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beks73 [17]
3 years ago
5

Use a factor tree to find the GCF of 32 and 80.

Mathematics
1 answer:
valentinak56 [21]3 years ago
8 0

Answer:

GCF of 32 and 80 is 16

Step-by-step explanation:

factors of 32 = 1, 2, 4, 8, 16, 32

factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

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A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
3 years ago
A tree was 5 feet tall. One year later, the tree was 13 feet tall. Write an equation and use mental math to find how many feet f
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Just minus 5 feet from the new height which is 13ft, and the equation will be 13-5, and therefore the tree grew 8 feet
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3 years ago
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icang [17]

Answer and Step-by-step explanation:

The actual answer is 348.

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1 square with area 36.

Each triangle face is 18 each, so 72.

<u>Add those together and the answer is 348 </u>ft^2<u> :).</u>

<u></u>

<u></u>

<u><em>#teamtrees #PAW (Plant And Water)</em></u>

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The ratio of the angles in a triangle is 3:10:7. what is the measure of the smallest angle?
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So add all of them and then see smallest one sorry if I'm wrong
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4 years ago
Use rounding to estimate 0.93+0.18 plz help me
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0.93 = 0.9
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Answer 1.1
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