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

P(x)=-12x^2+120xP(x)=−12x

2

+120xP, left parenthesis, x, right parenthesis, equals, minus, 12, x, squared, plus, 120, x

What is the maximum power generated by the circuit?

watts

Sagot :

Abidemiokinidn

Answer:

300watts

Step-by-step explanation:

Given the power generated by an electrical device modeled by the equation

P(x) = -12x²+120x

The maximum power generated occurs when dP(x)/dx = 0

dP(x)/dx = -24x+120 = 0

-24x + 120 = 0

-24x = -120

x = 120/24

x = 5

Substitute x = 5 into the modeled function to get the maximum power as shown;

Recall that: P(x)=-12x^2+120x

P(5) = -12(5)² + 120(5)

P(5) = -12(25) + 600

P(5) = -300+600

P(5) = 300

Hence the maximum power generated by the circuit is 300watts

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