Math Question?

Question

When current "i" flows through a given electrical circuit, the power "w" of the circuit can be determined by the formula W=120i - 12i^2. What amount of current "i" supplies the maximun power for "W"?

thanks for helping out :)

Answer 1

this is a quadratic equation problem
look at W = 120i - 12i² in this way
y = -12x² + 120x where a=-12 , b=120 , c=0
this would be a parabola that opens downward so the vertex would be the maximum point of the graph
to find the vertex x-coordinate do x = -b/2a
so x = -120/(2*-12) == 5
so your answer is i = 5 amperes and
power W = 300
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Answer 2

W=120i-12i^2;
dW/dt=120-24i
this =0 for maximum powerW;
so 120-24i=0
i=5ampere
d^2W/dI^2=-24;
as it is negative at i=5 ampere, it gives the maximum value of power.
so a current i=5 supplies the maximim powerW to the circuit.

Answer 3

From what I remember, you need to differentiate the equation:
W = 120i - 12i²
dW = 120 - 12(2)i
dW = (120 - 24i)di

If we equate our answer by zero, we get

0 = 120 - 24i

Transpose 24i to the left side of the equation, giving us,

24i = 120

Simplifying further, we have

i = 120 / 24
i = 5

Answer 4

plug that equation into the calculator and you'll get a quadratic with a maxiumum at 5.

when i = 5, W = 300 and 300 is it's highest point.

Answer 5

this is an eq with a max at -b/2a
-120/2*(-12) = 5

when i = 5; w = 300

Answer 6

differentiate and set dw/di =0 and find i when it is maximum
dw/di = 120 - 24 i=0
120=24i
now findi
the other guy before me has used another method.
you could also find i interecepts usign factorign and the zero property and find the half way point between them