Answer:
x = 12
prism's length = 36 centimeters
Prisms width = 25 centimeters
Step-by-step explanation:
volume of a rectangular prism, V = length × width × height
volume = 10,800 cubic centimeters
prism's length = 3x
Prisms height = 12 centimeters
Prisms width = (2x + 1)
volume of a rectangular prism, V = length × width × height
10,800 = 3x * 2x + 1 * 12
10,800 = 6x² + 3x * 12
10,800 = 72x² + 36x
72x² + 36x - 10,800 = 0
2x² + x - 300 = 0
Using quadratic formula
x = -b ± √b² - 4ac / 2a
= -1 ± √1² - 4*2*-300 / 2*2
= -1 ± √1 - (-2400) / 4
= -1 ± √1 + 2400 / 4
= -1 ± √2401 / 4
= -1 ± 49 / 4
x = (-1 + 49)/4 or (-1 - 49)/4
= 48/4 or -50/4
x = 12 or -12.5
x cannot be a negative value
Therefore, x = 12
prism's length = 3x
= 3(12)
= 36 centimeters
prism's length = 36 centimeters
Prisms width = (2x + 1)
= 2(12) + 1
= 24 + 1
= 25 centimeters
Prisms width = 25 centimeters
The profit equation which relates P, profit to N, quantity produced and sold is:
P=17.75N-750
What is the total cost function?
The total production cost function, whereby total cost is C is as given below:
C=750+15.95N(look at a similar question provided)
What is the total revenue function?
The total revenue function is as given below:
R=33.70N
The profit is the excess of total revenue over total cost, in other words, profit is the total revenue minus total cost
P=33.70N-(750+15.95N)
P=33.70N-750-15.95N
P=33.70N-15.95N-750
P=17.75N-750
Find out more about profit function on: brainly.com/question/25668243
#SPJ1
Similar question:
A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book printed. The total production cost C (in dollars) is given by the function C=650+18.95N , where N is the number of books. The total revenue earned (in dollars) from selling the books is given by the function R=32.80N . Let P be the profit made (in dollars). Write an equation relating P to N . Simplify your answer as much as possible.
Answer:
y=8
Step-by-step explanation:
(-2,8) (3,8)
x,y. x,y
y2-y1/X2-X1=
8-(8)= 0
3-(-2)= 5
since the two points have 8 in the Y space the line would be equal to y= 8
6 divided by 8 = 0.75
0.75+ 0.75+ 0.75+ 0.75+ 0.75+ 0.75+ 0.75+ 0.75= 6
So $0.75 is the amount per lemon
