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3 years ago

Which set of rational numbers is arranged from least to greatest?how can i put this number for least to greatest 0.5,1/5,1/9,1

Mathematics

2 answers:

sattari [20]3 years ago

6 0

i would put all fractions into decimals so you'd have

1/5=0.2

and

1/9=0.1 repeating

so now you can order them

o.1..., 0.2, 0.5, 1

which equals to

1/9, 1/5, 0.5, and 1

so the answer is

1/9, 1/5, 0.5, and 1

hope this helps:)

ivann1987 [24]3 years ago

3 0

1/9 ,1/5 ,0.5 ,1 is the answer

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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

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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 triangular pyramid with a height of 9 inches has a volume of 63 cubic inches. If the height of the triangular base is 6 inches

Bond [772]

Option D: 21 in is the base length of the triangular base.

Explanation:

Given that a triangular pyramid with a height of 9 inches has a volume of 63 cubic inches.

The height of the triangular base is 6 inches.

We need to determine the base length of the triangular pyramid.

The base length of the triangular pyramid can be determined using the formula,

$Volume =\frac{1}{3} \times Bh$

Substituting $Volume=63$ and $Height=9$ in the above formula, we get,

$63 =\frac{1}{3} \times B(9)$

Simplifying the terms, we get,

$63 =3B$

Dividing both sides by 3, we have,

$21=B$

Thus, the base length of the triangular pyramid is 21 in

Hence, Option D is the correct answer.

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