Answer:
the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Step-by-step explanation:
since the volume of a cylinder is
V= π*R²*L → L =V/ (π*R²)
the cost function is
Cost = cost of side material * side area + cost of top and bottom material * top and bottom area
C = a* 2*π*R*L + b* 2*π*R²
replacing the value of L
C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²
then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then
dC/dR = -2*a*V/R² + 4*π*b*R = 0
4*π*b*R = 2*a*V/R²
R³ = a*V/(2*π*b)
R= ∛( a*V/(2*π*b))
replacing values
R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm
then
L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm
therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
<a and <b :
answer
<span>A. Vertical</span>
Answer:
Side*side= 0.5625 inch
Step-by-step explanation:
Answer:
First, our answer is 18 yards long.
Step-by-step explanation:
It is 18 yards long because first, we have 9, the length of Jamie's car. Joey's car length is 27 feet. Then, since 1 foot converted is 0.333333...., it is very hard to convert so i turn it in to 9 foot converted into 3 yards. Then, both sides multiply by 3 so 27 foot equals to 9 yards. 9 yards+9 yards equals 18 yards.
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