Answer:
C
Step-by-step explanation:C
Let x represent the # of units produced and sold.
Then
Revenue = Costs
($40)x = $72000 + ($32)x
Solving for x: $8x = $72000. Thus, x = 9000.
Have to make and sell 9000 units to break even here.
Answer:
Step-by-step explanation:
Let the numbers be x and y. Then we got following equations:
- x + y = 34
- 1/2x + 1/3y = 14
<u>Double the second equation and subtract from the first one. Solve for y:</u>
- x + y - x - 2/3y = 34 - 2*14
- 1/3y = 6
- y = 3*6
- y = 18
<u>Find x:</u>
The <em><u>correct answer</u></em> is:
$236
Explanation:
Her annual property taxes are $1200. This means her escrow each month needs to have 1/12 of that amount; 1200/12 = $100 needs to be in the account each month.
Her mortgage insurance is $66 per month; this means a total of $100+66 = $166 needs to be in escrow every month.
Her homeowner's insurance is $840 per year; this means 1/12 of that needs to be in her escrow account each month:
840/12= 70
This gives us a total of $166+$70 = $236
Anwer: draw a square with side length equal to the square root of the area of the rectangle.
Explanation:
The rectangle that has the greatest perimeter given a fixed area is the square.
So, take the square root of the area and draw a square with that side length.
The demostration of that is done using the optimization concept from derivative. If you already studied derivatives you can follow the following demostration.
These are the steps:
1) dimensions of the rectangle:
length: l
width: w
perimeter formula: p = 2l + 2w
area formula: A = lw
2) solve l or w from the area formula: l = A / w
3) write the perimeter as a function of w:
p = 2 (A / w) + 2w
4) find the derivative of the perimeter, dp / dw = p'
p' = - 2A / w^2 + 2
5) The condition for optimization is p' = 0
=> -2A / w^2 + 2 = 0
=> 2A / w^2 = 2
=> w^2 = A
Which means that the dimensions of the rectangle are w*w, i.e. it is a rectangle of side length w = √A