Rui is a professional deep water free diver.
His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by:

d(x) = 1/2x^2-10x

how many seconds after diving will Rui reach his lowest altitude

Hint: use the formula -b± b^2 - 4ac /2a

use the formula for finding the time. The fastest person who answers gets brainiest. I'm bored so imma have a little friendly competition

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.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°