SOLUTION: In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface w

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface w      Log On


   

Question 981452: In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface water will the dolphin reach 25 feet to get the fish from the trainer's hand?
Found 3 solutions by macston, Boreal, Alan3354:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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h=-4t%5E2-20t
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For h=25 feet:
25ft=4t%5E2-20t
0=4t%5E2-20t-25
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 4t%5E2%2B-20t%2B-25+=+0) has the following solutons:

t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-20%29%5E2-4%2A4%2A-25=800.

Discriminant d=800 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+800+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+800+%29%29%2F2%5C4+=+6.03553390593274
t%5B2%5D+=+%28-%28-20%29-sqrt%28+800+%29%29%2F2%5C4+=+-1.03553390593274

Quadratic expression 4t%5E2%2B-20t%2B-25 can be factored:
4t%5E2%2B-20t%2B-25+=+4%28t-6.03553390593274%29%2A%28t--1.03553390593274%29
Again, the answer is: 6.03553390593274, -1.03553390593274. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-20%2Ax%2B-25+%29

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So t=6.04 seconds.
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ANSWER: The dolphin gets the fish 6.04 seconds after breaking water.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
h=25=-4t^2-20t;I think this has to be -4t^2+20t, because otherwise as t increases from zero, the height gets less and less.
4t^2-20t+25=0; if I move everything to the left side.
(2t-5)^2=0
2t=5
t=2.5 seconds. NOTE: if I use the equation given with -20t, I get t=-2.5 seconds
-4(2.5)^2+20(2.5)=-25+50=25
2.5 seconds

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface water will the dolphin reach 25 feet to get the fish from the trainer's hand?
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h(t) = -4t^2 - 20t = 25
That won't work.
It's h(t) = -4t^2 + 20t = 25
The 20 is its vertical speed when it leaves the water and becomes a projectile.
-4t^2 = 20t - 25 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B20x%2B-25+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2820%29%5E2-4%2A-4%2A-25=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2820%29%29%2F2%5C-4.
Expression can be factored: -4x%5E2%2B20x%2B-25+=+%28x-2.5%29%2A%28x-2.5%29

Again, the answer is: 2.5, 2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B20%2Ax%2B-25+%29

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t = 2.5 seconds.