Answer:
108 yards
Step-by-step explanation:
Let circle A be the circle with the 62 yard diameter
Let circle B be the circle whose diameter we are trying to solve for.
- Externally tangent circles are circles which touch each other and share a common external tangent.
- Circle A has a tangent of 62 yards and thus a radius ( half the diameter) of 31 yards.
- The distance between the centers of the 2 circles is 85 yards. If you subtract the radius ( distance from the center of the circle to its circumference) of circle A then we'll only be left with the radius of circle B.
- 85 - 31= 54 yards which is the radius of circle B
- To get the diameter: 54 x 2 = 108 yards
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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:
<h2>
6</h2>
Step-by-step explanation:
To find the width/length when you know the area and the length or width, you just divide the area by the known side.
45/7.5 = 6
9514 1404 393
Answer:
A side of the triangle is bisected
Step-by-step explanation:
The median of a triangle connects a vertex to the midpoint of the opposite side. That is, it bisects the side it meets:
A side of the triangle is bisected
_____
<em>Comment on other choices</em>
A median will be an angle bisector only if the triangle is isosceles. Likewise, it will only be perpendicular to the side if the triangle is isosceles.
There are several points called "center" of a triangle, including the centroid (on the median), the incenter, the circumcenter, and the orthocenter.
