Answer:
2nd dot
Step-by-step explanation:
Answer:
b = 252 in
Step-by-step explanation:
cos theta = adjacent side over hypotenuse
cos 38 = b/ 320
Multiply each side by 320
320 cos 38= b/320 * 320
320 cos 38 = b
252.1634412 =b
To the nearest whole number
252 =b
It is 15 / 1000 in the fraction form.
Hello!
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Prudence would get (as an estimation or prediction,) 4 silver earrings and 2 gold.
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WORK: 8+16=24
8/24=0.3333333
16/24=0.6666667
4/6=0.6666667
2/6=0.33333333
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Hope this helps and have a great day!
To solve this, we are going to use the formula for the area of the sector of a circle:
![A= \frac{1}{2} r^2 \alpha](https://tex.z-dn.net/?f=A%3D%20%5Cfrac%7B1%7D%7B2%7D%20r%5E2%20%5Calpha%20)
where
![A](https://tex.z-dn.net/?f=A)
is the area of the circular sector.
![r](https://tex.z-dn.net/?f=r)
is the radius of the circle.
![\alpha](https://tex.z-dn.net/?f=%20%5Calpha%20)
is the central angle in radians.
We know form our problem that that the measure of the central angle is 1 radian, so
![\alpha =1](https://tex.z-dn.net/?f=%20%5Calpha%20%3D1)
. We can also infer from the picture that the radius of the circle is 3in, so
![r=3in](https://tex.z-dn.net/?f=r%3D3in)
. Lets replace those values in our formula to find
![A](https://tex.z-dn.net/?f=A)
:
![A= \frac{1}{2} r^2 \alpha](https://tex.z-dn.net/?f=A%3D%20%5Cfrac%7B1%7D%7B2%7D%20r%5E2%20%5Calpha%20)
![A= \frac{1}{2} (3in)^2(1)](https://tex.z-dn.net/?f=A%3D%20%5Cfrac%7B1%7D%7B2%7D%20%283in%29%5E2%281%29)
![A=4.5in^2](https://tex.z-dn.net/?f=A%3D4.5in%5E2)
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:
![A_{L}=r \alpha](https://tex.z-dn.net/?f=A_%7BL%7D%3Dr%20%5Calpha%20)
where
![A_{L}](https://tex.z-dn.net/?f=A_%7BL%7D)
is the arc length.
![r](https://tex.z-dn.net/?f=r)
us the radius of the circle.
![\alpha](https://tex.z-dn.net/?f=%20%5Calpha%20)
is the central angle.
We know from our problem that
![r=3in](https://tex.z-dn.net/?f=r%3D3in)
, and
![\alpha =1](https://tex.z-dn.net/?f=%20%5Calpha%20%3D1)
, so lets replace those values in our formula:
![A_{L}=r \alpha](https://tex.z-dn.net/?f=A_%7BL%7D%3Dr%20%5Calpha%20)
![A_{L}=(3in) \alpha](https://tex.z-dn.net/?f=A_%7BL%7D%3D%283in%29%20%5Calpha%20)
![A_{L}=3in](https://tex.z-dn.net/?f=A_%7BL%7D%3D3in%20)
We can conclude that the length of the arc is indeed
3 inches.