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:
The number of whole loaves at each location = 5 loaves
Step-by-step explanation:
This problem is essentially testing your ability to use simple division within remainders, and the number of whole loaves is calculated as follows:
Numer of loaves of bread = 16
number of locations = 3
next, we will divide the number of loaves by the number of locations since Olivia placed an equal number of loaves in 3 different locations:

This means that there will be 5 whole loaves and 1 loaf that will be divided equally into the three places.
Therefore, the number of whole loaves at each location = 5 loaves
<em>but remember that there will be a remainder of 1 loaf.</em>
Answer:
x = 17 and y = 8
Step-by-step explanation:
Since (6x + 3) and (8x - 31) are alternate interior angles, they are congruent.
Therefore, you can set them equal to each other and solve for x.
8x - 31 = 6x + 3
Combine like terms
2x = 34
Divide both sides by two
x = 17
Since (5y + 35) and (6x + 3) are consecutive interior angles, they add up to 180. Plug in 17 for x.
(5y + 35) + (6(17) + 3) = 180
Add like terms
5y + 140 = 180
5y = 40
y = 8
Answer:
1) Amy can invite 17 people.
2) x > 76
3) 40 - 6 is greater than or equal to 3x
4) x is greater than or equal to 98
Step-by-step explanation:
1) 50 + 8x = 200
2) 200 < 3x - 28
3) 40 = 6 +3x
4) (95 + 78 + 89 + x)/4 is greater than or equal to 90
I think its 1.25ft but i could be wrong... sorry if im wrong