Check the picture below, notice those three quadrilaterals.
the square, is really a rectangle and is also a rhombus, but with right-angles and equal sides.
Hello there.
We have for a circle that:
Where:
is the measure of the arc
is the measure of the angle (radians)
is the radius of the circle
In our case, we have 
We have r = 3 cm, then:
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:
-14.5
Step-by-step explanation:
- Take - common: -(11.0+3.5)
- Just add them in the bracket: -(14.5)
- Remove the bracket: -14.5
Answer:
49.4 (rounded to the nearest tenth)
Step-by-step explanation:
You need to use the Pythagorean theorem -> 
-> 
is the hypotenuse
+ 
=
(7x
+ (5x7) =
+ 35 =
2436 =
= c
c = 49.355850717
c = 49.4 (round to the nearest tenth)
hope this helps, sorry if it is not right
