Question

The perimeter of a semicircle is doubled when the radius is increased by 3. Find the radius of the semicircle.

Answer 1

perimeter of a semicircle is r*pi + 2r

so the old perimeter is r*pi + 2r
and the new perimeter is (r+3)*pi + 2(r+3)

we know that the new perimeter is twice the old perimeter so:

2*(r*pi + 2r) = (r+3)*pi + 2(r+3)

solve for r

Answer 2

did you understand

Answer 3

\[2(\pi r+2r)=(r+3)\pi +2(r+3)\]
does it look like this

Answer 4

yes, do you know where to go from there?

Answer 5

\[\pi r =3\pi - 2r+6\]
i end up to this :(

Answer 6

i distributed first

Answer 7

hmm let's take it from the top

2*(r*pi + 2r) = (r+3)*pi + 2(r+3)

2*r*pi + 4r = pi*r + 3*pi + 2r + 6

pi*r + 2r = 3*pi + 6

we can factor r on the left side, and 3 on the right side giving us:

r(pi+2) = 3(pi + 2)

then we divide both sides by (pi + 2)

r = 3

is that clear?

Answer 8

oh, i did not factor... thanks. its now clear to me

Answer 9

uhmmmm can i ask 5 more problems?

Answer 10

sure

Answer 11

Joy is an instructional assistant in one of the college labs. She is on a very tight budget. She loves Jamaican Blue Mountain coffee, but it costs $15 a pound. She decides to blend this with regular coffee beans that costs $1.67 a pound. If she spends $14.25 on 3 pounds of coffee, how many pounds of each did she purchase?

Round your answers to two decimal places.

Answer 12

let's let b = number of pounds of blue mountain
and r = regular

r + b = 3 since there are 3 pounds of coffee
15b + 1.67r = 14.25

know where to go from there?

Answer 13

no :(

Answer 14

sorry

Answer 15

ok, that's fine, no need to apologize

we have 2 equations that will help us find what r and b are

r + b = 3
15b + 1.67r = 14.25

we can multiply the first equation by (-15), giving us

-15r - 15b = -45

now we can put the two equations together again

-15r - 15b = -45
15b + 1.67r = 14.25

now we can add the two equations together

-15r + 1.67r - 15b + 15b = -45 + 14.25

solve for r

Answer 16

i got 2.31 for r. that is for the regular? what about the pounds of jamaican blue mountain coffee?

Answer 17

i'll multiply r+b=3 to -1.67?

Answer 18

thanks!!! i got it right... thanks a lot! :)))

Answer 19

A patient requires an IV of 0.9% saline solution, also known as normal saline solution. How much distilled water, to the nearest milliliter, must be added to 100 milliliters of a 6 % saline solution to produce normal saline?