Question 314081
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.