Answer: the extraction is 18.2%.
Explanation:
Let's see few definitions:
TDS = Total Dissolved Solids = solids dissolved in the brew
PE = Percent Extraction = percent of solids extracted from the dry coffee grounds
The percent extraction can be calculated by the formula:
PE = TDS × Rm
where
Rm = ratio between the mass of the brew and the mass of dry grounds
Now, you need to consider the following facts:
1) every 1g of coffee absorbs 2g of water
2) the given brew ratio is 1:15, which means that for every 1g of grounds we use 15g of water
Let's call
x = grams of coffee grounds we want to use
Therefore the mass of the brew will be:
m(brew) = water we use - water absorbed by the coffee
= 15·x - 2·x
= 13·x
Therefore,
Rm = m(brew) / x
= 13·x / x
= 13
Hence, the percent of extraction will be:
PE = <span> TDS × Rm
= 1.4 </span>× 13
= 18.2
Answer: 32 paving stones
Step-by-step explanation:
Hi, to answer this question, first we have to convert the measures of the paving stones into meters.
Since: 1m = 100 cm
50 cm /100 = 0.5m
Now, we have to calculate the area of each paving stone:
Area of a square: s^2 = 0.5^2 = 0.25m2
Next, the area of the path.
Area of a rectangle = width x length = 1 x 8 = 8 m2
Finally, we have to divide the area of the path by the area of each paving stone:
8/0.25 = 32 paving stones
Feel free to ask for more if needed or if you did not understand something.
Rather than carrying out IBP several times, let's establish a more general result. Let
One round of IBP, setting
gives
This is called a power-reduction formula. We could try solving for explicitly, but no need. is small enough to just expand as much as we need to.
Finally,
so we end up with
and the antiderivative is