Consider the rectangular prism with length 3 cm, width 4 cm, and height of 6 cm. will doubling one of the dimensions of the rectangular prism double the surface area of the prism? justify your answer.

NO

Step-by-step explanation:

Surface area = 2lw+ 2 lh + 2 hw  Where h = height, w= width and l = length

We will double w

SA becomes 2l(2w) + 2lh + 2h(2w)

 SA = 4lw + 2lh + 4lw

Doubling the SA

2SA = 2(2lw+ 2 lh + 2 hw)

        = 4lw + 4lh +4 hw

2SA =? SA for 2w

4lw + 4lh +4 hw =   4lw + 2lh + 4lw

This is not the same

Doubling one dimension does not double the surface area

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

=7

​ 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

=3

​  

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

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

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!

2160ft3

step-by-step explanation: