A cooler has 12 apple juices and 15 grape juices. 9 of the apple juices are sugar free and 5 of the grape juices are sugar free.
2 answers:
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Since this is a 30-60-90 triangle, if the side against the 30 degree angle is equal to 2 the one against the 60 degree angle must be equal to 
and the side against the 90 degree angle must be equal to 4. (I will upload a picture, these are rules for right angles)
and the side against the 90 degree angle must be equal to 4. (I will upload a picture, these are rules for right angles)
To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder: 
where
is the volume
is the radius
is the height
We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words:
. We also know that the radius is r cm and height is h cm, so 
and 
. Lets replace the values in our formula:
Next, we are going to use the formula for the area of a cylinder:
where
is the area
is the radius
is the height
We know from our previous calculation that, so lets replace that value in our area formula:
By the commutative property of addition, we can conclude that:
where
We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words:
Next, we are going to use the formula for the area of a cylinder:
where
We know from our previous calculation that
By the commutative property of addition, we can conclude that: