Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and airplane B is flying north at 300 mi/h. If they are both heading to the same airport, located 30 miles east of airplane A and 40 miles north of airplane B, at what rate is the distance between the airplanes changing?
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
At a sand and gravel plant, sand is falling off a conveyor belt at a rate of 36 cubic feet per
minute forming an increasing conical pile under the belt. The pile of sand always has the
shape of a right circular cone. The radius of the cone is always three times its height.
Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h
and airplane B is flying north at 300 mi/h. If they are both heading to the same airport,
located 30 miles east of airplane A and 40 miles north of airplane B, at what rate is the
distance between the airplanes changing?
The volume of a cube decreases at a rate of 10 meters per second. Find the rate at which
the side of the cube changes when the side of the cube is 2 m.
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