Equation + maximum - math problems

Number of problems found: 15

  • Maximum of volume
    kuzel2 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?
  • Fall
    rocket The body was thrown vertically upward at speed v0 = 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach?
  • Tiles
    dlazdice From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
  • Curve and line
    parabol 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 co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
  • Two integers
    x-5-x-3-graph Two integers, a and b, have a product of 36. What is the least possible sum of a and b?
  • Ladder
    rebrik_4 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
  • Circle
    circles_2 Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
  • Derivative problem
    derive 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.
  • Paper box
    box 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 be side of the squares to be the largest volume of the box?
  • Secret treasure
    max_cylinder_pyramid 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. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  • The bridge
    bridge2 A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
  • The percent 2
    penize The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i
  • TV competition
    test_1 In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We g
  • Camel
    camels Camel's owner wants to get out of the city into an oasis. He bought 3000 bananas, which wants to sell in the oasis. However, an oasis from the city divided 1,000 kilometers of desert. Camel can carry up to 1000 bananas, and for every kilometer traveled, e
  • Reconstruction of the corridor
    koridor Calculate how many minutes will be reduced to travel 187 km long railway corridor, where the maximum speed increases from 120 km/h to 160 km/h. Calculate how many minutes will shorten travel time, if we consider that the train must stop at 6 stations, eac

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