Square root + expression of a variable from formula - examples

  1. Non linear eqs
    q2_non_linear Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
  2. Cuboid
    cuboid_1 The cuboid has a surface area 7705 cm2, the length of its edges are in the ratio 1:4:5. Calculate the volume of the cuboid.
  3. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 476 cm.
  4. IS trapezoid
    trapezoid_ABCD Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
  5. Cone
    cones Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
  6. R Trapezium
    Trapezium_example Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
  7. Prism X
    Cuboid_simple The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
  8. Sphere A2V
    sphere3 Surface of the sphere is 241 mm2. What is its volume?
  9. Chord
    chord In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
  10. Arc
    arc Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
  11. Square
    percent If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
  12. Shape
    some_airplane Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
  13. Brass tube
    Ms_trubka The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
  14. Tent
    stan Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
  15. Trapezoid 15
    trapezoid3 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
  16. Body diagonal
    kvadr Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
  17. Cube 8
    cubes2 The surface of the cube is 0.54 m2. Calculate the length of the cube edge.
  18. Triangle KLM
    klm_triangle In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
  19. Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  20. Gasoline tank cylindrical
    cisterna What is the inner diameter of the tank, which is 8 m long and contains 40 cubic cubic meters of gasoline?

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