Question

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

Answer 1

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