Help me understand this one?
- Thread starter thickmax
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Cubist
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Cubist
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Well, if a*b = 0 then a=0 and/or b=0
So, t=0 is a solution. To find the other solution what value must t have to make (9-4.9t)=0 ?
EDIT: This idea can be extended, so if you have ( x-2 )( 2x-3 )( x-5 ) = 0, then the possible solutions are x=2, x=? and x=?
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Again, I really do not know how to solve (9-4.9t)=0...
Your edit, x could also equal 1.5 and 5 right?
Cubist
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If you can solve for x, then would it help if I write...
x ( 9 - 4.9x) = 0
( x - 0 )( 9 - 4.9x ) = 0
- ( x - 0 )( 4.9x - 9 ) = 0
( x - 0 )( 4.9x - 9 ) = 0
Could you solve the last line? What value of x would make the second bracket zero?
EDIT: Think about how you got the (correct) 1.5 answer
Cubist
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Do you mean square rather than square root. Are you talking about the [imath] t^2 [/imath] from the original equation [imath] 0 = 9t-4.9t^2 [/imath] ?
sorry, yes, you are quite right, the square.
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The initial equation is a quadratic. It can be rewritten in a form that you might find more familiar...
[imath]4.9t^2-9t+0=0[/imath]
But there's no need to use the quadratic equation here. It's much easier to write the above as...
[imath] t ( 4.9t-9 ) = 0[/imath]
The [imath]t^2[/imath] is still there if you expand this. BUT in factored form you can (with practice!) directly see the TWO solutions t=0 and t=9/4.9. If you want to convince yourself, then you could use the quadratic equation on the top equation and you should obtain the same two answers. But I think you'll agree it's much easier, and quicker, to factor in this case!
[imath]4.9t^2-9t+0=0[/imath]
But there's no need to use the quadratic equation here. It's much easier to write the above as...
[imath] t ( 4.9t-9 ) = 0[/imath]
The [imath]t^2[/imath] is still there if you expand this. BUT in factored form you can (with practice!) directly see the TWO solutions t=0 and t=9/4.9. If you want to convince yourself, then you could use the quadratic equation on the top equation and you should obtain the same two answers. But I think you'll agree it's much easier, and quicker, to factor in this case!