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.
Answer:
x + 3y > 6
Step-by-step explanation:
Find two points that satisfy x + 3y = 6 and draw a DASHED line through them.
It is greater than so shade the section ABOVE that line.
Using the intercept method, the two points I chose are: (0, 2) & (6, 0)
y ≥ 2x + 4
Find two points that satisfy y = 2x + 4 and draw a SOLID line through them.
It is greater than so shade the section ABOVE that line.
The two points I chose are: (0, 4) & (1, 6)
The solution is where the shaded sections overlap.
Answer:

Step-by-step explanation:
To solve this problem, we need to find the linear function. We know that the constant rate of change is -0.5° Celsius per minute. Also, after 60 minutes the temperature was 10° Celsius. So, we have a one point and the slope of the linear function, let's use the point-slope formula

Where the y-intercept is at (0, 40).
Now, we have two points to graph the relation between minutes and Celsius degrees.
Therefore, the room's temperature as a function of time is

Its graph is attached.
You would add the 30 to the 40 And then add 45 to that and you will get 112
Answer:
50.40
Step-by-step explanation:
7 hours and 20 minutes times 7= 50 hours and 40 minutes
And then you have to change it into a mixed number and it is 50.40