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 is the maximum power possible? watts

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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 is the maximum power possible? watts

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Analyzing Quadratic Function: To find the maximum power possible, we need to analyze the quadratic function P(x) = -15x(x - 8). This is a parabola that opens downwards because the coefficient of x^2 is negative (-15). The maximum value of this function occurs at the vertex of the parabola.Finding Vertex: The vertex of a parabola given by the function f(x) = ax^2 + bx + c is at the point (h, k), where h = -b/(2a). In our case, the function P(x) = -15x^2 + 120x can be written in the form ax^2 + bx + c by expanding the given expression.Expanding Function: Expanding P(x) = -15x(x - 8) gives us P(x) = -15x^2 + 120x. Here, a = -15 and b = 120. There is no c term, so c = 0.Calculating x-coordinate: Using the formula for the vertex h = -b/(2a), we substitute a = -15 and b = 120 to find the x-coordinate of the vertex. h = -120 / (2 * -15) = -120 / -30 = 4.Substitute x into Function: The x-coordinate of the vertex is 4. To find the y-coordinate, which is the maximum power, we substitute x = 4 back into the function P(x). P(4) = -15 * 4 * (4 - 8).Calculate Maximum Power: Calculate P(4) = -15 * 4 * (4 - 8) = -15 * 4 * -4 = -15 * 16 = -240.

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

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The power generated by an electrical circuit (in watts) as a function of its current xxx (in amperes) is modeled by\newlineP(x)=−15x(x−8)P(x)=-15x(x-8)P(x)=−15x(x−8)\newlineWhat is the maximum power possible?\newlinewatts

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