anonymous
  • anonymous
The Height , H Of A Baksetball , in meters at t seconds after it is tossed out of a window is modeled by : H=-5t^2 + 20t +15. A Boy Shoots At The Baseball With A Paintball Gun . The Trajectory Of The Paintball Is Given By The Equation : H=3t + 3 . Will The Paintball Hit The Baseball ? IF So When? At What Height Will The Baseball bE ? @jtvatsim
Mathematics
schrodinger
  • schrodinger
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jtvatsim
  • jtvatsim
Alrighty, what have we got here...
jtvatsim
  • jtvatsim
"something is flying through the air, somebody does something to hit in midair" yep same problem type... :)
anonymous
  • anonymous
Yup Sooo... -5t^2 +20t+15=3t +3

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jtvatsim
  • jtvatsim
Yessiree! Will the heights be equal? And when? Let's find out. The audience waits in suspense...
anonymous
  • anonymous
Lets Fine Outt Next Step Add ?
jtvatsim
  • jtvatsim
Either add or subtract, whatever will make the other side 0. Try something, and I'll let you know what I think. :)
anonymous
  • anonymous
Ok Subtract Because there is only one negative .
jtvatsim
  • jtvatsim
You are right to subtract. But not because there is only one negative. Let's pause on this step to make sure you've got this part down. That way, you'll always have the confidence to get through this stage. :)
jtvatsim
  • jtvatsim
When I see -5t^2 + 20t + 15 = 3t + 3, I immediately focus my attention on the right side of the equation (look at 3t + 3).
anonymous
  • anonymous
Ok
jtvatsim
  • jtvatsim
Then, ask yourself, I see a 3t, how can I get rid of it? In this case I could just subtract a 3t from both sides like this: -5t^2 + 20t + 15 = 3t + 3 -3t -3t ___________________________ -5t^2 + 17t + 15 = 3 Then my 3t is gone!
jtvatsim
  • jtvatsim
But, then, of course, I still see a pesky 3 there. How could I get rid of that since I just want zero on that side? Well... subtract a 3 from both sides, just like we did before! -5t^2 + 17t + 15 = 3 -3 -3 -------------------- -5t^2 + 17t + 12 = 0
anonymous
  • anonymous
Ohhh i c
jtvatsim
  • jtvatsim
Great! It's not too hard once you see the pattern. But it is a little hard to say in words. :)
jtvatsim
  • jtvatsim
Here's one more example just to make sure you've got it. -66t^2 + 24t + 31 = -6t + 4 +6t +6t --------------------------- -66t^2 + 30t + 31 = 4 -4 -4 ---------------------- -66t^2 + 30t + 27 = 0
jtvatsim
  • jtvatsim
In this case, I added to get rid of the -6t, but subtracted to get rid of the +4. Any questions on that process?
jtvatsim
  • jtvatsim
And of course, what I just wrote above was a made-up example and has nothing to do with "our" current problem. :)
anonymous
  • anonymous
i noticed Lol Those Off #;s
jtvatsim
  • jtvatsim
Haha! I tried to make it obvious that I was going crazy there. ;) Anyways, we've got our equation now: -5t^2 + 17t + 12 = 0
jtvatsim
  • jtvatsim
From what I've seen, that should be the end of the "hard" part mathematically. The rest of the problem is just making sure our calculator does the right thing. :)
anonymous
  • anonymous
Yup Thats The Last Thing 2 do
jtvatsim
  • jtvatsim
OK, then. Once you have your proposed solutions from the quadratic formula, we'll compare notes.
anonymous
  • anonymous
Done
jtvatsim
  • jtvatsim
Awesome! What did you get?
anonymous
  • anonymous
x1=-0.5 x2 :4
jtvatsim
  • jtvatsim
Yep, that's pretty close to what I got, x1 = -0.59999 x2 = 4
anonymous
  • anonymous
i got the 9999 2 lol
anonymous
  • anonymous
didnt think i needed it
jtvatsim
  • jtvatsim
Oh, well, look at you! It's slightly different rounding -0.59 rounds to -0.6 (then I wouldn't have said anything...) You can feel that I'm becoming more nit picky! :) That's a good thing, it means you are moving beyond the basics. :)
anonymous
  • anonymous
Lol Im Trying .. Another One Then Ill Leave You Alone Lol
jtvatsim
  • jtvatsim
No worries! Glad to help. It's fun watching someone start out struggling, but then learn and start mastering it. It's really cool to see happen. :)
jtvatsim
  • jtvatsim
So, we've got our possible solutions, but we need to check them. Here goes...
jtvatsim
  • jtvatsim
Looks like t = -0.6 gives h = 1.2 and t = 4 gives h = 15
anonymous
  • anonymous
The Correct One Is ....4
jtvatsim
  • jtvatsim
I'd agree, even though the heights are both positive (and therefore possible), the negative time is weird. The answer is Yes, time is 4, and height is 15. Yahoo! :D
anonymous
  • anonymous
Yay !!!!!!!!!! You Helped Me Sooo Much ..After This Next One Ill Have Just Four More ...Wouldve Been Up All Night
jtvatsim
  • jtvatsim
You are welcome! Based on looking at the problems are they relatively similar? If not, I could help you look at one that is a different type if you feel comfortable with these "objects flying and hitting" questions.
anonymous
  • anonymous
This Next One Is A Different One .
anonymous
  • anonymous
Is a summer packet soo
jtvatsim
  • jtvatsim
Let's take a look at it then if you want. Even if I have to log off soon, I can at least try to come up with a plan of attack. :)
anonymous
  • anonymous
Sure
jtvatsim
  • jtvatsim
sounds good

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