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
Answer:
Let Craigs age = x
Therefore Dianes age = 25 + x ( since she's 25 years older)
Dianes + Craigs age = (25 + x) + x = 105 (They said both of their ages sums up to 105)
25 + 2x = 105
2x = 80
x = 40
Craigs age is 40 years old.
Dianes age is 65 years old.
Answer:
A
Step-by-step explanation:
Choice A is right because there is no dot above the two.
Choice B is not right because there is 2 dots above 1 and not 3.
Choice C is not right because the data doesn't go passed 5 to get to 8
Choice D is not right because it was 5 games because there is 5 dots above 3
Marco rounded the hundredths place since after the decimal it is the tenths then the hundredths then the thousands place