Rui is a professional deep water free diver. His altitude (in meters relative to sea level), x seconds after diving, is modeled by: d(x)=(1)/(2)x^(2)-10 x What is the lowest altitude Rui will reach? meters relative to sea level

Identify Quadratic Equation: Identify the quadratic equation that models Rui's altitude. The given equation is d(x) = (1/2)x^2 - 10x. Here, a = 1/2, b = -10, and c = 0, since there is no constant term.Find Vertex Time: Find the x-coordinate of the vertex of the parabola, which will give us the time at which Rui reaches his lowest altitude. The x-coordinate of the vertex of a parabola given by ax^2 + bx + c is found using the formula x = -b/(2a). Substitute a = 1/2 and b = -10 into the formula. x = -(-10)/(2*(1/2)) x = 10/(1) x = 10Calculate Lowest Altitude: Calculate the lowest altitude Rui will reach by substituting the x-coordinate of the vertex into the original equation. d(x) = (1/2)x^2 - 10x d(10) = (1/2)(10)^2 - 10(10) d(10) = (1/2)(100) - 100 d(10) = 50 - 100 d(10) = -50

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

d(x)=(1)/(2)x^(2)-10 x
What is the lowest altitude Rui will reach?
meters relative to sea level

Rui is a professional deep water free diver. $\newline$ His altitude (in meters relative to sea level), $x$ seconds after diving, is modeled by: $\newline$ $d(x)=\frac{1}{2} x^{2}-10 x$ $\newline$ What is the lowest altitude Rui will reach? $\newline$ $\square$ meters relative to sea level

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Q. Rui is a professional deep water free diver.

\newline

His altitude (in meters relative to sea level),

x

seconds after diving, is modeled by:

\newline

d(x)=\frac{1}{2} x^{2}-10 x

\newline

What is the lowest altitude Rui will reach?

\newline

\square

meters relative to sea level

Identify Quadratic Equation: Identify the quadratic equation that models Rui's altitude. $\newline$ The given equation is $d(x) = (\frac{1}{2})x^2 - 10x$ . $\newline$ Here, $a = \frac{1}{2}$ , $b = -10$ , and $c = 0$ , since there is no constant term.
Find Vertex Time: Find the $x$ -coordinate of the vertex of the parabola, which will give us the time at which Rui reaches his lowest altitude. $\newline$ The $x$ -coordinate of the vertex of a parabola given by $ax^2 + bx + c$ is found using the formula $x = -\frac{b}{2a}$ . $\newline$ Substitute $a = \frac{1}{2}$ and $b = -10$ into the formula. $\newline$ $x = -\frac{-10}{2*(\frac{1}{2})}$ $\newline$ $x = \frac{10}{1}$ $\newline$ $x = 10$
Calculate Lowest Altitude: Calculate the lowest altitude Rui will reach by substituting the $x$ -coordinate of the vertex into the original equation. $d(x) = \left(\frac{1}{2}\right)x^2 - 10x$ $d(10) = \left(\frac{1}{2}\right)(10)^2 - 10(10)$ $d(10) = \left(\frac{1}{2}\right)(100) - 100$ $d(10) = 50 - 100$ $d(10) = -50$