Question

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

Answer 1

Answer:

c = 4 A

Step-by-step explanation:

The given function P(c) = - 15 c (c-8) is actually quadratic function:

P(c) = - 15c² + 120c    or parabola

The standard form of a quadratic function is:

y = ax² + bx + c

For which x is the maximum of the parabola we can find with this formula

x = - b/2a

in this case a = -15 and b = 120 and input variable is current c

c = - 120/(2 · (-15)) = - 120/ (-30) = 4 A

c = 4 A

God with you!!!

Answer 2

Answer:

The maximum power is produced at current = 4 A

Step-by-step explanation:

Given:

The power generated by an electrical circuit (in watts) is modeled as a function of current as:

$P(c)=-15c(c-8)$

To find the current that will produce the maximum power.

Solution:

The function can be simplified using distribution.

$P(c)=-15c^2+120c$

We know that the power will be maximum at the point where the slope of the equation will be = 0 i.e. parallel to x-axis.

Finding the slope of the function using derivative.

$\frac{dP}{dc}=-30c+120$

We will equate the slope = 0 to get the current for maximum power.

Thus, we have:

$-30c+120=0$

Subtracting both sides by 120.

$-30c+120-120=0-120$

$-30c=-120$

Dividing both sides by -30.

$\frac{-30c}{-30}=\frac{-120}{-30}$

∴  $c=4$

Thus, the maximum power is produced at current = 4 A