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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 xx (in amperes) is modeled by:\newlineP(x)=−12x2+120xP(x)=-12x^{2}+120x\newlineWhat current will produce the maximum power?\newlineamperes

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Q. The power generated by an electrical circuit (in watts) as a function of its current xx (in amperes) is modeled by:\newlineP(x)=−12x2+120xP(x)=-12x^{2}+120x\newlineWhat current will produce the maximum power?\newlineamperes
  1. Identify Quadratic Equation: Identify the quadratic equation that models the power generated by the electrical circuit.\newlineThe given equation is P(x)=−12x2+120xP(x) = -12x^2 + 120x. This is a quadratic equation in the form of ax2+bx+cax^2 + bx + c, where a=−12a = -12, b=120b = 120, and c=0c = 0 (since it is not given).
  2. Determine Vertex Coordinate: Determine the xx-coordinate of the vertex of the parabola, which will give us the current that produces the maximum power.\newlineThe xx-coordinate of the vertex of a parabola given by ax2+bx+cax^2 + bx + c is found using the formula x=−b2ax = -\frac{b}{2a}. In this case, a=−12a = -12 and b=120b = 120.
  3. Calculate x-coordinate of Vertex : Calculate the x-coordinate of the vertex using the values of aa and bb.x=−120(2⋅−12)x = \frac{-120}{(2 \cdot -12)}x=−120−24x = \frac{-120}{-24}x=5x = 5
  4. Interpret Maximum Power: Interpret the result.\newlineThe current that produces the maximum power is 55 amperes. This is the xx-coordinate of the vertex of the parabola, which represents the maximum point on the graph of the quadratic equation.

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