The dimensions for this rectangle are b= 30 ft and h=20 ft.
<h3>Perimeter</h3>
The perimeter of a geometric figure is the sum of its sides.
The question gives:
- the geometric figure - rectangle
- the total perimeter - 120 ft
Therefore for the perimeter, you have
P= 
+ h+ h +h
P=2b+3h
2b+3h=120 (1)
From equation 1, you can write:
2b=120-3h
b=
b= 60 - 
(2)
The area for the rectangle is given by A= bh. Therefore, by replacing (2) in the formula for rectangle area, you have:
The maximum area will be calculated from the derivation of the previous equation of area.
The maximum area can be found when the first derivative is equal to zero. Thus,
60-3h=0
-3h=-60 *(-1)
3h=60
h=20
Now, you know the height and from equation 2 (b= 60 - ) you can find the base.
b= 60 -
b=60 - 3*10
b=60-30
b=30
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Answer:
608 cm^2
Step-by-step explanation:
<em>Top and bottom rectangles: </em>
2(10*16)
= 2(160)
= 320
<em>Middle rectangle:</em>
(12*16)
= 192
<em>Two triangles:</em>
2((12*8)/2)
= 2(96/2)
= 96
<em>Surface area of the whole prism:</em>
320 + 192 +96
= 608
Answer:
The domain is (-2,-1,) This relation is not a function because there are repeating x-values.
Step-by-step explanation:
The domain are the list of x values and x values are the first number in a given point. Ex: (0,9) x-value is 0
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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Complete Question
(Image Attached)
Answer:mass CO2 = (mass AS) - (final mass)
Step-by-step explanation:
