The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by P(x)=-15 x(x-8) What current will produce the maximum power? ◻ amperes

Analyze Quadratic Function: To find the current that will produce the maximum power, we need to analyze the quadratic function P(x) = -15x(x - 8). This is a parabola that opens downwards because the coefficient of the x^2 term is negative (-15). The maximum power will be at the vertex of this parabola.Compare to General Form: The general form of a quadratic function is ax^2 + bx + c. In our case, the function P(x) = -15x^2 + 120x can be compared to this form, where a = -15 and b = 120. The x-coordinate of the vertex of a parabola given by ax^2 + bx + c is found using the formula -b/(2a).Find x-coordinate of Vertex: We will apply the formula to find the x-coordinate of the vertex. For our function P(x) = -15x^2 + 120x, we have a = -15 and b = 120. Plugging these values into the formula gives us x = -120 / (2 * -15).Calculate x-coordinate: Calculating the x-coordinate of the vertex, we get x = -120 / (2 * -15) = -120 / -30 = 4.Current for Maximum Power: The x-coordinate of the vertex, which is 4 amperes, represents the current that will produce the maximum power in the electrical circuit.

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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)=-15 x(x-8)
What current will produce the maximum power?

◻ amperes

The power generated by an electrical circuit (in watts) as a function of its current $\newline$ $x$ (in amperes) is modeled by $\newline$ $P(x)=-15 x(x-8)$ $\newline$ What current will produce the maximum power? $\newline$ $\square$ amperes

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

\newline

x

(in amperes) is modeled by

\newline

P(x)=-15 x(x-8)

\newline

What current will produce the maximum power?

\newline

\square

amperes

Analyze Quadratic Function: To find the current that will produce the maximum power, we need to analyze the quadratic function $P(x) = -15x(x - 8)$ . This is a parabola that opens downwards because the coefficient of the $x^2$ term is negative ( $-15$ ). The maximum power will be at the vertex of this parabola.
Compare to General Form: The general form of a quadratic function is $ax^2 + bx + c$ . In our case, the function $P(x) = -15x^2 + 120x$ can be compared to this form, where $a = -15$ and $b = 120$ . The $x$ -coordinate of the vertex of a parabola given by $ax^2 + bx + c$ is found using the formula $-b/(2a)$ .
Find x-coordinate of Vertex: We will apply the formula to find the x-coordinate of the vertex. For our function $P(x) = -15x^2 + 120x$ , we have $a = -15$ and $b = 120$ . Plugging these values into the formula gives us $x = \frac{-120}{(2 \cdot -15)}$ .
Calculate x-coordinate: Calculating the x-coordinate of the vertex, we get $x = \frac{-120}{(2 \cdot -15)} = \frac{-120}{-30} = 4$ .
Current for Maximum Power: The $x$ -coordinate of the vertex, which is $4$ amperes, represents the current that will produce the maximum power in the electrical circuit.