Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
Answer:
Yes
Step-by-step explanation:
This relation is a function. Functions must have unique x-values for every y-value, this relation meets those requirements. Also, since this is a graph you can use the vertical line test. To pass the vertical line test you must be able to draw a vertical line on the graph and have it intersect with the function in no more than one place.
-10x. All you have to do is subtract -2 from -8 and then put an x there so it’s -10x
Answer: Supplementary angles
Step-by-step explanation: If you look at the image, the marked angles have a supplementary angle that will add up to 180 degrees. These acute angles will have an obtuse angle as their supplement.
