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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Related Questions
A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the station together?
Answers
Answer:
7:12 a.m
Step-by-step explanation:
Given that:
Train to New York city leaves station every 7 minutes
Train to Boston leaves station every 6 minutes
Current time = 6:30 a.m
Time both will leave station together is obtained by finding the least common multiple of 6 and 7
Multiples of ;
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...
7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...
The least common multiple of 6 and 7 is 42.
Hence, both trains will leave the station together after 42 minutes ;
Current time + 42 minutes
6:30 a.m+ 42 minutes = 7:12 a.m
evaluate [tex]2^{x}[/tex] for (a) x=-2 and (b) x=3. write your answer in simplest form
Answers
Will give brainliest
Answers
Answer:
Y= -1/3x + 8/3
Step-by-step explanation:
Expert Answer! Determine if the two triangles are congruent.
Answers
Answer:
SAS
Step-by-step explanation:
We have 2 sides that are congruent and the angle between them
We can use SAS ( side angle side) to prove congruency
help plz or my teacher will give me a zero
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
∵ 5 pounds of cashews and 8 pounds of peanuts cost $26.27
∴ 5x + 8y = 26.27 ⇒ (1)
∵ 7 pounds of cashews and 4 pounds of peanuts cost $23.89
∴ 7x + 4y = 23.89 ⇒ (2)
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)
∴ -14x - 8y = -47.78 ⇒ (3)
→ Add equations (1) and (3) to eliminate y
∵ (5x + -14x) + (8y + - 8y) = (26.27 + -47.78)
∴ -9x = -21.51
→ Divide both sides by -9 to find x
∴ x = 2.39
→ Substitute x in equation (1) or (2) to find y
∵ 5(2.39) + 8y = 26.27
∴ 11.95 + 8y = 26.27
→ Subtract 11.95 from both sides
∴ 8y = 14.32
→ Divide both sides by 8 to find y
∴ y = 1.79
∴ The price of 1 pound of cashews is $2.39
∴ The price of 1 pound of peanuts is $1.79
what is 22)572 please someone come help me
Answers
Answer:
0.03846153846
Step-by-step explanation:
Answer: 1/26 or 0.0384615
Step-by-step explanation: You Have To Figure Out How Many Times 22 can go into 57 The Answer is 2 leaving 13 bring down the 2 it makes 132 22 times 6 = 132 so the answer is 1/26.
What survival rate in the 10th year would make the average
rate of loss over the 10-year period equal to 38.0%?
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]
The rate of survival differs from the rate of loss, meaning the rate of survival were:
[tex]= 1 - loss\ rate \\\\= 1 - 37\% \\\\= 1 - \frac{37}{100} \\\\= \frac{100-37}{100} \\\\= \frac{63}{100} \\\\=63 \%[/tex]
A sporting goods store received a shipment of 500 baseball gloves. 200 were left handed. What is the ratio of right handed gloves to gloves?
WILL RECIEVE BRAINLIST
Answers
Answer:
300:500
Step-by-step explanation:
If there are 200 left handed gloves, then there are 300 right handed gloves.
The total amount of gloves is 500, so its 300:500.
Simply the expression 7y+4x+4-2x+8
Answers
help please !!!!!!!!!!!!!!
Answers
Answer:
two of the points are (0,5) and (2.5,0)
Answer:
Place one dot at y = 5 x = 0. This represents the y intercept or the "5" in the equation.
Then place dots at:
(-3,10)
(-2,9)
(-1,7)
(1,3)
(2,1)
(3,-1)
(4,-3)
(5, -5)
(6, -7)
(7, -9)
The slope is -2x which makes the line slope downward, and the points above are the points on the line. Starting at the y intercept we can use the rise over run method to plot the points.
I hope this helps!!
- Kay :)
find the value of x
Answers
Answer:
79 degrees
Step-by-step explanation:
Quadrilaterals have a total of 360 degrees. They already gave you three of them so you just have to add all the given degrees and subtract it by 360. 101+124+56=281 ; 360-281=79
The sum of 4 consecutive even numbers is 364 A. 91 B. 65 C. 89.5 D. 182
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,
⇒ (x - 2), x, (x + 2), (x + 4)
So, We can formulate;
⇒ (x - 2) + x + (x + 2) + (x + 4) = 364
Solve for x;
⇒ 4x + 4 = 364
⇒ 4x = 364 - 4
⇒ 4x = 360
⇒ x = 90
Hence, The two middle numbers are,
⇒ (x) = 90
⇒ (x + 2) = 90 + 2
= 92
So, Sum of two middle numbers = 90 + 92
= 182
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?
FREE BRAINLIEST ! Find the slope of the line that passes through:
(-3, -4) and (7, 6)
Answers
Answer:
10/10 =1 / 1 =1
m = ^^
Step-by-step explanation:
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.
So, the fraction of the yellow fabric used to make toys for her 7 dogs is
[tex]1-\dfrac{2}{3}=\dfrac{1}{3}[/tex]
The amount of fabric to make the 7 toys is
[tex]\dfrac{1}{3}\times 3.5=1.17\ \text{yards}[/tex]
Assuming that equal amount of fabric was used for 1 toy for 7 of her dogs each.
The amount of fabric used for 1 dog's toy is
[tex]\dfrac{1}{7}\times 1.17=0.17\ \text{yards}[/tex]
The amount of fabric used to make each banana is [tex]0.17\ \text{yards}[/tex].
Given a scale factor of 2, find the coordinates for the dilation of the line segment with endpoints left parenthesis negative 1 comma 2 right parenthesis and left parenthesis 3 comma negative 3 right parenthesis.
A.(2,4) and (6,6)
B. (-2,2) and(6,-3)
C. (-2,4) and (6,-6)
D. (2,-1) and (-3,3
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Answer:
i think its answer is option A
Listen Rachel babysat three children for five hours if they were paid $2.50 per hour for each child and divided their earnings equally how much did each girl receive
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
Payment for 5 hours per child = [tex]5\times\$2.50=\$12.5[/tex]
Payment to 3 children for 5 hours = [tex]3\times \$12.5=\$37.5[/tex]
So, the amount received by each girl = [tex]\dfrac{\text{Payment to 3 children for 5 hours}}{2}[/tex]
[tex]=\dfrac{37.5}{2}=\$18.75[/tex]
Hence, each girl will receive $18.75.
Z is..? The problem is attached as a png!
Answers
Answer:
Step-by-step explanation:
What i would do is multiply both sides by 2z + 1
so you get z-6=20z+10
-19z=16
z=-16/19
Answer:
z is every integer and the study of z and its properties is a general understanding save the satisfying of your rate of change
To convert 564 kL to mL, you move the decimal point _____ places to the _____. i need help ASAP please!
Answers
Answer:
6 places to the right....
A standard container measures 2.4 m by 2.4 m by 6 m.
Multiply the dimensions to work out its volume.
Answers
Answer:
34.56
Step-by-step explanation:
Find f(3) f(x)=x+2/x
A) -1/3
B)1/3
C)5/3
D)-5/3
Answers
Work Shown:
f(x) = (x+2)/x
f(-3) = (-3+2)/(-3) .... replace every x with -3
f(-3) = -1/(-3)
f(-3) = 1/3
* Ms. Quintero has visited 16 of the 50 states. What percent of the states has she visited? KEY Part (is) Whole(of) % 100 Whole
A.25%
B.32%
C.16%
D.8%
Answers
Answer:
B. 32%
Step-by-step explanation:
16/50 = 32% lol
goodluck!
Andrew has $15 less in his piggy bank than his friend Tom. Write an algebraic expression that represents the amount of money that Andrew has in his piggy bank.
Answers
Answer:
I think the answer is is X-15
23 more than twice a number
Answers
Answer:
2x +23
Step-by-step explanation:
Let the required number be x
Twice of number = 2x
23 more than twice a number = 2x + 23
Answer:
2x + 23
Step-by-step explanation:
Let x be the number
Twice a number = 2x23 more than twice a number = 2x + 23I hope this helps!
Help with this question please ~
Answers
Answer:
60°
Step-by-step explanation:
We can get the other two angles in the top triangle because they are alternate interior. Then we subtract them from 180.
180-82-38=60
cuales son las soluciones (o raices) de la ecuacion x^2 + 6x - 16 = 0?
Answers
Answer:
x = 2,-8
Step-by-step explanation:
5. Two-fifths of a number is -26. Find the number.
Answers
Answer:
x = -65
Step-by-step explanation:
To start off, we can create our equation. We know that "of" is just another word for multiply. We will then end up with [tex]\frac{2}{5}[/tex] * x = -26. To solve this equation, we will find [tex]\frac{2}{5}[/tex] of -26. To make things less confusing, lets take away the negative for now. 26 x 5 = 130 and 130 ÷ 2 is 65. We then add our negative back on and x = -65.
Jason is flying a kite and has 325 feet of kite string out. The angle of elevation between Jason’s hand and the kite string is 58˚. Jason’s hand is 3 feet above the ground. How high is the kite to the nearest tenth?
i need this asap pls
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
The angle of elevation of the kite string, θ = 58°
The height of Jason's hand, h = 3 feet above the ground
Therefore, we have;
The height of the kite = The vertical component of the length of the kite string + The height of Jason's hand above the ground
The height of the kite = l × sin(θ) + h
Substituting the values, we get
The height of the kite = 325 × sin(58°) + 3 ≈ 278.6 (which is obtained by rounding the answer to the nearest tenth)
The height of the kite ≈ 278.6 feet.
find the points of D(-3,-1), E(-1,2), F(4,-2) after a rotation 180° about the origin ASAP PLEASE ILL GIVE BRAINLIEST
Answers
Answer:
Step-by-step explanation:
D = 3,1
E = 1,-2
F= -4,2
Find the circumference of the circle, round to the nearest tenth. Answer: H
Answers
Answer:
H
Step-by-step explanation:
What is the length of a segment with endpoints at (-3,4) and (4,4)
Answers
Answer:
The length is 8
Step-by-step explanation: