The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount by pi and then multiply that by 4. This is written algebraically as S=4πr2, where S is the surface area, r is the radius, and the value of π is 3.14.

7 0

3 years ago

Which property is illustrated by the statement 6x4=4x6

pantera1 [17]

Answer:

commutative property of multiplication

8 0

2 years ago

It has been estimated that the population of Indianapolis is growing at a rate of 0.9% per year. Assuming that population growth

Mumz [18]

Answer:

2,136,605

Step-by-step explanation:

To estimate growth, we use the formula shown below:

$F=P(1+r)^t$

Where

F is the future amount (we want to find for Jan 2024)

P is the present amount (present population of 1,988,817)

r is the rate of growth (0.9% means 0.009)

t is the time in years (from Jan 2016 to Jan 2024 is 8 years, t = 8)

Let's put these into the formula and figure out F:

$F=P(1+r)^t\\F=1,988,817(1+0.009)^8\\F=2,136,604.5$

Rounding we get the population in Jan 2024 to be 2,136,605

3 0

3 years ago

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

2 years ago