Square (second power, quadratic) - math word problems

  1. Suppose
    linear_eq Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
  2. Triangular pyramid
    triangularPyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
  3. The ball
    sphere4 The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
  4. Uboid volume
    cuboid Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
  5. The schoolyard
    square_rot The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m2 and has a square shape again. How many meters was each side of the yard enlarged?
  6. Evaluate 5
    parabola2 Evaluate expression x2−7x+12x−4 when x=−1
  7. The parabolic segment
    ParabolicVolume The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
  8. 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.
  9. The tickets
    oriesky The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
  10. Simplify
    square Simplify powers multiplication: (3+22)(5-42)
  11. The sides 2
    trapezium_7 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
  12. Triangular pyramid
    TriangularPyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
  13. Completing square
    eq2_5 Solve the quadratic equation: m2=4m+20 using completing the square method
  14. Cube surface and volume
    cube_diagonals_5 The surface of the cube is 500 cm2, how much cm3 will be its volume?
  15. Two pipes
    roura_1 How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
  16. Area to volume
    two_cubes_2 If the surface area of a cube is 486, find its volume.
  17. Substitution method
    500px-Sine_cosine_plot.svg Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
  18. A tile
    tiles_9 A tile setter is covering 5ft by 5ft square shower wall. Each tile covers 4 5/8in by 4 5/8in square. How many rows of tile are needed to reach 5ft? How many tiles are needed to cover 5ft by 5ft square
  19. Non linear eqs
    q2_non_linear Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
  20. A car
    car_31 A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!

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