Answer:34.333 repeating
Step-by-step explanation:
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:
84
Step-by-step explanation:
Combinations
nCr
n (objects) = 9
r (sample) = 3
9C3
n! / r! (n – r)!
9! / 3! (9 – 3)!=
9! / (3! * 6!)=
9*8*7*6!/ (3! * 6!)=
6! cancels out
9*8*7/3*2*1=
3*4*7=
12*7=
84
$140 dollars,
Using the equation (1/2)J/7=x. J=Jeremy's total money.7 because it was divided into 7 piles. Then, since 6 piles are blown away, we don't need to care about that for now. After that, you take 2 dollars and give the rest to Jeremy which is 8 dollars. You can create the equation x-2=8. Solve for x which is $10. Finally substitute that into the first equation to get (1/2)J=70. Multiply 2 to both sides to cancel out the (1/2) and the 70 by 2 to get Jeremy's total money which is $140
