the power generated by an electrical circuit (in watts) as a function of its current $x$ (in amperes) is…
the power generated by an electrical circuit (in watts) as a function of its current $x$ (in amperes) is modeled by: $p(x)=-12x^{2}+120x$. what current will produce the maximum power? amperes
Answer
Explanation:
Step1: Identify the function type
The power function $P(x)=- 12x^{2}+120x$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-12$, $b = 120$, $c = 0$.
Step2: Use the formula for the x - coordinate of the vertex
For a quadratic function $y=ax^{2}+bx + c$, the x - coordinate of the vertex (which gives the maximum or minimum value depending on the sign of $a$; here $a<0$ so it gives the maximum) is $x=-\frac{b}{2a}$. Substitute $a=-12$ and $b = 120$ into the formula: $x=-\frac{120}{2\times(-12)}$.
Step3: Calculate the value of x
First, calculate the denominator: $2\times(-12)=-24$. Then, $x = \frac{120}{24}=5$.
Answer:
5