How much alfalfa does Helmut need to add to 30L of ostrich pellets to make a feed mix that is 40% alfalfa by volume?
1 answer:
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Answer: The required ratio in simplest form is 7 : 5 : 8.
Step-by-step explanation: Given that in a fruit punch drink, the 3 ingredients are apple juice orange juice and cranberry juice. of the drink is apple juice and
is orange juice.
We are to find the ratio of cranberry juice to apple juice to orange juice in its simplest form.
Let x, y and z be the fractions of the cranberry juice, apple juice and orange juice in the fruit punch drink.
Then, according to the given information, we have
Now,
Therefore, the ratio of cranberry juice to apple juice to orange juice is given by
Thus, the required ratio in simplest form is 7 : 5 : 8.
Answer:
98(1 + 2√2) in² ≈ 375 in²
Step-by-step explanation:
Assuming the shaded region is outside of the square and inside of the octagon, we can find the area by subtracting the area of the square from the area of the octagon.
The area of a regular octagon is 2 (1 + √2) s². We can show this by finding the area of the square outside of the octagon, and subtracting the triangles in the corners:
(s + √2 s)² − 4 (½ (½√2 s)²)
(1 + √2)² s² − 4 (½ (s²/2))
(1 + 2√2 + 2) s² − s²
2 (1 +√2) s²
The diagonal of the inner square is equal to the width of the octagon, (1+√2) s. So the side length of the square is:
½√2 (1+√2) s
½(2+√2) s
The area of the square is therefore:
(½(2+√2) s)²
¼(2+√2)² s²
¼(4+4√2+2) s²
¼(6+4√2) s²
½(3+2√2) s²
The area of the shaded region is therefore:
2 (1 +√2) s² − ½(3+2√2) s²
½ s² (4 (1 +√2) − (3+2√2))
½ s² (4 + 4√2 − 3 − 2√2)
½ s² (1 + 2√2)
The side length of the octagon is s = 14 in, so the area is:
½ (14 in)² (1 + 2√2)
= 98(1 + 2√2) in²
≈ 375 in²
