Answer:10 seconds pleb
Step-by-step explanation:
Rui's altitude is modeled by a quadratic function, whose graph is a parabola.
The lowest altitude is reached at the vertex.
So in order to find when that happens, we need to find the vertex's xxx-coordinate.
Hint #22 / 4
The vertex's xxx-coordinate is the average of the two zeros, so let's find those first.
Hint #33 / 4
\begin{aligned} d(x)&=0 \\\\ \dfrac12x^2 -10x&=0 \\\\ x^2-20x&=0 \\\\ x(x-20)&=0 \\\\ \swarrow\quad&\searrow \\\\ x=0\text{ or }&x-20=0 \\\\ x=\goldD{0}\text{ or }&x=\goldD{20} \end{aligned}
d(x)
2
1
x
2
−10x
x
2
−20x
x(x−20)
↙
x=0 or
x=0 or
=0
=0
=0
=0
↘
x−20=0
x=20
Now let's take the zeros' average:
\dfrac{(\goldD{0})+(\goldD{20})}{2}=\dfrac{20}{2}=10
2
(0)+(20)
=
2
20
=10start fraction, left parenthesis, start color #e07d10, 0, end color #e07d10, right parenthesis, plus, left parenthesis, start color #e07d10, 20, end color #e07d10, right parenthesis, divided by, 2, end fraction, equals, start fraction, 20, divided by, 2, end fraction, equals, 10
Hint #44 / 4
In conclusion, Rui will reach his lowest altitude 101010 seconds after diving.
