# Equation + derivation - math problems

#### Number of problems found: 11

• 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?
• 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.
• 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? 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
• Rectangle pool Find dimensions of an open pool with a square bottom with a capacity of 32 m3 to have painted/bricked walls with the least amount of material.
• 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?
• Goat Meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the perimeter of the meadow 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.
• 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?
• Fall The body was thrown vertically upward at speed v0 = 79 m/s. Body height versus time describe equation h = v0 * t - (1)/(2) * 10 * t2. What is the maximum height body reach?

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