Question

I have NO idea! :( anyone?
The arithmetic mean (A) of two numbers (a and b) is given by the formula A=a+b/2, and their geometric mean (G) is given by G=√ab. Their harmonic mean (H) is given by the formula
G= √AH. Which formula correctly gives H in terms of a and b?

Answer 1

H=2ab/a+b
H=sqrt2ab/a+b
H=a+b/2ab
H=ab/a(a+b)

Answer 2

Fan and medal who ever can help im desperate

Answer 3

\[\Large\rm \color{royalblue}{A=\frac{a+b}{2}},\qquad\color{orangered}{G=\sqrt{ab}}\]

And then,\[\Large\rm \color{orangered}{G}=\sqrt{\color{royalblue}{A}H}\]So we need to solve for H, the harmonic mean, ya?
It's stuck under a square root, what should be our first step to get rid of the root?

Answer 4

im back sorry.

Answer 5

I've been trying to figure it out. Hope you come back soon.

Answer 6

so, first step? :D

Answer 7

I guess I would have to rewrite it
H=G^2/A

Answer 8

\[\Large\rm H=\frac{(\color{orangered}{G})^2}{\color{royalblue}{H}}\]Ok good so far.

Answer 9

isolate lol

Answer 10

im super slow and have total malfunctions when it come to numbers sorry

Answer 11

\[\Large\rm H=\frac{(\color{orangered}{G})^2}{\color{royalblue}{H}}=\frac{\left(\color{orangered}{\sqrt{ab}}\right)^2}{\color{royalblue}{\frac{a+b}{2}}}\]Do you understand this step?
I'm replacing G, with what it is,
and replacing H, with what it is.

Answer 12

oh yes :0 one question sqrtab^2 ...why did you square?

Answer 13

oh nevermind i get it

Answer 14

:3

Answer 15

hopefully the colors help.
I'm not doing anything too fancy.
I'm just replacing the orange with the orange
and the blue with the blue.

you determined that the top is being squared.

Answer 16

so now I have to solve

Answer 17

so umm.. ya simplify.
I guess we could do some `keep change flip` business, ya?

Answer 18

give me a sec

Answer 19

If you remember that little trick :)
it tells us how to deal with fractions when we're dividing by them

Answer 20

now im lost what trick?

Answer 21

turn it upside down

Answer 22

\[\Large\rm \frac{\left(\frac{a}{b}\right)}{\left(\frac{c}{d}\right)}=\frac{a}{b}\times\frac{d}{c}\]Yes good, flip the bottom fraction,
turn the operation into multiplication.

Answer 23

Works the same way if the top is not a fraction:\[\Large\rm \frac{a}{\left(\frac{c}{d}\right)}=a\times\frac{d}{c}\]Just need the bottom to be a fraction to apply this trick.

Answer 24

ok

Answer 25

yeah im stuck on how to flip it being squared

Answer 26

is this the hardest part lol

Answer 27

Ok let's simplify the top before we do any flipping then :)
What happens when you square a square root?

Answer 28

multiply

Answer 29

\[\Large\rm H=\frac{\sqrt{ab}^2}{\left(\frac{a+b}{2}\right)}\]

Answer 30

Square root and square are inverse operations of one another,
so they will `undo` each other.

Answer 31

\[\Large\rm H=\frac{ab}{\left(\frac{a+b}{2}\right)}\]So this will happen to our top.

Answer 32

Uh oh, what's wrong Molly? :o
Confused?

Answer 33

no you so much quicker then me

Answer 34

you're

Answer 35

oh yes I'm following you now

Answer 36

Do you see how we're going to flip the (a+b)/2?

Answer 37

2/ab

Answer 38

no

Answer 39

2/(a+b)

Answer 40

\[\Large\rm H=\frac{ab}{\left(\frac{a+b}{2}\right)}\]The trick is called `keep` `change` `flip`.

We `keep` the top the same.
We `change` the operation from multiplication to division.
We `flip` the bottom fraction.

Ok good, our flip will look like that!
So we get,\[\Large\rm H=ab\times\frac{2}{a+b}\]

Answer 41

H=a+b/2ab

Answer 42

Oo something got mixed up there :O

Answer 43

see U are fast and I was wrong

Answer 44

sorry i gotta slow down hehe

Answer 45

your flip looked good though: 2/(a+b) is what it turned into, ya?

Answer 46

Take a minute to soak all that in >.<

Answer 47

wow! thank you so much for helping me . :)

Answer 48

Do you understand the final step?
We're so close! :O

Answer 49

It will probably take some practice but I wrote it down.

Answer 50

is my answer H=2ab/a+b

Answer 51

Good good good.
The ab will multiply into the numerator.

It should be written like this though 2ab/(a+b)
which is, I assume, what you meant :)

Answer 52

yes woohoo :) this openstudy is fun and I hate math :)

Answer 53

pshhh math is awesome c:

Answer 54

Ohhh you're kinda new huh?
Well then,
\(\Large\bf \color{#CC0033}{\text{Welcome to OpenStudy! :)}}\)

Answer 55

haha ok for you smart ones not me. takes me to long. I really appreciate it. Will you be on here this weekend? Can I ask for help again? I have to finish my review packet before monday exam. :(

Answer 56

Ya, I'll be off and on at different times.
Lots of other smart people on as well.

You can sent like a "page" or notification to a specific person by typing @(their name) somewhere in the comments of your thread.

Example @zepdrix
If you look in the lobby, the people with 99 scores tend to be some smarty pants. So if I'm not around, you can try asking one of them for assistance as well :)

Answer 57

ok thank you? :)

Answer 58

This thread is going to get kinda slow and laggy though because of all the LaTeX I used. If you have another question ready, you should probably close this one and start a new one.

np \c:/
hope the packet goes well!

Answer 59

no not tonight but maybe tomorrow. Most of the stuff/questions I know but there are some things that I have never seen and not even sure what they are... like this question. I had never seen. Is that Algebra?

Answer 60

I had a trig question too. Think my teacher hates me. lol

Answer 61

Yah that's pretty much smack dab right in the middle of Algebra :)
It's an algebraic expression that requires a bunch of simple steps (multiplication,division,etc) and some substitution.

Answer 62

I had never heard of harmonic mean.lol simple :) thanks again good night

Answer 63

usein Tex commands looks like what u would type in a minecraft command block lol