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Andrei [34K]
3 years ago
15

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

Mathematics
1 answer:
muminat3 years ago
7 0

Answer:

Lowest Current : c=0 and 6 Amp

Highest Current : 3 amp

Step-by-step explanation:

We are given our function as

P(c)=-20(c-3)^2 + 180

We are asked to determine the values of current c at which the power P(c) is equal to 0

Hence

0=-20(c-3)^2+ 180

Now we solve the above equation for c

subtracting 180 from each side we get

-180=-20(c-3)^2

Dividing both sides by -20

(c-3)^2=9

Taking square root on both sides

c-3= ±3

adding 3 on both sides

c=±3+3

hence

c= 0

or

c=6

At c=0 and 6 amperes the power will be minimum

Now we have to find the c at which the power will be the highest

P(c)=-20(c-3)^2+ 180

Represents a parabola

subtracting 180 from both sides we get

P-180=-20(c-3)^2

Comparing it with standard parabola

(y-k)^2=-4k(x-h)^2

(h,k) will be the coordinates of the vertex

Hence here

h=3 , k = 180

Hence in this equation P-180=-20(c-3)^2

The vertex will be (3,180)

Or at c=3, P = 180 the maximum

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