Question

The power generated by an electrical circuit (in watts) as a function of its current ccc (in amperes) is modeled by: P(c)=-12c^2+120cP(c)=?12c 2 +120cP, left parenthesis, c, right parenthesis, equals, minus, 12, c, start superscript, 2, end superscript, plus, 120, c What current will produce the maximum power?

Answer 1

Answer:

5 amperes will produce the maximum power of 300 watts.

Step-by-step explanation:

The general form of a quadratic function presents the function in the form

$f(x)=ax^2+bx+c$

The vertex of a quadratic function is the highest or lowest point, also known as the maximum or minimum of a quadratic function.

We can define the vertex by doing the following:

• Identify a, b, and c
• Find, the x-coordinate of the vertex, by substituting a and b into

$x-coordinate =-\frac{b}{2a}$

• Find, the y-coordinate of the vertex, by evaluating

$y-coordinate =f(x-coordinate )=f(-\frac{b}{2a} )$

We know that the power generated by an electrical circuit is modeled by

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

This function is a quadratic function.

To find the current that produce the maximum power you must

• Identify a and b

a = -12 and b = 120

• Find, the maximum current of the vertex, by substituting a and b into

$maximum-current =-\frac{b}{2a}$

$maximum-current =-\frac{120}{2(-12)}\\\\maximum-current = 5$

• Find, the maximum-power, by evaluating

$maximum-power =P(maximum-current)=P(-\frac{b}{2a} )$

$P(5)=-12(5)^{2}+120(5)=300$

5 amperes will produce the maximum power of 300 watts.

We can check our work with the graph of the function $P(c)=-12c^{2}+120c$ and see that the maximum is (5, 300).