# Maximum + derivation - math problems

#### Number of problems found: 15

- Martians

A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - Megapizza

Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion? - Maximum of volume

The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - The shooter

The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting each of them is 0.2. The shooter fires until he hits the target for the first time, then stop firing. (a) What is the most li - Derivative problem

The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal. - Shopping malls

The chain of department stores plans to invest up to 24,000 euros in television advertising. Ads will place all commercials on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers. Durin - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Curve and line

The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C? - Cylindrical container

An open-topped cylindrical container has a volume of V = 3140 cm^{3}. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Ladder

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Paper box

The hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box? - Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diago - Cone

Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder. - Fall

The body was thrown vertically upward at speed v_{0}= 79 m/s. Body height versus time describe equation h = v_{0}* t - (1)/(2) * 10 * t^{2}. What is the maximum height body reach? - Statue

On the pedestal high 4 m is a statue 2.7 m high. At what distance from the statue must the observer stand to see it at the maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.

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Maximum - math problems. Derivation - math problems.