the power generated by an electrical circuit (in watts) as a function of its current ccc (in amperes) is modeled by:
p(c)=−20(c−3)^2 + 180
which currents will produce no power (i. e. 000 watts)?
enter the lower current first.
lower current: amperes
higher current:

Lowest Current : c=0 and 6 Amp

Highest Current : 3 amp

Step-by-step explanation:

We are given our function as

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

Hence

Now we solve the above equation for c

subtracting 180 from each side we get

Dividing both sides by -20

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

Represents a parabola

subtracting 180 from both sides we get

Comparing it with standard parabola

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

Hence here

h=3 , k = 180

Hence in this equation

The vertex will be (3,180)

Or at c=3, P = 180 the maximum

Lower current: 0 amperes  

Higher current: 6 amperes

Step-by-step explanation:

Hi, to answer this question we have to replace the value of P by 0 and solve.

0 = -20 (c-3)² +180

-180 = -20 (c-3)²

-180/-20 =(c-3)²

9=(c-3)²

√9 = c-3

±3= c-3

3+3= c

6 =c

-3 =c-3

-3+3 =c

c=o

Lower current: 0 amperes  

Higher current: 6 amperes

Feel free to ask for more if needed or if you did not understand something.

step-by-step explanation: