What is the circumference of the circle if the radius is:
5x-My answer was 57(x)pi.
What is the radius if the circumference is:
30x(pi)-My answer was 2x.
(x + y)pi -My answer (x+y)/7.
What is the length of the arc if:
radius=3 degree of measurement of arc=6- My answer was pi/9.
radius=4 degree of measurement of arc=7- My answer was 9(pi)/18.
radius=2 degree of measurement of arc=x- My answer was x(pi)/15.
My answers for these questions were incorrect. I am unsure of how to redo them.Cheers!
1. circumf = 2πr
= 2π(5x) = 10πx
2. using the above ...
30xπ = 2πr
r = 30xπ/(2π) = 15x
3. arclength = rØ , where Ø is the central angle in radians
if r=3
if arcangle =6° , then Ø = π/30
(to change ° to radians, multipy your degree unit by π/180) ..... 6(π/180) = π/30
so:
arc = 3(π/30) = π/10
The others in this third part of your post are done the same way
To find the circumference of a circle with a given radius, you can use the formula:
Circumference = 2 * π * radius
1. Given a radius of 5x, the circumference would be:
Circumference = 2 * π * (5x) = 10πx
So your initial answer of 57(x)π is incorrect. The correct answer is 10πx.
To find the radius of a circle with a given circumference, you can rearrange the formula:
Circumference = 2 * π * radius
2. Given a circumference of 30xπ, you can solve for the radius:
30xπ = 2 * π * radius
Divide both sides by 2π:
15x = radius
Therefore, the correct answer is the radius equal to 15x.
3. Given a circumference of (x + y)π, you can solve for the radius:
(x + y)π = 2 * π * radius
Divide both sides by 2π:
(x + y)/2 = radius
Therefore, your initial answer of (x+y)/7 is incorrect. The correct answer is the radius equal to (x + y)/2.
To find the length of an arc on a circle, you can use the formula:
Length of Arc = (degree of measurement of arc / 360°) * 2 * π * radius
4. Given a radius of 3 and degree of measurement of arc equal to 6, the length of the arc would be:
Length of Arc = (6/360) * 2 * π * 3 = π/30
So your initial answer of π/9 is incorrect. The correct answer is π/30.
5. Given a radius of 4 and degree of measurement of arc equal to 7, the length of the arc would be:
Length of Arc = (7/360) * 2 * π * 4 = (28π)/90 = (14π)/45
So your initial answer of 9π/18 is incorrect. The correct answer is (14π)/45.
6. Given a radius of 2 and degree of measurement of arc equal to x, the length of the arc would be:
Length of Arc = (x/360) * 2 * π * 2 = (xπ)/90
So your initial answer of xπ/15 is correct. Well done!
To find the circumference of a circle when given the radius, you can use the formula C = 2πr, where C represents the circumference and r represents the radius.
For the first question, if the radius is 5x - M, you can substitute this value into the formula:
C = 2π(5x - M)
This can be simplified by distributing the 2π term:
C = 10πx - 2πM
Therefore, your answer of 57xπ is incorrect because it should be 10πx - 2πM.
To find the radius when given the circumference, you can rearrange the formula to solve for r:
C = 2πr
Divide both sides by 2π:
r = C / (2π)
Now let's analyze your given answers:
1. 30xπ - Your answer was 2x.
While you correctly recognized that the circumference is 30xπ, your answer of 2x is incorrect. It should be r = (30xπ) / (2π) which simplifies to r = 15x.
2. (x + y)π - Your answer was (x + y) / 7.
Here, you mistakenly divided by 7 instead of 2π. The correct answer is r = (x + y)π / (2π), which simplifies to r = (x + y) / 2.
To find the length of an arc, you can use the formula L = (θ / 360°) * 2πr, where L represents the length of the arc, θ represents the degree of the arc, and r represents the radius.
Let's analyze your given answers:
1. radius = 3, degree of arc = 6 - Your answer was π/9.
To find the length of the arc, you can substitute the given values into the formula:
L = (6 / 360°) * 2π(3)
Calculating this yields L = π/30, which means your answer of π/9 is incorrect.
2. radius = 4, degree of arc = 7 - Your answer was 9π/18.
By substituting the given values into the formula, we have:
L = (7 / 360°) * 2π(4)
Calculating this yields L = 7π/45, so your answer of 9π/18 is incorrect.
3. radius = 2, degree of arc = x - Your answer was xπ/15.
Again, substitute the given values into the formula:
L = (x / 360°) * 2π(2)
This simplifies to L = xπ/90, so your answer of xπ/15 is incorrect.
I hope this clarification helps you revise your answers correctly!