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Vinil7 [7]
3 years ago
6

At a party, everyone shook hands with everybody else. These were 66 handshakes. How many people were at the party?

Mathematics
1 answer:
nignag [31]3 years ago
7 0
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
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  • k for the units down  ⇒4*3=12

So the equation is : y=(x-6)²+12

b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2

  • We khow that a parabola is written this way : y=(x-h)²+k
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  • we khow tha the derivative of a quadratic function is null in the maximum value
  • so let's derivate (x-h)²+k= x²+h²-2xh+k
  • f'(x)= 2x-2h    h is 1 since the axe of simmetry is x=1
  • f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
  • Now we khow that 1 is the point where the derivative is null
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the maximum height is where the derivative equals 0

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When the height was at max t=4s

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