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Setler79 [48]
3 years ago
10

1. How many mL of 70% and 40% alcohol elixirs

Mathematics
1 answer:
denpristay [2]3 years ago
8 0

Answer:

that they are 200 mL of 70% and 100 mL of 40%

Step-by-step explanation:

We have to build a 2x2 system of equations with the information from the statement as follows:

0.70 * x + 0.4 * y = 300 * 0.6

x + y = 300 => x = 300 - y

where x is elixir 1 (70%) and y elixir 2 (40%).

replacing we have:

0.70 * (300 - y) + 0.4 * y = 300 * 0.6

210 * - 0.7 * y + 0.4 * y = 180

-0.3 * y = 180 - 210

y = -30 / -0.3

y = 100

now for x:

x = 300 - 100

x = 200

Which means that they are 200 mL of 70% and 100 mL of 40%

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Consider \arccos(-x)+\arccos(x), where x \in [-1,1].

This means there exists a \theta \in [0, \pi] such that \cos \theta=x and \cos (\pi -\theta)=-\cos \theta=-x.

Thus, taking the inverse cosine of both of these equations, we get that:

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Subtracting arccos(x) from both sides, we get the required result.

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