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jarptica [38.1K]
4 years ago
15

Please help me!

Mathematics
1 answer:
Virty [35]4 years ago
6 0

Answer:

 2\frac{1}{2} cups

Step-by-step explanation:

Given, a recipe uses 8\frac{3}{4} cups of milk for every 3\frac{1}{2} cups of oatmeal.

So, For each 8.75 cups of milk ,3.5 cups of oatmeal is required.

Or,

we can say 3.5 cups of oatmeal require 8.75 cups of milk.

Thus,

1 Cup of oatmeal will require  \frac{8.75}{3.5} cups of milk.

                                              =   2.5 cups of milk .

Thus answer is 2.5 cups, Which we can write 2 + 0.5 cups

                                                                      =  2\frac{1}{2} cups (In mixed form)

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  • width: 24 cm
  • height: 36 cm

Step-by-step explanation:

When margins are involved, the smallest area will be the one that has its dimensions in the same proportion as the margins. If x is the "multiplier", the dimensions of the printed area are ...

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_____

<em>Comment on margins</em>

It should be obvious that if both side margins are 4 cm, then the width of the poster is 8 cm more than the printed width. Similarly, the 6 cm top and bottom margins make the height of the poster 12 cm more than the height of the printed area.

_____

<em>Alternate solution</em>

Let w represent the width of the printed area. Then the printed height is 384/w, and the total poster area is ...

  A = (w+8)(384/w +12) = 384 +12w +3072/w +96

Differentiating with respect to w gives ...

  A' = 12 -3072/w^2

Setting this to zero and solving for w gives ...

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__

<em>Generic solution</em>

If we let s and t represent the side and top margins, and we use "a" for the printed area, then the above equation becomes the symbolic equation ...

  A = (w +s)(a/w +t)

  A' = t - sa/w^2

For A' = 0, ...

  w = √(sa/t)

and the height is ...

  a/w = a/√(sa/t) = √(ta/s)

Then the ratio of width to height is ...

  w/(a/w) = w^2/a = (sa/t)/a

  width/height = s/t . . . . . . the premise we started with, above

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3 years ago
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