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Fed [463]
3 years ago
6

3/5 x 15/16 simplest form

Mathematics
1 answer:
Olin [163]3 years ago
3 0
The answer is 9/16...............
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The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by: P(x)=-12x^2 +12
Minchanka [31]

Given:

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

P(x)=-12x^2+120x

To find:

The current that will produce the maximum power.

Solution:

We have,

P(x)=-12x^2+120x

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is f(x)=ax^2+bx+c, then

Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)

In the given function, a=-12 and b=120. So,

-\dfrac{b}{2a}=-\dfrac{120}{2(-12)}

-\dfrac{b}{2a}=-\dfrac{120}{-24}

-\dfrac{b}{2a}=5

Putting x=5 in the given function, we get

P(5)=-12(5)^2+120(5)

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

P(5)=-300+600

P(5)=300

Therefore, 5 watt current will produce the maximum power of 300 amperes.

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