1 and 47, because 47 is a prime number.
To solve this, we are going to use the formula for the area of the sector of a circle:
where
is the area of the circular sector.
is the radius of the circle.
is the central angle in radians.
We know form our problem that that the measure of the central angle is 1 radian, so
. We can also infer from the picture that the radius of the circle is 3in, so
. Lets replace those values in our formula to find
:
We can conclude that the area of the circular sector in the picture is
4.5 square inches.
To prove that the arc length is indeed 3 inches, we are going to use the formula:
where
is the arc length.
us the radius of the circle.
is the central angle.
We know from our problem that
, and
, so lets replace those values in our formula:
We can conclude that the length of the arc is indeed
3 inches.
4 is bigger than n, so either the second or fourth one
Answer:
24
Step-by-step explanation:
Jayla has a couple of options for cutting her original piece of paper.
- she can cut the 3 inch length from the long dimension of the paper, giving her 5 strips from the length and 4 strips from the width for a total of 20 3×2 pieces
- she can cut the 3 inch length from the short dimension of the paper, giving her 3 strips from the 9-inch width, and 8 strips from the 16-inch length, for a total of 3×8 = 24 pieces.
The greatest number of 3×2 pieces Jayla can cut is 24.
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The attachments show the different cuts as described above.