Derivation - practice problems - last page
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 48
- Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w
- Goat
The meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the meadow's perimeter to allow the goat to eat half of the meadow?
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
- Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder.
- Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
- Derivation
Does there exist a function whose derivation is the same function?
- Fall
The body was thrown vertically upward at speed v0 = 39 m/s. Body height versus time describes equation h = v0 * t - (1)/(2) * 9.8 * t². What is the maximum height of body reach?
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