Question

Brian is creating a collage on a piece of cardboard that has an area of 110r3 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 fifth power square centimeters. Use the given information to determine an expression for the total number of pieces of paper used.

Answer 1

@jim_thompson5910

Answer 2

ok and the total area is \[\large 110r^3\] right?

Answer 3

yup

Answer 4

well you have to solve the equation below for k

\[\large k*\sqrt{r^5} = 110r^3\]

Answer 5

how do i solve it ?

Answer 6

divide both sides by \(\large \sqrt{r^5} \)

Answer 7

to isolate k

Answer 8

..... what would it be ? i tried a million times

Answer 9

\[\large k*\sqrt{r^5} = 110r^3\]

\[\large k = \frac{\110r^3}{\sqrt{r^5}}\]

Then you rationalize the denominator

Answer 10

`r^3/2

Answer 11

not quite

Answer 12

,-,

Answer 13

@jim_thompson5910 help ;P

Answer 14

\[\large k*\sqrt{r^5} = 110r^3\]

\[\large k = \frac{\110r^3}{\sqrt{r^5}}\]

\[\large k = \frac{\110r^3\sqrt{r^5}}{\sqrt{r^5}\sqrt{r^5}}\]

\[\large k = \frac{\110r^3\sqrt{r^5}}{(\sqrt{r^5})^2}\]

\[\large k = \frac{\110r^3\sqrt{r^5}}{r^5}\]

\[\large k = \frac{\110\sqrt{r^5}}{r^2}\]

\[\large k = \frac{\110\sqrt{r^4*r}}{r^2}\]

\[\large k = \frac{\110\sqrt{r^4}*\sqrt{r}}{r^2}\]

\[\large k = \frac{\110r^2\sqrt{r}}{r^2}\]

\[\large k = \110\sqrt{r}\]

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So the expression

\[\large \110\sqrt{r}\]

models how many pieces of paper total that are needed

Answer 15

thats the answer? or ur asking me ?

Answer 16

@jim_thompson5910