The most difficult problems

Number of problems found: 5745

  • Sum of two primes
    prime_1 Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
  • Population growth
    exp_growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
  • Butter
    factory_butter At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain?
  • Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
  • Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  • Prime factors
    prime Write 98 as product of prime factors
  • Paper box
    prism3s_4 Calculate how much we'll pay for a three-side shaped prism box with a triangular base, and if it measures 12cm and 1.6dm, the hypotenuse measures 200mm. The box is 34cm high. We pay 0,13 € per square meter of paper.
  • Isosceles
    rr_lichobeznik_1 Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
  • Rectangles
    rectangles2_3 How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm)
  • Square into three rectangles
    stvorcove-cisla_1 Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
  • Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
  • Sandbox
    sand_2 Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox.
  • Digits
    seq_5 Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
  • Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  • Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  • Simplify 3
    fractal_14 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  • Adding mixed numerals
    zlomky_18 3 3/4 + 2 3/5 + 5 1/2 Show your solution.
  • Equilateral cylinder
    sphere_in_cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
  • An oil
    valec2_13 An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
  • Lampshade
    kuzel_2 The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste?

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