Consider the following two circles.
Segment d1 is a diameter of ⨀A, and segment d2 is a diameter of ⨀B.
Two circles, A and B, with diameters d sub 1 and d sub 2 as described in the problem. Circle B has a larger diameter than circle A.
If d1=1 and d2=2r, and if CB denotes the circumference of ⨀B, which equation is true?
1/2r=2π/CB
1/2r=π/CB
1/2r=CB/2π
1/2r=CB/π
CB = π*d2 = π*2r = 2πr
π/CB = 1/(2r)
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Oh, I see you're in a circular mood! Let's see if we can figure this out together.
Since d1 is the diameter of circle A, we know that the radius of circle A is d1/2, which is 1/2.
Now, let's talk about circle B. We know that d2 is the diameter of circle B, and it's described as 2r. Since the diameter is equal to 2 times the radius, we can say that r equals d2/2, which simplifies to r.
Now, looking at the answer choices:
1/2r = 2π/CB
Well, let's substitute r with d2/2: 1/2(d2/2) = 2π/CB. Simplifying further, we get d2/4 = 2π/CB.
Hmm, that doesn't look like any of the answer choices. Let's check the next one.
1/2r = π/CB
Again, substituting r with d2/2: 1/2(d2/2) = π/CB. Simplifying gives us d2/4 = π/CB.
Hey, that looks a bit closer to one of the answer choices! Let's keep going.
1/2r = CB/2π
Once again, substituting r with d2/2: 1/2(d2/2) = CB/2π. Simplifying, we get d2/4 = CB/2π.
Hmm, not quite there yet. Let's check the last option.
1/2r = CB/π
One more time, substituting r with d2/2: 1/2(d2/2) = CB/π. Simplifying, we find d2/4 = CB/π.
Yes! That looks like a match to the second answer choice, 1/2r = π/CB.
So, the correct equation is 1/2r = π/CB.
I hope I didn't go around in circles too much with my explanation!
To find the correct equation, we need to understand the relationship between the diameter and circumference of a circle.
The diameter of a circle is double the length of the radius, so we can write d2 = 2r.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that d1 = 1, which means the radius of circle A is 1/2.
Now, let's look at the equation options:
1/2r = 2π/CB
This equation is incorrect because it is missing the factor of 2 in the numerator. The radius should be multiplied by 2 since the diameter is given, not the radius.
1/2r = π/CB
This equation is incorrect because it doesn't account for the factor of 2 in the numerator. Again, the radius should be multiplied by 2.
1/2r = CB/2π
This equation is incorrect because it has the wrong ordering of terms. The numerator should be CB and the denominator should be 2π.
1/2r = CB/π
This equation is correct. It correctly represents the relationship between the radius and the circumference. Circle B has a diameter of d2, which is 2r, so the radius is r. The equation 1/2r = CB/π correctly states that the radius of B is half of the circumference of B divided by π.
Therefore, the correct equation is 1/2r = CB/π.