The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
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Answer:
Part a) Tim has completed the greater amount of work
Part b) They have completed together of the project or of the project
Step-by-step explanation:
Part a) Who has completed the greater amount of work?
we have
Jaime has 5/11 of a project completed
Tim has 7/13 of a project completed
Multiply 5/11 by 13/13 and 7/13 by 11/11
so
Jaime --->
Tim --->
Remember that
When fractions have the same denominator, the larger fraction is the one with the larger numerator
therefore
Tim has completed the greater amount of work
Part b) How much of the project have they completed together?
we have that
Jaime has 65/143 of a project completed
Tim has 77/143 of a project completed
Sum the fraction of the project completed by Jaime plus the fraction of the project completed by Tim
Convert to percentage
Multiply by 100
Answer: 5
Step by Step Explanation:
Answer:
concave pentagon
Step-by-step explanation: