Answer:
64/3 tablespoons of sugar for 32 ounces of water
Step-by-step explanation:
In these kinds of questions it is nice to find how muc of 1 thing there is for every ONE of another. so 8 tablespoons of sugar for 12 ouncesof water you can divide both sides by 8 or 12.
Dividing it by 8 gets 8/8 = 1 tablespoon of sugar for 12/8 = 1.5 ounces of water.
Dividing by 12 gets 8/12 = 2/3 tablespoon of sugar for 12/12 = 1 ounce of water.
Now you can take one or the other and multiply it to fit whichever you want to fit a ratio.
It asks what happens if you use 32 ounces of water, so lets use the ratio where we hae 1 ounce, then multiply everything by 32.
2/3 tablespoon of sugar for 1 ounce of water
Multiply by 32 and you get 32*(2/3) = 64/3 tablespoons of sugar for 32 ounces of water
Answer:
d. 8 units
Step-by-step explanation:
If AC = 16 units then the length of CB is 8 units because DB is perpendicular bisector from the centre of circle.
Answer:
![\cos (a-b)=\cos a \cos b+\sin a \sin b](https://tex.z-dn.net/?f=%5Ccos%20%28a-b%29%3D%5Ccos%20a%20%5Ccos%20b%2B%5Csin%20a%20%5Csin%20b)
Step-by-step explanation:
Given : ![\cos (180^{\circ}-q)=-\cos q](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-%5Ccos%20q)
We have to write which identity we will use to prove the given statement.
Consider ![\cos (180^{\circ}-q)=-\cos q](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-%5Ccos%20q)
Take left hand side of given expression ![\cos (180^{\circ}-q)](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29)
We know
![\cos (a-b)=\cos a \cos b+\sin a \sin b](https://tex.z-dn.net/?f=%5Ccos%20%28a-b%29%3D%5Ccos%20a%20%5Ccos%20b%2B%5Csin%20a%20%5Csin%20b)
Comparing , we get, a= 180° and b = q
Substitute , we get,
![\cos (180^{\circ}-q)=\cos 180^{\circ} \cos (q)+\sin q \sin 180^{\circ}](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D%5Ccos%20180%5E%7B%5Ccirc%7D%20%20%5Ccos%20%28q%29%2B%5Csin%20q%20%5Csin%20180%5E%7B%5Ccirc%7D)
Also, we know
and ![\cos 180^{\circ}=-1](https://tex.z-dn.net/?f=%5Ccos%20180%5E%7B%5Ccirc%7D%3D-1)
Substitute, we get,
![\cos (180^{\circ}-q)=-1\cdot \cos (q)+\sin q \cdot 0](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-1%5Ccdot%20%5Ccos%20%28q%29%2B%5Csin%20q%20%5Ccdot%200)
Simplify , we get,
![\cos (180^{\circ}-q)=-\cos (q)](https://tex.z-dn.net/?f=%5Ccos%20%28180%5E%7B%5Ccirc%7D-q%29%3D-%5Ccos%20%28q%29)
Hence, use difference identity to prove the given result.