Brian is creating a collage on a piece of cardboard that has an area of 150r2 square centimeters. The collage is covered entirely by pieces of paper that do not overlap. Each piece has an area of radical(r^3) square centimeters. Use the given information to determine an expression for the total number of pieces of paper used. - HELP

Question

amistre64 · Answer

this one?

anonymous · Answer

yeah

amistre64 · Answer

looks like we need to determine how many peices of $\sqrt{r^3}$ can fit into 150r^2

amistre64 · Answer

$$n\sqrt{r^3}=150r^2$$

we can convert a radical to an exponent:$$\sqrt[c]{B^a}=B^{a/c}$$

anonymous · Answer

i don't need the answer just the expression to use

amistre64 · Answer

$$nr^{3/2}=150r^2$$
divide off that r^3/2
$$n\frac{r^{3/2}}{r^{3/2}}=150\frac{r^2}{r^{3/2}}$$
$$n=150\frac{r^2}{r^{3/2}}$$

and then we would have to simplify the right side

amistre64 · Answer

$$\frac{B^t}{B^b}\to \ B^{t-b}$$

amistre64 · Answer

$$n=150\frac{r^2}{r^{3/2}}$$
$$n=150\ r^{2-\frac{3}{2}}$$
$$n=150\ r^{\frac{4}{2}-\frac{3}{2}}$$
$$n=150\ r^{\frac{1}{2}}$$

anonymous · Answer

wait but what does n represent?

amistre64 · Answer

and since division in an exponent expresses a radical we get:

$$n=150 \sqrt{r} $$

amistre64 · Answer

the "n"umber of pieces we are looking to fit into the clooage

amistre64 · Answer

or whatever its called :)

anonymous · Answer

o ok thanks

anonymous · Answer

i have a few more questions so watch for when i post them please

amistre64 · Answer

if im available

anonymous · Answer

o ok