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:
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:
[tex]P(c)=-15c(c-8)[/tex]
To find the current that will produce the maximum power.
Solution:
The function can be simplified using distribution.
[tex]P(c)=-15c^2+120c[/tex]
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.
[tex]\frac{dP}{dc}=-30c+120[/tex]
We will equate the slope = 0 to get the current for maximum power.
Thus, we have:
[tex]-30c+120=0[/tex]
Subtracting both sides by 120.
[tex]-30c+120-120=0-120[/tex]
[tex]-30c=-120[/tex]
Dividing both sides by -30.
[tex]\frac{-30c}{-30}=\frac{-120}{-30}[/tex]
∴ [tex]c=4[/tex]
Thus, the maximum power is produced at current = 4 A
