LAST ONE..for now ;) Brian is creating a collage on a piece of cardboard that has an area of 160r4 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of the square root of r to the seventh power square centimeters. Use the given information to determine an expression for the total number of pieces of paper used.

Question

hartnn · Answer

total area:160r^4
area of one piece = $$\sqrt{r^7}$$
so total pieces = $$\frac{160 r^4}{\sqrt{r^7}}$$
can u solve further?

anonymous · Answer

no? im so confused..:(

hartnn · Answer

which step did u not understand? or u confused with simplification??

anonymous · Answer

yea i realy just dont get the whole concept of this..:p so you divide them but like how?

hartnn · Answer

ok, tell me if i have 1 big rectangle with area=100,how many rectangles of area 10 would i fit in??

anonymous · Answer

10

hartnn · Answer

what did u do?? divide,right??
this is the same thing...thats why i divided...

anonymous · Answer

but you have to divide the 160r^4 over Sqrt r^7? 
right?

hartnn · Answer

thats what i did....

anonymous · Answer

i know but like how do you divide it?

hartnn · Answer

now u just need to simplify...
i will give a hint...
$$\sqrt{a}=a^{1/2}$$
and
$$\frac{a^x}{a^y}=a^{x+y}$$
try to solve it...if u can't i will explain afterwards...

anonymous · Answer

explain please ...... :(

hartnn · Answer

okk...
$$\frac{r^4}{\sqrt{r^7}}=r^{4-7/2}=r^{1/2} = \sqrt{r}$$
so final answer is 
$$160 \sqrt{r}$$

anonymous · Answer

um okay..thanks.really lost but yea .i am totally not ready for this complicated stuff in life. good luck becoming a professor :) you'll be great!

hartnn · Answer

thank u :)