anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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jtvatsim
  • 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
  • anonymous
This One Is Tricky .
jtvatsim
  • 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
  • anonymous
Ok.
jtvatsim
  • jtvatsim
Let's try it and see what we get. We'll start with the first equation -5(t-1)^2 + 5
jtvatsim
  • 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
  • jtvatsim
Does that make sense so far?
anonymous
  • anonymous
Kind Of
jtvatsim
  • 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
  • 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
  • anonymous
Look Like Something I Seen Before
jtvatsim
  • jtvatsim
That's a good thing... I suppose. When it comes to math, we're basically saying "Yep, I've seen Godzilla before." :)
anonymous
  • anonymous
Lol Right .
jtvatsim
  • 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
  • anonymous
ok got it
jtvatsim
  • 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
  • jtvatsim
Oh, well you said you got it, but just checking... :)
anonymous
  • anonymous
i was saying i got the 1st step lol but the whole binomial never heard of it
jtvatsim
  • jtvatsim
No worries, you may have heard it called something different. Terminology is replaceable. :)
anonymous
  • anonymous
i heard of terminology
jtvatsim
  • 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
  • anonymous
soooo -5t^2 +10t=-5t^2 + 20t - 15
jtvatsim
  • 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
  • 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
  • anonymous
yay this one was fun but different
jtvatsim
  • 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
  • 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
  • anonymous
very ..
jtvatsim
  • 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
  • anonymous
thanks , ill stay in touch your awesome
jtvatsim
  • 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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