consecutive even number.
What is Addition?The process of combining or adding two or more numbers is called the Addition.
We have to given that;
Sum of 4 consecutive even numbers = 364
Let 4 consecutive even numbers are,
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So, We can formulate;
⇒ (x - 2) + x + (x + 2) + (x + 4) = 364
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Learn more about the addition visit:
https://brainly.com/question/5454147
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The complete question is this,
The sum of 4 consecutive even numbers is 364. What is the sum of the middle two numbers?
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Answers
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Step-by-step explanation:
If there are 200 left handed gloves, then there are 300 right handed gloves.
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Step-by-step explanation:
Let the required number be x
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Step-by-step explanation:
Let x be the number
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Step-by-step explanation:
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