If the rectangular field has notional sides X and y then it has area
A(x) =xy { =6•10^6 sq ft }
The length of fencing required, if
x
is the letter that was arbitrarily assigned to the side to which the dividing fence runs parallel, is:l (x) = 3x +2y
It matters not that the farmer wishes to divide the area into 2 exact smaller areas.
Assuming the cost of the fencing is proportional to the length of fencing required, then
C(x)=a L (x)
To optimise cost, using the Lagrange Multiplier
λ
, with the area constraint :
So the farmer minimises the cost by fencing-off in the ratio 2:3, either-way
Answer:
combine LIKE terms
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
you are adding
Answer:
52 ft²
Step-by-step explanation:
When you are calculating the amount of cardboard needed to make a box, you are trying to the the <u>surface area</u>.
The formula for surface area of a rectangular prism is:
SA = 2(lw + hl + wh)
The dimensions for the box are written l X w X h (length times width times height).
We know:
l = 4
w = 3
h = 2
The units for surface area is the unit squared. Feet squared is ft². Be sure the include the units.
Substitute these numbers into the formula. When solving, solve in the BEDMAS order (brackets, exponents, division and multiplication, addition and subtraction).
SA = 2(lw + hl + wh) u²
SA = 2((4*3) + (2*4) + (3*2)) ft² Multiply within each smaller bracket
SA = 2(12 + 8 + 6) ft² Add inside the brackets
SA = 2(26) ft² Multiply
SA = 52 ft² Final answer
Therefore 52 square feet of cardboard will be needed to make the box.
Here's a graph of those terms.
