Answer:
<h2>
x² + 9 + 6x </h2>
Step-by-step explanation:
expand and simplify (x+3)²
(x+3)² =
x² + 9 + 2 × x × 3 =
x² + 9 + 6x
Answer:
Step-by-step explanation:
First, you should put the axis of symetry as 5, -7 because f(x)= (x-h)^2+k and h is 5 and k is -7. the axis of symetry is x=5 because that is the "folding point" of the graph. Next, you would have to plug In 4 and 6 as your helping points to tell you where the other points of the function are going to be.
Plug 4 in and you get -6. plug 6 in and you get -6. plot the points (4, -6) and (6,-6).
Hope this helps!
:)
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:
0.0227272727
Step-by-step explanation:
what I got on calculator
