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
The answer to number 1 is $7.78. all ya got to do is divide 140 by 18 to find out how much is just one foot squared.
The answer to number 2 is $0.21. same as number one just divide $2.99 by 14lbs, to find out how much money is needed to pay for one pound.
numbers 3 and 4 are a bit more tricky, i suggest getting those denominators to 100 first to be able to find the percentage value of everything, number 3 seems pretty easy when using this strategy, the denominator is 25 so just multiply both the top and bottom numbers by 4 so that the 25 equals out to 100 and 56X4=224. now the second one the denominator is 15 so i would first divide both numbers by 3 to get that 15 into an easier number like 5. so divide $32.05 by 5 to equal $6.41. now its $6.41 over 5. so multiply the top and bottom numbers by 20 to make the denominator into 100. so $6.41X100=$641.00. so essentially what we've done is make the denominators into (like) denominators. Now treat the numbers as a fraction, so the one that has a smaller number is the better deal. so $56/ 25 gal is the better deal.
for number 4, you're basically doing the same thing but they've made it pretty easy for us, all you got to do on this one is make that denominator on the second proportion a 5. so divide the second proportion by nine to make the denominator into a 1. so dividing $315 by 9 will equal 35. so now multiply the (35/1) by 5 to equal ($175/5) now just pick the answer choice that has the bigger numerator and that'll be the best deal. so number 4 is ($160/5 g).
Making the denominators into like terms makes the units the same, so getting the numerators to the prices for however many units will show you the pricings for that many units. so if your wanting to pick the best deal, then at that point u would pick the proportion that cost less for that many units.
The answer to the second question is 8/15
Answer:
3 ways
Step-by-step explanation:
7 and 3
6 and 4
5 and 5
I think you would combine like Terms
