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.
Rectangle A ~ Rectangle B
32 students choose a favorite topping for their slices.
Let x be the total number of students.
1/2 of the total students, or 1/2x, choose pepperoni.
1/4 of the total students, or 1/4x, choose extra cheese.
1/8 of the total students, or 1/8x, choose sausage.
4 students choose mushrooms.
We know that together, these equal the total number of students, x:
1/2x+1/4x+1/8x+4=x
We will use 8 as the common denominator:
4/8x+2/8x+1/8x+4=x
Combining like terms:
7/8x+4=x
Subtract 7/8x from both sides:
7/8x+4-7/8x=x-7/8x
4=1x-7/8x
4=1/8x
Divide both sides by 1/8:
4÷(1/8) = 1/8x÷(1/8)
4/1÷(1/8) = x
4/1×8/1 = x
32/1 = x
32 = x
To get the equation of the line, you need two points that belong to this line.
From the given graph, we can choose any two points: (0,-4) and (-2,0)
The general for of the linear straight line is:
y = mx + c where m is the slope and c is the y-intercept
First, we will calculate the slope using the following rule:
slope = (y2-y1) / (x2-x1)
slope (m) = (0--4) / (-2-0) = 4/-2 = -2
The equation of the line now is: y = -2x + c
Then, we will get the value of the c. To do so, we will choose any point and substitute in the equation. I will choose the point (0,-4)
y = -2x + c
-4 = -2(0) + c
c = -4
Based on the above calculations, the equation of the line is:
y = -2x - 4
