Two Cirque Du Soleil Performers Are Launched Toward Each Other From Two Slightly Offset Seesaws The First Performer Is Launched And One Second later , The Second Performer Is Launched in other Direction .They Both Performed A Flip And gave a high five in the air each performer is in the air for 2 seconds . The Height above the seasaw (h) at any given time (t) is approximated by parabolas
h=-5(t-1)^2 +5
h=-5 ( t-2)^2 +5
determine the height of the performers when they ''high fived '' @jvatsim

- anonymous

- jamiebookeater

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- jtvatsim

Hmm... interesting. I see that the second equation is just as nasty as the first one (the only difference is a t-1 vs. a t-2). But I bet the big picture idea is still the same. :)
1) Set equal
2) Solve for t
3) Check answer.

- anonymous

This One Is Tricky .

- jtvatsim

Yeah, I notice that on the surface we also have a weird (t-1)^2 and (t-2)^2 expansion needed too. We have to "expand the binomial" in math speak.

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- anonymous

Ok.

- jtvatsim

Let's try it and see what we get. We'll start with the first equation
-5(t-1)^2 + 5

- jtvatsim

Alright, well I don't like the whole parenthesis squared thing so let's remember that exponents just mean to multiply the same thing twice:
-5(t-1)^2 + 5 --> -5(t-1)(t-1) + 5

- jtvatsim

Does that make sense so far?

- anonymous

Kind Of

- jtvatsim

Alright, keep track of what you are thinking and what is confusing. Let me finish the full thought here and see if that helps. :)

- jtvatsim

We rewrite:
-5(t-1)^2 + 5 -> -5(t-1)(t-1) + 5
then, we use FOIL or distribution (whichever you learned) to get:
-5(t-1)(t-1) + 5 -> -5( t^2 - t - t + 1) + 5
simplifying:
-5(t^2 - t - t + 1) + 5 -> -5(t^2 - 2t + 1) + 5
distribute the -5 (watch out for sign changes!):
-5(t^2 - 2t + 1) + 5 -> -5t^2 + 10t - 5 + 5
simplifying:
-5t^2 + 10t - 5 + 5 -> -5t^2 + 10t
I know that is a lot, but see if you can follow the thought process. If you have any questions, I'll be happy to try and answer them. There are several algebra ideas floating around here.

- anonymous

Look Like Something I Seen Before

- jtvatsim

That's a good thing... I suppose. When it comes to math, we're basically saying "Yep, I've seen Godzilla before." :)

- anonymous

Lol Right .

- jtvatsim

Ahh! Error.... Here it is corrected. :)
Well, if you are brave, we can do the same thing with the other equation -5(t-2)^2 + 5.
If we do it carefully, we get
-5(t-2)^2 + 5
-5(t-2)(t-2) + 5
-5(t^2 - 2t - 2t + 4) + 5
-5(t^2 - 4t + 4) + 5
-5t^2 + 20t - 20 + 5
-5t^2 + 20t - 15
Yikes... but, OK. :P Should have been -15 at the end.

- anonymous

ok got it

- jtvatsim

Is there any step in particular that is confusing? Hopefully most of the make sense.
The concepts here (in case you remember the names, which I never did):
expand binomial: (t-1)^2 = (t-1)(t-1)
FOIL: (t-1)(t-1) = first + outer + inner + last = t*t + t*-1 + -1*t + -1*-1 = t^2 -t -t + 1 = t^2 - 2t + 1

- jtvatsim

Oh, well you said you got it, but just checking... :)

- anonymous

i was saying i got the 1st step lol but the whole binomial never heard of it

- jtvatsim

No worries, you may have heard it called something different. Terminology is replaceable. :)

- anonymous

i heard of terminology

- jtvatsim

Well, now we are actually through most the hard part of this question.
1) Expand the equations we got
-5(t-1)^2 + 5 ---> -5t^2 + 10t
and
-5(t-2)^2 + 5 ---> -5t^2 + 20t - 15
All we do now is set these two equations equal to each other, and proceed as before.

- anonymous

soooo -5t^2 +10t=-5t^2 + 20t - 15

- jtvatsim

Right! Now, we can choose to move one side or the other it doesn't matter. I'll move the left side since it is shorter (less steps). :)

- jtvatsim

-5t^2 + 10t = -5t^2 + 20t - 15
+5t^2 +5t^2
------------------------
10t = 20t - 15
ooooh nice, the t^2's are gone!
10t = 20t - 15
-10t -10t
-------------
0 = 10t - 15
I don't like it written backwards, so I will spin it around
10t - 15 = 0
There. We don't even need the quadratic formula for this one!

- anonymous

yay this one was fun
but different

- jtvatsim

Yes, the mathematical definition of "fun" is "utterly tortuous and ridiculous". :) If you get into math at the master's level the definition of an "interesting problem" is one that "you have no clue how to solve". lol

- jtvatsim

Just to finish it off (though I'm sure you already finished the missing steps)... 10t = 15, so t = 15/10 = 1.5.

- anonymous

very ..

- jtvatsim

I've got to head out now. But I do want to give you a link to a very good resource: Check out desmos.com It is a very powerful graphing calculator that lets you "see" the answer visually. It is not a replacement for knowing the algebra (in class you still need to solve it manually), but I think it is cool to know that there is technology that does these problems instantly. :)
For example, I did this problem we just solved: https://www.desmos.com/calculator/1h08m4ibe7

- anonymous

thanks , ill stay in touch your awesome

- jtvatsim

Of course, whoever wrote the code for the computer needed to know the handwritten algebra first... :)
Thanks! I hope you got something out of all the crazy math notation I threw at you. It's still weird that little symbols allow us to communicate ideas... crazy stuff... Take care! :)

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