Mathematics, 15.12.2019 04:31 Mlmyers81

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volume and surface area are often compared by manufacturers in order to maximize how much of something can go inside of a package (volume) while keeping how much material is required to create the package (surface area) low. pick a product that might be packaged in the shape of a rectangular prism. a rectangular prism has three dimensions: length, width, and height. the surface area of a rectangular prism can be found using the formula sa = 2lw + 2wh + 2lh. the volume of a rectangular prism can be found using the formula v = lwh. write an expression for the ratio of surface area to volume for the figure. choose an appropriate length, width, and height for your package so that it can fit the product you are shipping. using these dimensions, what is the ratio of surface area to volume?

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l = length

w = width

h = height

SA = 2lw + 2wh + 2lh.

V = lwh.

Write an expression for the ratio of surface area to volume:

SA / V = [ 2lw + 2wh + 2lh] / lwh

SA / V = 2lw / lwh + 2wh / lwh + 2lh / lwh

SA / V = 2/h + 2/l + 2/w

Choose an appropriate length, width, and height for your package so that it can fit the product you are shipping. Using these dimensions, what is the ratio of surface area to volume?

I will work with an hypothetical figure where you have , l, w and the volume.

I suppose you know the volume, because it is the amount of product you need to pack. Make V = 1000 cm^3, l = 10 cm and w = 5 cm.

Wtih two dimensions and the volumen you can find the other dimension.

V = lwh = 1000 cm^3 => h = 1000 cm^3 / (lw) = 1000 cm^3 / (10 cm * 5 cm)

h = 1000 cm^3 / (50 cm^2) = 20 cm

Now you have the three dimensions to pack 1000 cm^3 of your product:

l = 10 cm
w = 5 cm
h = 20 cm

And the ratio of surface area to volume is:

SA / V = 2/h + 2/l + 2/w = 2/(20cm) + 2/(10cm) + 2/(5cm) = 0,7 (cm)^-1

Answer from: Quest

50.6

step-by-step explanation:

Answer from: Quest

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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