Question 314081: 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.If you could, please explain to me how you worked the answers out so that I may understand fully. I would be grateful for assistance. Cheers!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! First problem is:
What is the circumference of the circle if the radius is:
5x-My answer was 57(x)pi.
The formula for the cicumference of a circle is C = 2 * pi * r
If the radius is equal to 5 * x, then the circumference of the circle is C = 2 * pi * 5 * x which becomes C = 10 * pi * x
That's your answer.
To confirm:
C = 2 * pi * r becomes 10 * pi * x = 2 * pi * r.
Divide both sides of this equation by 2 I pi to get 5 * x = r which is the same as r = 5 * x which is the radius you started with.
Second question is:
What is the radius if the circumference is:
30x(pi)-My answer was 2x.
The formula for the circumference of a circle is C = 2 * pi * r
Since C = 30 * x * pi, this formula becomes:
30 * x * pi = 2 * pi * r
Divide both side of this equation by 2 * pi to get:
r = 15 * x
that's your answer.
To confirm:
Since C = 2 * pi * r, this means that C = 2 * pi * 15 * x which simplifies to C = 30 * pi * x which is the circumference you started with.
Third question is:
What is the radius if the circumference is:
(x + y)pi -My answer (x+y)/7.
C = 2 * pi * r
Since C = (x + y) * pi, then this equation becomes:
(x + y) * pi = 2 * pi * r
Divide both sides of this equation by pi to get:
(x + y) = 2 * r
Divide both sides of this equation by 2 to get:
r = (x+y)/2
That's your answer.
To confirm:
Since C = 2 * pi * r, this equation becomes C = 2 * pi * (x+y)/2 which simplifies to C = pi * (x+y) which is the circumference you started with.
Fourth question is:
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.
The formula for the length of the arc is given by L = D/360 * C where L is the length of the arc and D is the degree of the arc and C is the circumference of the circle.
Since the circumference of a circle is equal to 2 * pi * r, then the equation of L = D/360 * C can be made equivalent to:
L = D/360 * 2 * pi * r
You now have all the information you need to solve these problems.
First problem is:
radius = 3 degree of measurement of arc = 6 - My answer was pi/9.
Formula becomes L = 6/360 * 2 * pi * 3 which simplifies to:
L = 1/60 * 6 * pi which simplifies further to:
L = 6/60 * pi which simplifies further to:
L = 1/10 * pi.
Second problem is:
radius = 4 degree of measurement of arc = 7 - My answer was 9(pi)/18.
Formula is L = D/360 * 2 * pi * r which becomes:
L = 7/360 * 2 * pi * 4 which simplifies to:
L = 56/360 * pi which is equivalent to:
L = (7 * 8) / (45 * 8) * pi which simplifies to:
L = 7/45 * pi
Third problem is:
radius = 2 degree of measurement of arc = x - My answer was x(pi)/15.
Formula to use is L = D/360 * 2 * pi * r
This formula becomes:
L = x/360 * 2 * pi * 2 which simplifies to:
L = x/360 * 4 * pi which simplifies further to:
L = x/90 * pi
The key to solving these problem is to know that:
C = 2 * pi * r
L = D/360 * C
C = circumference of the circle.
r = radius of the circle
D = degree of the arc
L = length of the arc.
All of the problems you had were applications of these formulas.
Go through the problems again to see where you went wrong.
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