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

To find:
The current which will produce the maximum power.
Solution:
We have,


Differentiate with respect to x.

...(i)
To find the extreme point equate P'(x)=0.


Divide both sides by -30.

Differentiate (i) with respect to x.

(Maximum)
It means, the given function is maximum at x=4.
Therefore, the current of 4 amperes will produce the maximum power.
the answer for the second problem is x=99 degrees and y= 261 degrees
dunno the first problem :/
Y coordinate on solving both equations comes out to be 0
-2x+3y=-6
3y = -6+2x
put the value of 3y in equation 2nd
5x-2(-6+2x) =15
5x+12-4x = 15
x=3
put value of X in 3y = -6+2x
3y = -6+2*3 = -6+6 = 0
thus y = 0
Tn=3n-5
therefore: T(3)=3(3)-5
T(3) =4