Darius uses 6 2/3 cup of bread cubes to make a batch of stuffing for his family. How many cups of bread cubes will he need to ma
1 answer:
Answer:
Darius needs cups of bread cubes to make four batches of stuffing for a family reunion.
Step-by-step explanation:
Given:
bread cubes to make a batch of stuffing = 6 2/3 cup
To Find:
Number of cups of bread cubes needed to make four batches of stuffing for a family reunion = ?
Solution:
According to the question, to make one batch of stuffing Darius needs cups of bread cubes
So if he wants to make four batched, then the number of cups of bread cubes will be four times as needed for making one batch
Then
Number of cups of bread cubes needed to make four batches = 4 x bread cubes needed to make a batch of stuffing
Number of cups of bread cubes needed to make four batches
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Answer:
½
Step-by-step explanation:
Draw a picture of the triangle with the rectangle inside it.
Let's say the width and height of the triangle are w and h (these are constants).
Let's say the width and height of the rectangle are x and y (these are variables).
The area of the triangle is ½ wh.
The area of the rectangle is xy.
Using similar triangles, we can say:
(h − y) / h = x / w
x = (w/h) (h − y)
So the rectangle's area in terms of only y is:
A = (w/h) (h − y) y
A = (w/h) (hy − y²)
We want to maximize this, so find dA/dy and set to 0:
dA/dy = (w/h) (h − 2y)
0 = (w/h) (h − 2y)
0 = h − 2y
y = h/2
So the width of the rectangle is:
x = (w/h) (h − y)
x = (w/h) (h − h/2)
x = (w/h) (h/2)
x = w/2
That means the area of the rectangle is:
A = xy
A = ¼ wh
The ratio between the rectangle's area and the triangle's area is:
(¼ wh) / (½ wh)
½
So no matter what the dimensions of the triangle are, the maximum rectangle will always be ½ its area.
Answer:
Step-by-step explanation:
The formula for continuous compounding is
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