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bonufazy [111]
3 years ago
7

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?
Mathematics
2 answers:
katen-ka-za [31]3 years ago
3 0

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!!!

juin [17]3 years ago
3 0

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.

<em>Finding the slope of the function using derivative.</em>

\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

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