Answer:
The chance of him pulling out another blue marble is 6/10 or 3/5
Step-by-step explanation:
Answer:
![BC=11\ cm](https://tex.z-dn.net/?f=BC%3D11%5C%20cm)
Step-by-step explanation:
step 1
Find the measure of the arc DC
we know that
The inscribed angle measures half of the arc comprising
![m\angle DBC=\frac{1}{2}[arc\ DC]](https://tex.z-dn.net/?f=m%5Cangle%20DBC%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20DC%5D)
substitute the values
![60\°=\frac{1}{2}[arc\ DC]](https://tex.z-dn.net/?f=60%5C%C2%B0%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20DC%5D)
![120\°=arc\ DC](https://tex.z-dn.net/?f=120%5C%C2%B0%3Darc%5C%20DC)
![arc\ DC=120\°](https://tex.z-dn.net/?f=arc%5C%20DC%3D120%5C%C2%B0)
step 2
Find the measure of arc BC
we know that
----> because the diameter BD divide the circle into two equal parts
step 3
Find the measure of angle BDC
we know that
The inscribed angle measures half of the arc comprising
![m\angle BDC=\frac{1}{2}[arc\ BC]](https://tex.z-dn.net/?f=m%5Cangle%20BDC%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20BC%5D)
substitute the values
![m\angle BDC=\frac{1}{2}[60\°]](https://tex.z-dn.net/?f=m%5Cangle%20BDC%3D%5Cfrac%7B1%7D%7B2%7D%5B60%5C%C2%B0%5D)
![m\angle BDC=30\°](https://tex.z-dn.net/?f=m%5Cangle%20BDC%3D30%5C%C2%B0)
therefore
The triangle DBC is a right triangle ---> 60°-30°-90°
step 4
Find the measure of BC
we know that
In the right triangle DBC
![sin(\angle BDC)=BC/BD](https://tex.z-dn.net/?f=sin%28%5Cangle%20BDC%29%3DBC%2FBD)
![BC=(BD)sin(\angle BDC)](https://tex.z-dn.net/?f=BC%3D%28BD%29sin%28%5Cangle%20BDC%29)
substitute the values
![BC=(22)sin(30\°)=11\ cm](https://tex.z-dn.net/?f=BC%3D%2822%29sin%2830%5C%C2%B0%29%3D11%5C%20cm)
Answer:
B of course you dummy
Step-by-step explanation:
You need a graph to go with it
Answer:
1,2 and 4 are conservatives
3 is not conservative
Step-by-step explanation:
We calculate the Curl F
Remember that:
Curl F = <
>
1. Curl F = <0,0,5-5> = <0,0,0>
The potential function f so that ∇f=F
f(x,y,z) = ![-3x^{2} +5xy + 5y^{2}](https://tex.z-dn.net/?f=-3x%5E%7B2%7D%20%2B5xy%20%2B%205y%5E%7B2%7D)
Then F is conservative
2. Curl F = < 0, 0 ,0>
The potential function f so that ∇f=F
f(x,y,z) = ![-3/2x^{2} -y^{2}+z](https://tex.z-dn.net/?f=-3%2F2x%5E%7B2%7D%20-y%5E%7B2%7D%2Bz)
Then F is conservative
3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>
= <0 ,0 , 10 +3xsin(y) + cos(y)<
How the field's divergence is not zero the vector field is not conservative
4. Curl F = <0, 0, 0>
The potential function f so that ∇f=F
f(x,y,z) =
Then F is conservative