What is the radius if:
degree of measurement of arc=30
length=1/3xy(pi)
My answer was 8xy.
degree of measurement of arc=40
length=8/9(t)(pi)
My answer was 9t.
degree of measurement of arc=18
length=6(y)pi
My answer was 45y.
These are the questions I missed, along with my answers. I would be grateful if someone could explain what I did wrong and work out the problem, so that I may understand it fully. Cheers!
These questions use the same formula
arc = rØ as we saw in the third part of your previous post.
I will do the first one:
r = ?
Ø = 40(π/180) = 2π/9 radians
arc = (8/9)tπ
r(2π/9) = (8/9)tπ
r = 4t
do the others the same way
To find the radius in these problems, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the length of the arc and r is the radius.
Let's go through each problem and explain how to find the correct radius:
1. Degree of measurement of arc = 30, length = (1/3)xyπ
To find the radius, we need to rearrange the formula for the circumference: C = 2πr.
Divide both sides of the equation by 2π to isolate r: r = C / (2π).
In this case, the length of the arc is given as (1/3)xyπ, so we substitute it into the formula: r = [(1/3)xyπ] / (2π).
Now simplify the expression: r = (1/3)xy / 2.
Your answer of 8xy is incorrect. You made a mistake in simplifying the expression. To simplify it correctly, we need to multiply 1/3 by xy and divide the result by 2. So the correct answer is r = (1/6)xy.
2. Degree of measurement of arc = 40, length = (8/9)tπ
Following the same steps as in the previous problem, we rearrange the formula for the circumference: C = 2πr.
Divide both sides of the equation by 2π to isolate r: r = C / (2π).
Substitute the length of the arc, (8/9)tπ, into the formula: r = [(8/9)tπ] / (2π).
Now simplify the expression: r = (8/9)t / 2.
Your answer of 9t is incorrect. Similar to the previous problem, you made a mistake in simplifying the expression. To simplify it correctly, we need to multiply 8/9 by t and divide the result by 2. So the correct answer is r = (4/9)t.
3. Degree of measurement of arc = 18, length = 6yπ
Again, rearrange the formula for the circumference: C = 2πr.
Divide both sides of the equation by 2π to isolate r: r = C / (2π).
Substitute the given length of the arc, 6yπ, into the formula: r = (6yπ) / (2π).
Now simplify the expression: r = 6y / 2.
Your answer of 45y is incorrect. As in the previous two problems, you made a mistake in simplifying the expression. To simplify it correctly, we need to divide 6y by 2. So the correct answer is r = 3y.
Remember to carefully simplify expressions and double-check your calculations to get the correct answers!