The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by: P(x)=-12x^(2)+120 x What current will produce the maximum power? amperes

Identify Quadratic Equation: Identify the quadratic equation that models the power generated by the electrical circuit. The given equation is P(x) = -12x^2 + 120x. This is a quadratic equation in the form of ax^2 + bx + c, where a = -12, b = 120, and c = 0 (since it is not given).Determine Vertex Coordinate: Determine the x-coordinate of the vertex of the parabola, which will give us the current that produces the maximum power. The x-coordinate of the vertex of a parabola given by ax^2 + bx + c is found using the formula x = -b/(2a). In this case, a = -12 and b = 120.Calculate Vertex x-coordinate: Calculate the x-coordinate of the vertex using the values of a and b. x = -120 / (2 * -12) x = -120 / -24 x = 5Interpret Maximum Power: Interpret the result. The current that produces the maximum power is 5 amperes. This is the x-coordinate of the vertex of the parabola, which represents the maximum point on the graph of the quadratic equation.

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The power generated by an electrical circuit (in watts) as a function of its current
x (in amperes) is modeled by:

P(x)=-12x^(2)+120 x
What current will produce the maximum power?
amperes

The power generated by an electrical circuit (in watts) as a function of its current $x$ (in amperes) is modeled by: $\newline$ $P(x)=-12x^{2}+120x$ $\newline$ What current will produce the maximum power? $\newline$ amperes

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Q. The power generated by an electrical circuit (in watts) as a function of its current

x

(in amperes) is modeled by:

\newline

P(x)=-12x^{2}+120x

\newline

What current will produce the maximum power?

\newline

amperes

Identify Quadratic Equation: Identify the quadratic equation that models the power generated by the electrical circuit. $\newline$ The given equation is $P(x) = -12x^2 + 120x$ . This is a quadratic equation in the form of $ax^2 + bx + c$ , where $a = -12$ , $b = 120$ , and $c = 0$ (since it is not given).
Determine Vertex Coordinate: Determine the $x$ -coordinate of the vertex of the parabola, which will give us the current that produces the maximum power. $\newline$ The $x$ -coordinate of the vertex of a parabola given by $ax^2 + bx + c$ is found using the formula $x = -\frac{b}{2a}$ . In this case, $a = -12$ and $b = 120$ .
Calculate x-coordinate of Vertex : Calculate the x-coordinate of the vertex using the values of $a$ and $b$ . $x = \frac{-120}{(2 \cdot -12)}$ $x = \frac{-120}{-24}$ $x = 5$
Interpret Maximum Power: Interpret the result. $\newline$ The current that produces the maximum power is $5$ amperes. This is the $x$ -coordinate of the vertex of the parabola, which represents the maximum point on the graph of the quadratic equation.