OpenStudy (anonymous):

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

5 years ago
OpenStudy (amistre64):

this one?

5 years ago
OpenStudy (anonymous):

yeah

5 years ago
OpenStudy (amistre64):

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

5 years ago
OpenStudy (amistre64):

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

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (amistre64):

\[nr^{3/2}=150r^2\] 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

5 years ago
OpenStudy (amistre64):

\[\frac{B^t}{B^b}\to \ B^{t-b}\]

5 years ago
OpenStudy (amistre64):

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

5 years ago
OpenStudy (anonymous):

wait but what does n represent?

5 years ago
OpenStudy (amistre64):

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

5 years ago
OpenStudy (amistre64):

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

5 years ago
OpenStudy (amistre64):

or whatever its called :)

5 years ago
OpenStudy (anonymous):

o ok thanks

5 years ago
OpenStudy (anonymous):

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

5 years ago
OpenStudy (amistre64):

if im available

5 years ago
OpenStudy (anonymous):

o ok

5 years ago